Auditing Hw Solutions

Chapter 1 SOLUTIONS FOR EXERCISES AND PROBLEMS 1. 47 Audit, Attestation, and Assurance Services Students may encounter some difficulty with this matching question because the Special Committee on Assurance Services (SCAS) listed many things that heretofore have been considered â€Å"attestation services† (long before assurance services were invented). As a result, we believe that this question is a good vehicle for discussing the considerable overlap between attestation and assurance services. ? ? ? ? ? ? ? ? ? ? ? ? ? ? Real estate demand studies: Assurance serviceBallot for awards show: Assurance service Utility rates applications: Assurance service Newspaper circulation audits: Assurance service Third-party reimbursement maximization: Assurance service Annual financial report to stockholders: Audit service Rental property operations review: Assurance service Examination of financial forecasts and projections: Attestation service Customer satisfaction surveys: Assurance serv ice Compliance with contractual requirements: Attestation service Benchmarking/best practices: Assurance serviceEvaluation of investment management policies: Assurance service Information systems security reviews: Assurance service Productivity statistics: Assurance service ? ? Internal audit strategic review: Assurance service Financial statements submitted to a bank loan officer: Audit service 1. 48 Controller as Auditor When Hughes Corporation hired the CPA, she or he can no longer be considered independent with respect to the annual audit and, as a result, can no longer perform an independent audit of the financial statements.It is true that the in-house CPA can perform all procedural analyses that would be required of an independent audit; however, it is extremely unlikely that the CPA could inspire the confidence of users of financial statements outside the company. Because she or he is no longer independent of the company, the CPA cannot modify the perception of potential con flict of interest that creates demand for the independent audit. As a matter of ethics rules, this CPA would be prohibited from signing the standard unqualified attest opinion.Moreover, if Hughes were a public company, under Sarbanes-Oxley, it would be restricted from hiring one of its auditors into a senior accounting position for a full year under Section 206 of the law. 1. 49 ASB Assertions PCAOB Assertion Corresponding ASB assertion Nature of assertion Existence or Occurrence Existence Occurrence Balance Transactions Disclosures Rights and Obligations Rights and Obligations Balances Disclosures Completeness Completeness Transactions Balances Disclosures Cutoff Valuation and Allocation Accuracy Transactions Transactions Disclosures Valuation Balances DisclosuresPresentation and Disclosure Classification Transactions Disclosures Understandability Disclosures 1. 51 Auditor as Guarantor. Loot Starkin appears to be uninformed on the following points: Inform your neighbor that Dodge m anagement is primarily responsible for preparing the financial statements and deciding upon the appropriate accounting principles. The auditors did not prepare the Dodge Corporation financial statement. An unqualified opinion does not mean that an investment is safe. Rather, it merely means that the financial statements are free of material misstatement.Tell your neighbor that the financial statements are a historical record of the business’ performance. The value of Loot’s investment depends on future events, including the many factors that affect market prices. Thus, the financial statements are just one piece of information that should be analyzed. Tell Loot that the unqualified opinion means only that the statements conform to the appropriate reporting framework (e. g. , GAAP) and that the financial statements are free of material misstatement. 1. 52 Identification of Audits and Auditors The responses to this matching type of question are ambiguous.The engagement e xamples are real examples of external, internal, and governmental audit situations. You might point out to students that the distinctions among compliance, economy and efficiency, and program results audits are not always clear. The â€Å"solution† is shown in the following matrix form, showing some engagement numbers in two or three cells. The required schedule follows. Type of Audit Engagement Financial Statement Auditor Independent CPA Internal auditor Governmental (GAO) auditor IRS auditor Bank examiner 5 7 2, 10 6, 8 4, 8 1, 3 1, 3, 9 Compliance Economy and Efficiency Program ResultsType of Audit 1. Proprietary school’s training expenses Advertising agency financial statements Dept. of Defense launch vehicle Municipal services Tax shelters Test pilot reporting Bank solvency Economy and efficiency or program results Financial statement Economy and efficiency or program results Economy and efficiency Compliance Compliance Compliance Type of Auditor Governmental (GAO ) auditors Independent CPAs Governmental (GAO) auditors Internal auditors IRS auditors Internal auditors Bank examiners 2. 3. 4. 5. 6. 7. 8.Materials inspection by manufacturer States’ reporting chemical use data Sports complex forecast Compliance or Economy and Efficiency Program goal Internal auditors 9. Governmental (GAO) auditors Independent CPAs 10. Financial statement 1. 53 Financial Assertions and Audit Objectives The objectives for the audit of Spillane’s securities investments at December 31 are to obtain evidence about the assertions implicit in the financial presentation, specifically: 1. Existence. Obtain evidence that the securities are bona fide and held by Spillane or a responsible custodian. Occurrence.Obtain evidence that the loan transaction and securities purchase transactions actually took place during the year under audit. 2. Completeness. Obtain evidence that all the securities purchase transactions were recorded. 3. Rights. Obtain evidence that S pillane owned the securities. Obligation. Obtain evidence that $500,000 is the amount actually owed on the loan. 4. Valuation. Obtain evidence of the cost and market value of the securities held at December 31. Decide whether any write-downs to market are required by the appropriate reporting framework. 5. Presentation and disclosure.Obtain evidence of the committed nature of the assets, which should mean they should be in a noncurrent classification like the loan. Obtain evidence that restrictions on the use of the assets are disclosed fully and agree with the loan documents. Chapter 2 2. 54 Independence a. Independence in fact relates to the auditors’ â€Å"state of mind† and reflects an unbiased and impartial perspective with respect to the financial statements and other information they audit. Independence in appearance relates to others’ (particularly financial statement users’) perceptions of the auditors’ independence.The two general types o f relationships that compromise auditors’ independence are financial relationships (owning shares of stock or having an outstanding loan to or from a client) and managerial relationships (acting in a decision-making capacity on behalf of a client or providing advice on systems or information that will be audited). (1) Although auditors might still be independent in fact with respect to the audit of the client, the large revenues resulting from these services create a financial interest that many users would find to be troubling.For example, consider the possibility that clients might use the revenues from these services as a bargaining tool with auditors if an issue arises during the audit engagement. Currently, no prohibitions exist on the extent of consulting services or revenues other than the prohibition of certain types of services and the required approval of nonaudit services by the client’s audit committee. This would clearly pose a compromise to auditorsâ€⠄¢ independence and would not be permitted under current guidelines.The issues in this case are (1) the fact that the auditor is directly involved with the engagement and (2) the executive-level position occupied by his or her spouse with a client. This introduces a similar issue to (2) but would be less likely to compromise the auditors’ independence. The major differences in this scenario are (1) the auditor is not directly involved with the engagement, (2) the level of position held by the auditor’s relative is not at the executive level, and (3) the relationship between the auditor and other individual is not as close.Professional standards would likely not conclude that this situation would compromise the auditor’s independence. This represents a direct financial interest in a client. The issue is whether the fact that the staff member is not a part of the engagement team compromises her independence. Professional guidelines would not conclude that this sit uation compromises the independence of the staff member, but many firms have adopted the practice of not permitting any of their professional staff to hold financial interests in their audit clients. . c. (2) (3) (4) 2. 57 Performance Principle: Evidence a. Sufficiency refers to the amount of evidence, which is the number of transactions or components of an account balance of class of transactions examined by the audit team. As it relates to evidence, the term appropriate refers to the quality of evidence. Appropriateness is affected by the information the evidence provides to the audit team (relevance) as well as the extent to which the audit team can trust the evidence (reliability).Relevance refers to the nature of information provided by the audit evidence (the assertion or assertions supported by the evidence). Reliability refers to the extent of trust the audit team can place in the evidence. Relevance and reliability both affect the appropriateness of audit evidence; as the r elevance and reliability of evidence increases, the appropriateness of evidence increases. b. c. The five basic sources of evidence (from most reliable to least reliable) follow. The solution provides one example, but other possible answers would also be acceptable. 1) (2) (3) (4) (5) The auditors’ direct, personal knowledge, such as physical observation of inventory counts. External documentary evidence, such as confirmations returned directly to auditors from one of the client’s banks. External-internal documentary evidence, such as a vendor’s invoice received by auditors from the client. Internal documentary evidence, such as an invoice prepared by the client for the sale of products or services to one of its customers. Verbal evidence, such as client responses to auditors’ inquiries about potential litigation. d.As the entity’s internal control is more effective, auditors would assess lower levels of the risk of material misstatement. This woul d allow them to permit a higher level of detection risk, which means that they could gather less sufficient and less appropriate evidence. In contrast, as the entity’s internal control is less effective, auditors would assess higher levels of the risk of material misstatement. This would require auditors to control detection risk to lower levels, which means that they would be required to gather more sufficient and more appropriate evidence. . 61 Responsibilities and Performance Principles a. While auditors typically cannot influence the susceptibility of accounts to misstatements or the effectiveness of the entity’s internal control (both of which comprise the risk of material misstatement), this risk needs to be considered in order to determine the nature, timing, and extent of substantive tests. This statement is correct; if internal control is less effective, auditors are required to gather more sufficient and more appropriate evidence.However, in addition to the n umber of transactions and reliability of evidence, auditors should also consider the relevance of the evidence they gather and the extent to which that evidence supports the assertions of interest. Auditors are not required to provide absolute assurance as to the fairness of the financial statements, which is what is being suggested in this statement. It is true that a great deal of time and effort is necessary in an audit engagement, but auditors are required only to provide reasonable assurance with respect to the ability to detect material misstatements.This statement relates to the concept of materiality and is appropriate. However, it is important to note that the consideration of materiality in an audit is highly complex and requires an extremely high level of professional judgment. While physical inspection of the stock certificates provides more reliable evidence than confirming the certificates held with the custodian, it may not be necessary for auditors to conduct such an inspection. In many cases, a less reliable but still effective procedure such as confirmation with the custodian would be appropriate. . c. d. e. 2. 64 Fundamental Principles (Comprehensive) a. This situation is related to the competence and capabilities element of the responsibilities principle. In this case, auditors can accept this engagement assuming that they take appropriate measures to obtain the knowledge necessary to perform the audit and understand important issues affecting this client. It is important to note that the existence of industry-specific accounting issues will require auditors to obtain the knowledge necessary to complete the engagement.This situation is related to the reporting principle, which addresses the conformity of the financial statements with GAAP. If the client elects to treat these leases as operating leases in violation of GAAP, auditors should issue either a qualified or adverse opinion, depending upon the materiality of the departure from GAAP. This situation is related to the performance principle, which indicates that the audit should be properly planned. In this case, auditors should evaluate whether the client’s deadline will allow an audit to be properly planned and conducted according to generally accepted auditing standards.The fact that this would be an initial audit makes this possibility even more questionable than usual. This situation is related to the performance principle, which requires auditors to obtain sufficient appropriate audit evidence. Given the low level of control risk, auditors would then proceed to perform the necessary auditing procedures, which provide the basis for their opinion on the client’s financial statements. In this case, confirming a smaller number of customer accounts would be appropriate. This situation is related to the responsibilities principle, which requires auditors to be independent.In this particular case, the fact that the husband of one of the partner is an officer of the prospective client would likely result in the firm declining this particular engagement because of a lack of independence. This situation is related to the reporting principle. Auditors should insist upon disclosure of the potential litigation and, if the client refuses, issue either a qualified opinion or adverse opinion, depending upon the materiality of the omission of the disclosures. In addition, the auditors’ report should provide information regarding the omitted disclosures.This situation is related to the performance principle, which requires auditors to assess the risk of material misstatement, which includes obtaining an understanding of the entity and its internal control. Once this understanding has been obtained, auditors would then proceed to perform the necessary substantive audit procedures. This situation is related to the performance principle, which requires proper planning and supervision. An important element of supervision is critical rev iew of work performed by persons at various levels within the firm.Because the supervisor’s review of the work performed by the assistant indicates that the work supports the opinion on the financial statements, no further actions are necessary. b. c. d. e. f. g. h. Chapter 24 (Module C) C. 62 Liability to Clients a. b. Clients may bring suit against auditors for either breach of contract or tort actions. To bring suit against auditors, clients must ordinarily demonstrate: (1) (2) (3) (4) They suffered an economic loss. Auditors did not perform in accordance with the terms of the contract (for breach of contract).Auditors failed to exercise the appropriate level of professional care (for tort actions). The breach of contract or failure to exercise the appropriate level of professional care caused the loss. c. Auditors’ defenses against legal actions brought by their clients include: (1) (2) (3) Auditors exercised the appropriate level of professional care (tort) or per formed the engagement in accordance with terms of the contract (breach of contract). The client’s economic loss was caused by a factor other than auditors’ failure to exercise appropriate levels of professional care or breach of contract.Actions on the part of the client were, in part, responsible for the loss. d. The potential basis for legal action in each of these cases is as follows: Brown Company: Because the delay in completing the audit resulted in additional costs of financing, Brown’s legal action would be based on Thomas’s inability to complete the audit on a timely basis. Green Stores: Green Stores’ legal action would be based on Thomas’s failure to identify the embezzlement scheme during its audits of Green Stores’ financial statements.Green Stores would likely seek recovery of the $2 million in losses. Fuchsia, Inc: Fuchsia’s legal action would be based on any additional costs associated with changing auditors and any costs associated with delays in providing audited financial statements to its lenders as a result of the need to change auditors. e. Note to instructor: Depending upon the assumptions made by students, they may arrive at different conclusions with respect to Thomas’s liability to its clients in some of these scenarios.The key is that they considered the relevant facts and potential defenses that may either increase or decrease the likelihood of an unfavorable outcome to Thomas. Brown Company: It appears that Brown Company’s most viable action for recovery will be alleging that it informed Thomas of the need to have the audit completed by a certain date and that failure to do so would constitute a breach of contract. There is no evidence that a substandard audit has been conducted or that Thomas did not exercise the appropriate level of professional care. In this case, the following are important considerations: ?Was a deadline or other date explicitly communicated by Brown Company to Thomas or otherwise identified in the engagement letter? If no such date was communicated, or any deadline known by Thomas, it would not appear that Brown Company has a viable suit for breach of contract. Regardless of the response to the preceding point, did Brown Company’s actions result in delays or otherwise affect Thomas’s ability to complete the engagement on a timely ? basis? If so, this might serve as a defense for Thomas in the form of contributory negligence on the part of Brown Company.Green Stores: Green Stores would most likely bring suit for tort liability, alleging that an audit conducted under generally accepted auditing standards would have revealed the existence of the embezzlement scheme and prevented the $2 million loss. In this case, the following are important considerations: ? Were Thomas’s audits conducted in accordance with generally accepted auditing standards? If so, Thomas would likely use the defense that it exerc ised appropriate levels of care during the engagement and emphasize that a GAAS audit cannot be relied upon to detect all instances of fraud.Regardless of the response to in the preceding point, could Green Stores have taken actions (through strengthening internal controls or other) to create an environment that would have made the creation and execution of this embezzlement scheme more difficult? Certainly, if Thomas had communicated internal control deficiencies to Green Stores in previous audits related to the treasurer’s role or controls surrounding this function, it would appear that Thomas could assert contributory negligence as a defense. ? Fuchsia, Inc. This may appear to be a frivolous suit, but that would not prevent Fuchsia from alleging that Thomas’s actions resulted in the losses described in the scenario. Although it is difficult to comprehend how Fuchsia’s decision to change auditors would result in liability to Thomas, Thomas would appear to have a strong defense that its actions were, in fact, done to exercise appropriate levels of professional care by demonstrating how Fuchsia’s accounting treatment departed from generally accepted accounting principles. C. 65 Auditors’ Liability for Fraud a.Auditors will be liable for fraud to all third-party users of financial statements under common law or statutory law. Fraud is a misrepresentation of fact that an individual knows to be false. Constructive fraud (sometimes referred to as gross negligence) is the failure to provide any care in fulfilling a duty owed to others. The primary difference between these two levels of professional care is actual knowledge on the part of auditors, which is present under fraud but not under constructive fraud. Auditors will be liable for constructive fraud to all third-party users under common law and the Securities Act of 1933.To be held liable under the Securities Exchange Act of 1934, scienter (or intent to deceive, manipulate, or defraud) must be shown. Although scienter may be present in situations representing constructive fraud, this will not always be the case. b. c. Clearly, auditors should be liable in cases for which they intend to deceive. Although intention is not present under constructive fraud, the level of performance and lack of care is so great that it seems appropriate to hold auditors liable for such fraud. C. 69Common Law Liability Exposure a. Yes, Smith will be liable to the bank. The elements necessary to establish an action for liability for fraud under common law are clearly present. There was a material misstatement in the financial statements, intent and knowledge of the misstatements (scienter), actual reliance by the bank on the materially misstated financial statements, and economic damages resulting from that reliance. If action is based upon fraud, there is no requirement that the bank establish privity of contract with Smith.If the action by the bank is based on ordinary negl igence, the bank may still be in position to bring suit, depending upon the extent to which Smith was aware that his work would be used by the bank and the jurisdiction in which this case occurred. Based on the facts presented, it is difficult to determine whether the bank is a primary beneficiary. However, because Smith was aware that the financial statements would be used to obtain a loan, the bank would appear to be at least a foreseen third party and could prevail under the restatement of torts doctrine. . No, Smith will not be liable to the lessor because the lessor was a party to the â€Å"secret† written agreement. As such, the lessor cannot claim reliance on the financial statements and cannot recover uncollected rents. Even if the lessor were damaged indirectly, his own fraudulent actions led to his loss, and the equitable principle of â€Å"unclean hands† (â€Å"contributory negligence†) precludes him from obtaining relief. c. C. 71 Smith was not indep endent with respect to the audit of Juniper.The lack of independence is raised by Juniper’s threat to sue Smith in the event the loan was not obtained. Common Law Liability to Third Parties a. Because these parties provided loans to Madeoff and are nonshareholder third parties, they would pursue litigation against Allen based on common law rather than statutory law. Because First Trust and Bank was specifically known to Allen by name (in fact, First Trust and Bank was explicitly identified by name in the engagement letter), it would be classified as a primary beneficiary.Allen was aware that the purpose of the audit examination was to enable Madeoff to obtain financing. Because of this knowledge, as well as the fact that Madeoff had previous business relationships with MoonTrust, MoonTrust would likely be classified as a foreseen third party. The classification of Alice Lay is somewhat debatable. On one hand, any third party could potentially provide funding to Madeoff; using this rationale, one might classify Alice Lay as a foreseeable third party.However, because it is not common practice for entities to obtain financing from customers and Alice Lay had never entered into a loan agreement of this nature in the past, a justification could be made that she does not meet the classification as a foreseeable third party. c. The failure of Allen’s audit to comply with generally accepted auditing standards represents ordinary negligence, assuming that Allen’s audit did not demonstrate a lack of minimum care or Allen did not possess actual knowledge of the material misstatements. For ordinary negligence, the following represents these parties’ abilities to prevail against Allen: ?As a primary beneficiary who relied upon the audited financial statements and Allen’s report on the financial statements, First Trust and Bank would likely be able to bring suit and prevail against Allen. Although MoonTrust’s classification as a for eseen third party suggests that it would be able to prevail against Allen in certain jurisdictions, the fact that MoonTrust did not rely b. ? on the audited financial statements and Allen’s report on the financial statements would make it unlikely that MoonTrust could bring suit against Allen.If MoonTrust did bring suit against Allen and Allen could prove that the loan decision was made prior to receipt of the audited financial statements and auditors’ report, Allen could attempt to successfully assert the causation defense. ? Given Alice Lay’s very remote and unusual relationship to Madeoff as a provider of capital, it is unlikely that Alice would have an appropriate level of standing to bring suit against Allen. However, if Alice could demonstrate that she was a foreseeable third party and could meet the other criteria for bringing suit under common law, she could potentially prevail against Allen. . C. 80 If Allen had been aware of the material misstatements, this situation would be classified as fraud. Both First Trust and Bank and Alice Lay would be highly likely to prevail against Allen because auditors are liable to all third-party users (regardless of their relationship and classification) for acts of gross negligence or fraud. MoonTrust would still have the burden of demonstrating that it relied on the materially misstated financial statements and Allen’s report in bringing suit against Allen. Independence and Securities Exchange Act of 1934 a.One of the important concepts governing auditors’ independence is that auditors should not be in a position of serving as advocates for their clients. Testifying in court on behalf of the client’s damage claim is perilously close to serving as an advocate, although many auditors will claim that litigation support services (in general) are appropriate and do not impair independence. Although the litigation consulting itself may not impair independence, independence is lik ely impaired by the unpaid consulting fee of $265,000.AICPA interpretations and rulings hold that past due fees may impair auditors’ independence in certain situations. b. Violations of generally accepted auditing standards are based on the failure of auditors to exercise the appropriate level of professional care (third general standard). This violation is based on Ward’s (and, therefore, AOW’s) not insisting upon disclosure of the appeal of the Civic case, improper deferral of losses on new product start-up costs, and inappropriate accrual of sales revenue.Ward and AOW appear to have violated section 10(b) by being actively involved in using a â€Å"scheme or artifice to defraud,† namely management’s issuing the materially misstated financial statements with full knowledge of the auditors. Ward, and hence AOW, acted with scienter, which is required by section 10(b). In addition, by willfully enabling the 10-K to be filed with the SEC, Ward seemin gly violated section 32 of the Securities Exchange Act of 1934 by knowingly causing materially misstated statements to be filed (the financial statements and the auditors’ opinion).Chapter 23 (Module B) B. 45 SEC Independence Rules In these solutions, the following responses do not try to contemplate all exception conditions cited in the text related to the SEC independence rule exceptions. The solution focuses on the primary conditions. a. b. Yes. A member of the engagement team cannot hold a direct financial interest. Yes. No other partner in the Santa Fe office (covered persons) can own direct financial interest in CCC. Yes. Immediate family members of covered persons in the firm cannot hold direct financial interest in CCC. Yes.The son (presumed a dependent) is also an immediate family member. No. According strictly to the definition, the father is a close family member (not an immediate family member), so the financial interest in CCC does not impair independence. Yes. C ontrolling interests in audit clients when held by close family members of covered persons in the firm impair independence. c. d. e. f. g. B. 48 Yes. Independence is impaired when close family members of a covered person in the firm (Javier) holds a job with a client in an accounting or financial reporting role.Independence, Integrity and Objectivity Cases The following interpretation is relevant for responses a, b, c, d, e, and f. Interpretation 101-6: In general, when the present management of a client commences or expresses an intention to commence legal actions against its public accounting firm, the public accounting firm and the client management may be placed in adversary positions in which the management's willingness to make complete disclosures and the auditors’ objectivity may be affected by self-interest.Independence may be impaired whenever the auditors and the client or its management are in positions of material adverse interest by reason of actual or threatene d litigation. Various situations are sometimes difficult to generalize, and the following responses are guidelines expressed in AICPA Ethics Interpretations (Effect of Litigation). a. Independence would be impaired: An expressed intention by the client to begin litigation alleging deficiencies in audit work is considered to impair independence if the public accounting firm concluded that there is a strong possibility that such a claim will actually be filed.Independence would be impaired: The commencement of litigation alleging deficiencies in audit work impairs independence. Independence would be impaired: The commencement of litigation by the public accounting firm alleging management fraud or deceit would definitely impair independence. Independence could be impaired: The claim under subrogation by the insurance company would not necessarily affect auditors’ independence on its client. In this case, the client and members of management are not the plaintiffs. However, this situation would have to be carefully evaluated by the CPA firm.If members of Contrary management are going to testify on behalf of the insurance company's interest and thus act in an adversary relation to the public accounting firm, independence would likely be impaired. b. c. d. e. Independence would not be impaired: Litigation not related to the audit work, whether threatened or actual, for an amount that is not material to the audit form or to the financial statements of the client would not usually be considered to affect the CPA-client relationship in such a way as to impair independence. . Independence would not necessarily be impaired: The class action lawsuit against both public accounting firm and company in itself would not alter fundamental relationships between the management and directors and the public accounting firm and therefore would not be considered to have an adverse impact on the auditors’ independence.These situations should be examined carefully, howe ver, because the potential for adverse interests may exist if cross-claims alleging that the covered member is responsible for any deficiencies or if the covered member alleges fraud or deceit by the present management as a defense are filed against the covered member. g. Interpretation 101-15: Independence is impaired. The CPA's financial interest in Dove Corp. (as an investor) is sufficiently large to allow Lisa to potentially influence the actions of Dove.Because Dove has a significant ownership interest in Tate Company, the CPA's independence would be considered impaired for the audit of Tate Company. Simply stated, the CPA's ability to influence Dove Corp. could permit Lisa to exercise a degree of control over Tate Company that would place the CPA in a capacity equivalent to that of a member of management. Interpretation 101-15: Independence is impaired. Queens’s financial interest in Hydra is sufficiently large enough (12 percent) for it to exert influence. Because Quee ns’s audit client, Howard, owns 46 percent of Hydra, Queens can clearly exert influence over Hydra.Because Howard’s financial position will be dependent in part on the financial performance of Hydra, Queens cannot possibly be independent in its audit of Howard because of its ownership in Hydra. Interpretation 101-2: (1) Assuming that the First National Bank is a profit-seeking enterprise, the independence of the auditors is not impaired by the association of the two individuals who served both as members of the auditing firm and as directors for the client during the period examined as long as they have ended all ties with the bank and are not involved in the audit.The auditors’ services may consist of advice and technical services, but the former controller must not make management decisions or take positions that might impair objectivity. The independence of the auditing firm would be compromised by any partner making a decision on loan approvals and the minim um balance checking account policy but normally not by the former controller’s performing a computer feasibility study.If the former controller's participation in the feasibility study was objective and advisory, and if the former controller’s advice was subject to effective client review and decision, the firm's independence has not been compromised. It is desirable, however, that the former controller could not participate in the audit of the First National Bank's financial statements. h. h. (2) i. Rule 101: The acceptance by the CPA of the unsecured interest-bearing notes in payment of unpaid fees would not be construed as discrediting the CPA's independence in relation to Cather because the notes are merely a substitution for an open account payable.The rule of professional conduct that prohibits a CPA from having any financial interest in a client does not extend to the liability for the CPA's fee. Under SEC rules, however, a definite arrangement for paying the no tes must be stated by the client. However, the acceptance of two shares of common stock (or prior commitment to accept stock) would be a violation of Rule 101. Any direct financial interest such as common stock holdings are construed as discrediting the CPA's independence. Rule 101: The Code of Ethics does not apply to Debra.She's neither a CPA nor a member of AICPA. However, the ruling does apply to independence of a firm if an employee accepts more than a token gift. Independence is impaired because an AICPA member cannot permit employees to break rules that she or he is obligated to observe. k. l. Rule 101. 4. A: Ruling 52 (ET 191. 104): Independence is considered impaired. At the time a member issues a report on financial statements, the client should not be indebted for more than one year's fees. In the Groaner case, the debt would be for last year and the current year audit fees.Groaner will have to pay the fees for last year when the current year report is ready (or else get a non-independent disclaimer). The past due fees take on characteristics of a loan within the meaning of Rule 101, and collection may depend on the nature of the auditors’ report on the financial statements. Rule 102—Integrity and Objectivity: The CPA has violated the rule. The CPA (1) lacked integrity, (2) knowingly misrepresented facts by omitting the gain in the current-year tax return, and (3) subordinated CPA judgment to another (the client).The proper action is to file an amended return for last year and request a refund and then file a correct return for this year. m. n. Rule 102—Integrity and Objectivity: Both CPAs probably violated Rule 102. Lestrade has a conflict of interest in owning another business that provides services to her employer and (apparently) not disclosing the business to Baker's board of directors. The â€Å"prepaid expenses† classification is wrong. Lestrade has falsified an entry in the accounts and in the financial statements (a violation of Rule 501). Both CPAs have fooled the external auditors by lying about the related-party loan and the repayment erms. B. 58 Conflict of Clients' Interests. This situation raises a typical â€Å"Who's the client? † question. Unfortunately, the relevant relationships are William's individual engagements with Jack and Bill because Williams would have essentially the same problem if Oneway Corporation were not a client. The situation is â€Å"unfortunate† because Williams is in a no-win situation. If he keeps Bill informed, he might save the Oneway engagement and Bill's friendship, but he will suffer the guilt of having engaged in industrial espionage and might face an ethics complaint for having ignored the rule of accountants' confidentiality.If Jon keeps quiet, he might lose the engagement and a significant portion of his personal income at least temporarily. If Williams believes rules are the most important element of ethical behavior and the consequenc es of action or inaction must fall where they may, he will refuse Bill's request with an eloquent and sympathetic explanation of the professional reasons for not discussing other clients' business affairs.A happy outcome for this approach depends upon Bill's understanding the difficult situation he has created for Williams. If Williams believes in weighing the â€Å"good and evil consequences† of ethics-related choices, he will need to decide which ultimate outcome is most desirable: Bill's well-being (and his own income) or Jack's and Jill's well-being, whatever it may be. B. 61 Ethics Case a. Sally violated Rule 501.According to interpretation 501-7, a member who fails to comply with applicable federal, state, or local laws or regulations regarding the timely filing of his or her personal tax returns or tax returns of the member’s firm, or the timely remittance of all payroll and other taxes collected on behalf of others may be considered to have committed an act dis creditable to the profession in violation of rule 501. Sally could receive any of the penalties available to the AICPA and the state board including admonishment, suspension, or expulsion. A discussion of the penalties should ensue.Opinions may range from the least punitive penalty because Sally has now resolved her legal difficulties to the most severe penalties because the publicity regarding a member of the profession portrays a negative image of the profession and will send a message to the public regarding professional conduct of other members. That is, some students will want to make an example of Sally’s behavior. b. c. Engagement Planning 3. 48 General Audit Procedures and Financial Statement Assertions PCAOB Assertions Existence or occurrence Completeness Raises questions that may be relevant to all assertions but may not produce actual â€Å"evidence. Because it is performed on recorded amounts, it works best for existence or occurrence, valuation and allocation, r ights and obligations, and presentation and disclosure. When applied to source documents, it might work for the completeness assertion. Existence or occurrence, valuation Existence or occurrence, valuation Existence or occurrence Rights (ownership) Valuation (sometimes) Completeness (sometimes) All assertions; however, responses typically yield more assertions that in turn are subject to audit with corroborating evidence.ASB Assertions Existence, occurrence Completeness Existence Occurrence Valuation and allocation Rights and obligations Completeness Accuracy Classification Existence, valuation Existence, valuation Existence Rights (ownership) Valuation (sometimes) Completeness (sometimes). All assertions; however, responses typically yield more assertions that in turn are subject to audit with corroborating evidence Existence, valuation Valuation Existence Occurrence Valuation Completeness Audit Procedures 1a. Inspection of records or documents (vouching) 1b.Inspection of records o r documents (tracing) 1c. Inspection of records or documents (scanning) 2. Inspection of tangible assets 3. Observation 4. Confirmation 5. Inquiry 6. Recalculation 7. Reperformance 8. Analytical procedures Existence, valuation Valuation Existence or occurrence Valuation Completeness 3. 50 Confirmation Procedure a. Audit confirmation, a procedure widely used in auditing, refers to direct correspondence by the auditor with independent parties. It can produce evidence of existence and ownership and sometimes of valuation and cutoff.Auditors typically limit their use of confirmation to balances about which outside parties could be expected to provide information. The two main characteristics a confirmation should possess are: (1) The party supplying the information requested must be knowledgeable and independent (i. e. , must have knowledge of information of interest to the auditors and must be outside the scope of influence of the organization being audited). (2) The auditors must obta in the information directly from the informed party.In addition, the auditors must maintain control (at all times) over the mailing and receipt of confirmation requests. To be considered competent evidence, the client cannot have an opportunity to handle confirmation requests at any point in the process. b. 3. 52 Audit Documentation a. (1) Audit documentation is the auditors’ record of the procedures performed and conclusions reached in the audit. The functions of audit documentation are to aid the CPA in the conduct of the audit work and to provide support for the auditor’s opinion and compliance with auditing standards.Audit documentation can be classified in two categories: (1) permanent files (which contain information that is relevant to ongoing client relationships) and (2) current files (which relate to just one year of the client relationship). The documentation (usually in the form of either electronic files or hard copy work papers) should contain detailed su pport for the decisions regarding planning and performing the audit, procedures performed, evidence obtained, and conclusions reached. (2) b.The factors that affect the auditors’ judgment of the type and content of the audit documentation for a particular engagement include: (1) (2) (3) (4) (5) The nature of the auditors’ report. The nature of the client’s business. The nature of the financial statements, schedules, or other information on which the auditors are reporting and the materiality of the items included therein. The nature and condition of the client’s records and internal controls. The needs for supervision and review of work performed by assistants. c.Evidence that should be included in audit documentation to support auditors’ compliance with generally accepted auditing standards includes: (1) (2) (3) (4) (5) The financial statements or other information on which the auditors are reporting were in agreement or reconciled with the client ’s records. The client’s system of internal control was reviewed and evaluated to determine the nature, timing, and extent of audit procedures. The audit procedures performed in obtaining audit evidence for evaluation. How exceptions and unusual matters disclosed by audit procedures were resolved or treated.The auditors’ conclusions on significant aspects of the engagement with appropriate commentaries. d. The audit team should perform an adequate examination at minimum cost and effort, and the prior year’s plans will aid in doing this. Those audit plans ordinarily contain information useful in the current examination (such as descriptions of the unique features of a client’s operations or records, a formalized sequence of audit steps in logical order, and approximate time requirements to perform various phases of the work. ) The audit team should ecide whether to use the old plan or prepare a new one. 3. 54 Predecessor and Successor Auditors Wells & Ratley (W&R) needs to initiate communications with both predecessor auditors. The situation is unusual, but W&R needs to obtain complete information from all predecessors involved since the last audit (2007 financial statements). Both Canby & Co. and Albrecht & Hubbard (A&H) are predecessors. (If Canby & Co. had completed the 2007 audit and W&R had been hired to perform the 2008 audit, then Canby & Co. would be the only predecessor.A&H would be history. ) Inquiry of only one of the predecessors would not result in complete information because the circumstances surrounding each auditor change may be different. The two predecessors, having served at different times and for different lengths of time, may have different knowledge about Allpurpose Loan Company and its president. If the company is public and subject to SEC reporting requirements, forms 8-K for both changes should have also been filed. Management Fraud and Audit Risk 4. 46 Analytical Procedures and Interest Expense a.Th e audit estimate of interest expense for these notes is about $24,400. Notes Payable Balances Balance Rate Time $150,000 10. 0% $200,000 10. 0% $225,000 10. 0% $285,000 10. 0% $375,000 10. 0% $375,000 9. 5% $430,000 9. 5% $290,000 9. 5% $210,000 9. 5% $172,000 9. 5% $95,000 9. 5% 1 month Auditors’ Interest Calculation Interest 1 month 1 2 months 1 month 1 1 month 1 1 month 1 1 month 1 1 month 1 1 month 1 1 month 1 1 month 1 1 $752 12 months $1,250 2 $3,334 $1,875 $2,375 $3,125 $2,969 $3,404 $2,296 $1,663 $1,362 Date Jan 1 Feb 1 Apr 1 May 1 Jun 1 Jul 1 Aug 1 Sep 1 Oct 1 Nov 1 Dec 1Weighted Average $250,583 9. 75% 12 $24,405 $24,432 Calculated on Average Balance and Average Rate b. The type of analytical procedure is â€Å"study of the relationships of current-year account balances with relevant nonfinancial information. † While the interest rate may not seem to be an item of â€Å"nonfinancial information,† it is not a direct entry or element in the clientâ€℠¢s financial statements. Three of the other four types of analytical procedures do not describe the estimate (because it does not compare to prior periods, to budget, or to industry information).However, a case might be made that the estimate is an â€Å"evaluation of a relationship of current-year account balances (notes payable) to other current-year balances (related interest expense) for conformity with a predictable pattern (interest rate relation) based on the company’s experience. c. The recorded interest expense appears to be too small. The company may have forgotten or miscalculated the year-end interest expense accrual. (In fact, this amount was specified because the missing amount is approximately the $750 of the accrual for the December interest. ) d.The recorded interest expense is about right. Some differences in timing and calculation might explain the small difference, but it is not material enough to warrant further work. e. The recorded interest expense app ears to be too large. Maybe the company has other debt on which interest is being paid, but the debt is not recorded in the accounts. (In fact this amount was specified in terms of an extra $100,000 being borrowed in July at 9. 5% interest, not recorded, but paid back by August 1 before the next recorded borrowing. This would account for about $800 additional interest: $100,000 x 9. % x 1/12 = $792. ) Could be that Weyman found he could borrow the company’s cash for himself, earn interest, and then pay back the principal! ) Actually, this kind of maneuver could have been carried out in any month and not noticed by auditors who saw only the first-of-the-month balances. 4. 49 Analysis of Accounting Estimates The company has fudged the write-offs as being as small as possible, hoping to satisfy the auditors. Taken one at a time, only the uncertainty about the deferred subscription costs is large enough to break the materiality threshold. But the set of problems cannot be taken o ne at a time.Here is a suggested low-high audit estimate: Low Estimate High Estimate Write-off deferred subscription costs (1) $ 6,000,000 $12,000,000 Provide allowance for bad debts (2) $ 4,000,000 $ 4,000,000 Provide for expected warranty expense (3) $ 2,000,000 $ 6,000,000 Lower of cost or market inventory write-down (4) $ 5,600,000 $ 5,600,000 Loss on government contract refund (5) $ 1,000,000 $ 2,000,000 Total write-offs and losses $18,600,000 $29,600,000 (1) The low estimate gives the benefit of doubt to the survival of the business, writing off half the deferred costs as if one-half might be written off over the next two years.The company seems to have taken the 50% probability ($6 million) and allocated half to each of the two years. (2) (3) The company seems ready to provide the allowance for all the doubtful accounts receivable. There is not much information for the audit team (such as a probability distribution). (4) It appears that the company plans to rebuild the invent ory and recover as much as it can, namely the $4,400,000 that can be realized from selling the rebuilt parts, but the lower of cost or market was figured incorrectly.The company seems to have subtracted the selling price ($8 million) from the inventory cost ($10 million) to get the $2 million write-down. The correct calculation is: Net realizable value Selling price proceeds $ 8,000,000 Cost to rebuild $(2,000,000) Cost to market and ship (20% x $8 million) $ (1,600,000) Ceiling (net realizable value) $ 4,400,000 Floor; subtract â€Å"normal profit† (5% x $8 million) $ (400,000) Floor $ 4,000,000 Replacement cost is apparently $6 million for the modern part, so the â€Å"market† for lower of cost or market is NRV = $4,400,000, and the inventory write-down is $10,000,000 – $4,400,000 = $5,600,000.Sale of the rebuilt parts will produce zero profit in subsequent period(s): Selling price $ 8,000,000 Cost of goods sold Inventory sold (written-down cost) 4,400,000 Reb uilding cost 2,000,000 $(6,400,000) Cost to market and ship ($1,600,000) Profit $ 0 (5) For a contingency such as this government contract dispute, GAAP suggests recognizing loss at the lower end of a range for loss, so a $1 million loss provision would satisfy GAAP. Recommended adjustment: Management’s suggestion of $11,000,000 cost/loss recognition is not sufficient.It â€Å"leaves† $7,600,000 income overstatement, even using the auditors’ low estimate of $18,600,000. Even booking the low estimate â€Å"leaves† $10,000,000 unrecognized (including the government contract contingency at $1 million instead of $2 million). The minimum adjustment, given the limited information available in this problem, follows. Adequate disclosures should be made about the $6 million deferred subscription costs remaining and the prospects for the business as well as about the warranty expense estimate because these are the items that leave uncertain assets and liabilities i n the financial statements.Debit Credit Subscription expense $ 6,000,000 Bad debt expense $ 4,000,000 Warranty expense $ 2,000,000 Cost of goods sold $ 5,600,000 Government contract loss $ 1,000,000 Deferred subscription costs $ 6,000,000 Allowance for doubtful accounts $ 4,000,000 Estimated warranty liability $ 2,000,000 Inventory $ 5,600,000 Estimated liability on contract $ 1,000,000 4. 54 Audit Risk Model Evaluation of risk assessment conclusions with AR = IR x CR x DR as a model. 1.Paul is not justified in acting on a belief that IR = 0. He may have seen no adjustments proposed because (1) none were material or (2) Tordik’s control system has functioned well in the past and prevented or detected and corrected material errors. If IR = 0, then AR = 0, and no further audit work need be done. Conservative auditing standards and practice do not permit this level of (non)work based on this little evidence and knowledge. 2. Hill is not justified in acting upon a belief that CR = 0.She may well know that Edward’s internal accounting control is exceptionally good, but (1) her review did not cover the last month of Edward’s fiscal year and (2) control activities are always subject to lapses. If CR = 0, then AR = 0, and no further audit work need be done. Conservative audit practice does not permit assessment of control risk at 0% to the exclusion of other audit procedures. 3. Insofar as audit effectiveness is concerned, Fields’ decision is within the spirit of audit standards. Even if IR = 1 and CR = 1, if DR = 0. 02, the AR = 0. 02.This audit risk (AR) seems quite small. However, Fields’ decision may result in an inefficient audit. 4. This case was deliberately left ambiguous without quantifying the audit risks. Students will need to experiment with the model. One approach is to compare the current audit to a hypothetical last year’s audit when â€Å"everything was operating smoothly. † Assume: Last year: Current ye ar: AR = IR (0. 50) + CR (0. 20) x DR (0. 20) = 0. 02 AR = IR (1. 0) + CR (1. 0) x DR (0. 25) = 0. 25 Features of the hypothetical comparison: (1) Inherent risk is greater than last year. 2) Control risk is greater than last year. (3) The audit was less extensive, possibly resulting in more detection risk. (4) Audit risk appears to be very high. An alternative analysis is that Shad perceived higher inherent and control risk early, and he did not put any audit time into trying to assess the risks at less than 100%. He proceeded directly to performance of extensive substantive procedures and worked fewer total number of hours yet still performed a high-quality audit by keeping AR low by keeping DR low. 4. 6 Risk Assessment We gratefully acknowledge the assistance of Jeanie Folk in developing the following solution: Recall that audit risk is the risk that the auditor will give an inappropriate opinion on financial statements (e. g. , giving an unqualified opinion on the financial state ments that are misleading because of material misstatements that auditors failed to discover. The problem adds the perspective that the audit risk at the overall financial statement level is influenced by the risk of material misstatements, which may be indicated by a combination of factors related to management, the industry, and the company. . Decrease. Ordinarily, the fact that this is the first profitable year after a string of losses would cause concern. The auditor might suspect an overstatement of revenues or understatement of expenses. However, in this situation, the increase in revenues (and net income) appears to be the result of additional federal and state funding for environmental purposes to TWD’s customers, which are municipalities. Given that TWD has a limited number of customers, the year-end receivables (and even revenue) can be confirmed with those municipalities.As such, there would be no increase in audit risk. The decrease in audit risk would result from lessening the company’s need to get through a â€Å"difficult period,† that is, the years of losses. 2. Increase. TWD’s board of directors is controlled by its major stockholder who also acts as the company’s CEO. That person may act in his or her best interests rather than in accordance with those of the minority shareholders and other financial statements.The potential for financial statement fraud would increase as a result. 3. Increase. The internal auditor reports to the Controller, who has responsibility for the company’s accounting system and the preparation of its financial statements. The internal auditor should report to the audit committee so that objectivity is maintained. Because the controller could steer the internal auditor away from problem areas, audit risk would be increased. 4. Increase. Turnover is a red flag that the department might have problems.Additionally, turnover resulted in the hiring of inexperienced people (at least inexperienced with respect to TWD). 5. Decrease. Having an external party such as a bank loan officer involved in an ongoing review of the company’s performance would enhance the company’s system of internal controls. 6. No effect. The payment of employees on a weekly, biweekly, monthly, or other basis would have no effect on audit risk. 7. Decrease. Bond has audited TWD for five years.As a result, because Bond is familiar with the industry, the company, and its management team, Bond is in a position to identify information necessary to assess fraud risk factors, identify those risk factors, and assess fraud risk than the firm would be if it had little or no experience with this client. 8. Increase. Changing accounting practices increases inherent risk (the susceptibility of the accounts to misstatement). 9. Increase. TWD sold one-half of its controlling interest in UEL; its remaining interest is significant.As such, TWD now has significant influence over but no longe r controls the operations of UEL. With its lower influence and knowledge of UEL, TWD is not as able to assess the risk of fraudulent financial reporting by UEL. UEL’s results still impact TWD’s financial statements (because the equity method would be used in cases of significant influence) and, as such, the audit risk relating to TWD’s financials would accordingly increase. 10. Decrease. If the litigation were disclosed in prior years, either the potential loss was probable but could not be reasonably estimated or it was reasonably possible.In either case, the amount of potential loss must have been material. Because the litigation was dropped by the state, there is less uncertainty about the impact of this pending litigation on the company’s financial position and results of operations. 11. Increase. Related-party transactions generally increase the risk of fraud, especially because the transactions were not previously disclosed. 12. Increase. In Decembe r, This barter transaction is not only unusual, but will also present problems in terms of the measurement of the revenue earned. As such, audit risk will increase. 13.No effect. Inherent risk is a component of risk of material misstatement. However, insurance coverage, or the lack thereof, has no impact on inherent risk, which is the risk that, in the absence of internal controls, material errors or frauds could enter the accounting system used to develop financial statements. Furthermore, having such coverage would lower the business risk for the company. 14. Increase. Recall that revenues must be matched with all costs incurred to earn that revenue. As such, the cost, if any, of the guarantees issued must be estimated and recorded in the current year.Given the lack of historical information and difficulties involved in estimating the potential cost of its guarantee (and even considering the difficulties involved of determining whether the municipality has any responsibility for a ctions that might impact the results of the site inspections) that may materially impact the current year’s financial statements, audit risk will increase. 15. Increase. Generally, public offerings are successful for companies with strong financial performance. As such, going public often creates motivation for making the company appear as strong as possible.Audit risk would increase as a result. 4. 61 Errors and Frauds Students can probably think of many examples for each of the cases. This solution does not purport to be exhaustive. a. Overstate an asset, understate another asset Hold cash receipts journal open past the year-end (cutoff date) and record additional cash receipts occurring after year-end, reducing accounts receivable. b. Overstate an asset, overstate stockholder equity Record appraised value of property, plant, and equipment with a corresponding credit to a capital account. c.Overstate an asset, overstate revenue (1) Hold the sales journal open past the year- end (cutoff date) and record too much sales revenue and cash or accounts receivable. (2) Record fictitious sales and accounts receivable. d. Overstate an asset, understate an expense (1) Capitalize maintenance expense, making the asset amount higher than warranted and the expense amount lower. Subsequent depreciation would reverse this misstatement, but the first effect would be to overstate the asset and understate the expense. (2) Record an expenditure as a prepaid expense instead of a current expense. . Overstate a liability, overstate an expense Accrue too much liability for expenses not yet paid, such as wages, rent, interest, product warranties f. Understate an asset, overstate an expense (1) Calculate too much depreciation expense on assets. (2) Classify expenditures as curre

Professionalism in Sports

PROFESSIONALISM IN SPORTS August 1890 – The North American Review It is hardly necessary at the present day to enter a plea for athletic exercise and manly outdoor sports. During the last twenty-five years there has been a wonderful growth of interest in and appreciation of healthy muscular amusements; and this growth can best be promoted by stimulating, within proper bounds, the spirit of rivalry on which all our games are based. The effect upon the physique of the sedentary classes, especially in the towns and cities, has already been very marked.We are much less liable than we were to reproaches on the score of our national ill health, of the bad constitutions of our men, and of the fragility and early decay of our women. There are still plenty of people who look down on, as of little moment, the proper development of the body; but the men of good sense sympathize as little with these as they do with the even more noxious extremists who regard physical development as an end instead of a means.As a nation we have many tremendous problems to work out, and we need to bring every ounce of vital power possible to their solution. No people has ever yet done great and lasting work if its physical type was infirm and weak. Goodness and strength must go hand in hand if the Republic is to be preserved. The good man who is ready and able to strike a blow for the right, and to put down evil with the strong arm, is the citizen who deserves our most hearty respect.There is a certain tendency in the civilization of our time to underestimate or overlook the need of the virile, masterful qualities of the heart and mind which have built up and alone can maintain and defend this very civilization, and which generally go hand in hand with good health and the capacity to get the utmost possible use out of the body. There is no better way of counteracting this tendency than by encouraging bodily exercise, and especially the sports which develop such qualities as courage, r esolution, and endurance.The best of all sports for this purpose are those which follow the Macedonian rather than the Greek model: big-game hunting, mountaineering, the chase with horse and hound, all wilderness life with all its keen, hardy pleasures. The hunter and mountaineer lead healthier lives in time of need they would make better soldiers than the trained athlete. Nor need these pleasures be confined to the rich. The trouble with our men of small means is quite as often that they do not know how to enjoy pleasures lying at their doors as that they cannot afford them.From New York to Minneapolis, from Boston to San Francisco, there is no large city from which it is impossible to reach a tract of perfectly wild, wooded or mountainous land within forty-eight hours; and any two young men who can get a months holiday in August or September cannot use it to better advantage than by tramping on foot, pack on back, over such a tract. Let them go alone; a season or two will teach th em much woodcraft, and will enormously increase their stock of health, hardihood, and self-reliance.If one carries a light rifle or fowling-piece, and the other a fishing rod, they will soon learn to help fill out their own bill of fare. Of course they must expect to find the life pretty hard, and filled with disappointments at first; but the cost will be very trifling, and if they have courage, their reward is sure to come. However, most of our people, whether from lack of means, time, or inclination, do not take to feats of this kind, and must get their fun and exercise in athletics proper.The years of late boyhood and early manhood say from twelve or fourteen to twenty-eight or thirty, and often until much later are those in which athletic sports prove not only most attractive, but also most beneficial to the individual and the race. In college and in most of the schools which are preparatory for college rowing, foot-ball, base-ball, running, jumping, sparring, and the like have assumed a constantly increasing prominence. Nor is this in any way a matter for regret.Of course any good is accompanied by some evil; and a small number of college boys, who would probably turn out badly anyhow, neglect everything for their sports, and so become of little use to themselves or any one else. But as a whole college life has been greatly the gainer by the change. Only a small proportion of college boys are going to become real students and do original work in literature, science, or art; and these are certain to study their best in any event.The others are going into business or law or some kindred occupation; and these, of course, can study but little that will be directly of use to them in after-life. The college education of such men should be largely devoted to making them good citizens, and able to hold their own in the world; and character is far more important than intellect in making a man a good citizen or successful in his calling meaning by character not onl y such qualities as honesty and truthfulness, but courage, perseverance, and self-reliance.Now, athletic sports, if followed properly, and not elevated into a fetish, are admirable for developing character, besides bestowing on the participants an invaluable fund of health and strength. In each of the larger colleges there are from fifty to a hundred men who, on the various class and college crews and ball teams, or in the track and gymnasium games, compete for the different championships; and for every one such man who actually competes there are five or ten who take part in the practice games, train more or less, and get a great deal of benefit from the work.The careful system of measurements which have been taken at Harvard shows a marked improvement in the physique of the men even during the last ten years; and what is more important this shows that this improvement is, if anything, more marked in the case of the average man than in that of the picked champions. The colleges con tain but a small proportion of the men interested in amateur athletics, as can be seen by the immense number of ball clubs, rowing clubs, polo clubs, hunt clubs, bicycle clubs, snow-shoe clubs, lacrosse clubs, and athletic clubs proper which are to be found scattered among our cities and towns.Almost any man of sedentary life who wishes to get exercise enough to keep him in vigorous health can readily do so at one of these clubs; and an increasing proportion of our young men are finding this out and acting accordingly. More than one of our most famous athletes originally took to athletics for his health; and, on the other hand, be it remembered always that the sports which prove most bene- ficial bodily to a man are those which interest and amuse him.If he belongs to a rowing club or baseball nine, the eagerness and excitement of a contest with a rival association spur him on to keep his body in good condition; and, as with the college athletes, there are scores of outsiders, whom t hese championship contests attract, and whose love for athletics is increased thereby, for every individual contestant who directly participates in them. It is needless to say that under the head of manly sports I do not in elude pigeon-shooting; and still less rabbit-coursing, or any other game where the man does nothing but look on.Already this awakening of interest in manly sports, this proper care of the body, have had a good effect upon our young men; but there are, of course, accompanying dangers in any such movement. With very few exceptions the man who makes some athletic pursuit his main business, instead of turning to it as a health-giving pastime, ceases to be a particularly useful citizen. Of course I do not refer to the men who act as trainers and instructors at the different colleges and clubs ; these perform a most useful and honorable function, and among them several could be named who have rendered as high service as any men in the community.But the amateur athlete who thinks of nothing but athletics, and makes it the serious business of his life, becomes a bore, if nothing worse. A young man who has broken a running or jumping record, who has stroked a winning club crew, or played on his college nine or eleven, has a distinct claim to our respect; but if, when middle-aged, he has still done nothing more in the world, he forfeits even this claim which he originally had. It is so in an even more marked degree with the professional athlete.In America the difference between amateurs and professionals is in one way almost the reverse of what it is in England, and accords better with the ways of life of our democratic community. In England the average professional is a man who works for his living, and the average amateur is one who does not; whereas with us the amateur usually is, and always ought to be, a man who, like other American citizens, works hard at some regular calling, it matters not what, so long as it is respectable, while the profess ional is very apt to be a gentleman of more or less elegant leisure, aside from his special pursuit.The mere statement of the difference is enough to show that the amateur, and not the professional, is the desirable citizen, the man who should be encouraged. Our object is to get as many of our people as possible to take part in manly, healthy, vigorous pastimes, which will benefit the whole nation; it is not to produce a limited class of athletes who shall make it the business of their lives to do battle with one another for the popular amusement. Most masterful nations have shown a strong taste for manly sports. In the old days, when we ourselves were still a people of backwoodsmen, at every merrymaking there were sure to be trials f skill and strength, at running, wrestling, and rifleshooting, among the young men. We should encourage by every method the spirit which makes such trials popular; it is a very excellent revival of old-time American ways. But the existence of a caste of gladiators in the midst of a population which does not itself participate in any manly sports is usually, as it was at Rome, a symptom of national decadence. The Romans who, when the stern and simple strength of Rome was departing, flocked to the gladiatorial shows, were influenced only by a ferocious craving for bloody excitement; not by any sympathy with men of stout heart and tough sinew.So it is, to a lesser extent, today. In baseball alone, the professional teams, from a number of causes, have preserved a fairly close connection with non-professional players, and have done good work in popu- larizing a most admirable and characteristic American game ; but even here the outlook is now less favorable, and, aside from this one pastime, professionalism is the curse of many an athletic sport, and the chief obstacle to its healthy development. Professional rowing is under a dark cloud of suspicion because of the crooked practices which have disgraced it. Horse-racing is certainly no t in an ideal condition.A prize-fight is simply brutal and degrading. The people who attend it, and make a hero of the prizefighter, are, excepting boys who go for fun and dont know any better,to a very great extent, men who hover on the border-line of criminality; and those who are not are speedily brutalized, and are never rendered more manly. They form as ignoble a body as do the kindred frequenters of rat-pit and cock-pit. The prizefighter and his fellow professional athletes of the same ilk are, together with their patrons in every rank of life, the very worst foes with whom the cause of general athletic development has to contend – THEODORE ROOSEVELT.

Antarctica

White fields of snow, surrounded by ice covered mountains and no civilization around for miles. This may sound like a fantasy land but is the blank canvas of Antarctica. Some people think of it as an arctic waste land but I see it as an unexplored frontier. Antarctica is one of last places on the planet that has not been thoroughly explored. It gives the land a kind of mystery; like anything could exist there. It represents an older simpler time in the world, before industrialization, automobiles, and roads. People have not breached this still natural and wild habitat. This natural world holds a magnificent beauty that is unparalleled anywhere else. It is one of the last uncultivated places left in the world where nature still reigns, free from the influence of human kind.Antarctica intrigues me because I am also interested in what is new and developing. This land has the opportunity to be created into anything. Any kind of government or economy; a whole new way of life could be crea ted here. Any type of society could develop from a colonial government controlled by some world power or a new sovereign nation. The unknown ignites my imagination. It makes me ask the question what new advancement in technology can be found or scientific discoveries can be made? I am intrigued by the unknown and of all the places in the world Antarctica is the epitome of the unknown.

Sickle Cell Transition Placement Essay Example | Topics and Well Written Essays - 2500 words

Sickle Cell Transition Placement - Essay Example According to Anon (2009) about 7 percent of patients often die due to the increase of liver iron, and other causes including strokes and infection are also considered causes of deaths among these patients. This essay will be a reflection of my sickle cell placement as a student nurse. This topic was chosen because I wanted to observe what sickle cell nurses do for patients in order to enhance my learning; moreover, I also believe that this learning associates well to my course. I also chose to observe what sickle cell nurses do for patients because I of the likelihood of encountering patients with sickle cell disease in the future. This essay shall first undertake a reflection on the transition activity; secondly, it will demonstrate a detailed knowledge of the transition activity, which in this case is sickle cell disease. This second part will also demonstrate the impact of the topic and the transition activity to my area of professional practice. This second portion shall also dis cuss the role of sickle cell nurses and shall then provide reasons why the activity was chosen. Thirdly, this essay will analyse how this transition activity has contributed to my own learning and skills development. Lastly, by focusing on this transition activity, this paper will also determine further areas for personal and professional development and how this might be taken forward through future research and further study as a registered nurse. In accordance with the requirements of the Nursing and Midwifery Council (2008), any personal confidential information regarding the patient/s and individuals involved in this placement shall not be disclosed. The Trust where I conducted my placement shall also be kept confidential. Body Reflection on the Transition Activity I had my transition placement on sickle cell disease, and initially during my placement, I had a discussion at the hospital with the patients and later visited them in their own homes. In general, the activities duri ng my placement were varied. I met with the multidisciplinary team regarding patients who suffered from sickle cell and how best to care for them. I also discussed the findings/results of the tests. I also observed how the sickle cell nurses administered care to the patients, addressing their needs physically, mentally, psychologically and emotionally. I also observed how nurses explained the disease to parents and their children, including the consequences of their illnesses as well as its risks/effects. I also observed how the nurses discussed with parents about the loss of their children, discussing with them the possible therapeutic options they can take as grieving parents. The transition activity initially provoked feelings of anxiety. However, in the process of learning, my anxiety soon vanished and I was able to transition gradually into the crucial duties of a sickle cell nurse. Duncan and DePew (2010) discuss that with more experience, the transition process among students of nursing can somehow be eased. In considering what I was able to get from this learning professionally, I was able to learn the qualities of the disease, including the specific role of the sickle cell nurse in ensuring efficient patient care. On a personal level, I was also able to get a specific feel for the nursing practice, including its

Applauding William Paterson Universitys Concert Performance Essay

Applauding William Paterson Universitys Concert Performance - Essay Example As the school’s Concert Band and Wind Ensemble played such favorites as Allegro Giocoso and Folk Song Suite, there were elements of strong orchestral harmony throughout the duration of their performances, which provided a competent musical event. No tangible discrepancies were noticed in relation to keeping up with the conductor’s tempo, suggesting a group which has practiced and rehearsed to remain harmonious. However, the Wind Ensemble appeared struggle through I Am – Richard Boysen, Jr. which may have been due to the difficulty of the piece as it is associated with a saxophone player who died in a car accident. The violent clashing of symbols to represent the accident’s hideous disgrace really emphasized the importance of the contemporary concert piece. Percussion dominated much of this series of performances, which added grandeur and excitement to the music. I have often thought that cymbals are often some of the most important instruments in the conce rt performance, as a slightly off-tempo clash can interrupt the harmony of the music. This performance lacked nothing in relation to maintaining the appropriate pace. Cymbals are used to represent a variety of emotions, perhaps as a stylistic tribute to history or as a remembrance piece to an influential person of interest.

Macroeconomics. The Solow model Essay Example | Topics and Well Written Essays - 1000 words

Macroeconomics. The Solow model - Essay Example The steady state condition is now that s*f(k) = (+n) * k:" (Introducing Population Growth). The Golden rule of Capital maximized the consumption at a steady state. This implies that the marginal product of capital net of depreciation must be equal to the technological progress and population hence growing for ever isn't possible without population and technological progress. The steady state is "c" and this is what is required. The values of steady state are substituted for both output. "(f(k*)) and investment which equals depreciation in steady state (k*) giving usc*=f(k*) - k*" (The Solow Model) 5. The Solow model is very simple and it creates a link between capital-output ratio and in addition to this it also it also creates a link between investment-depreciation ratio. All this is done in a dynamic model. "The main test for any model is how well it holds up against the data. Perhaps the biggest surprise is that despite its simplicity the Solow growth model can be applied to economic data. The results have been mixed though as Acemoglu writes in an extensive review of the literature. This is not necessarily bad news, for it points at some of the other factors that contribute to economic growth and differences across countries. One conclusion that can be drawn from the empirical literature is that cross-country differences in income per capita cannot be understood on the basis of differences in physical and human capital alone." (Solow growth Model) The economic growth is studied with this model and it has laid down a general basis for studying economic growth of an economy. The rate of capital accumulation and the rate of technological progress are two things that this model does not throw light upon and many models have been derived from the Solow model. The world is divided into capital and labour under this model and this is how the model progresses. The firms and households are treated as constants by this and the neoclassical growth model and this is rather considered a very odd feature of this model. "Now the question some may ask is to what extent economic growth is predicated on the use of non-renewable natural resources and thereby ultimately finite. Economic growth and capitalism rely on profit and not so much on production. Therefore both capitalism and economic growth are, in theory at least, reconcilable with sustainability. Differentiating between models of sustainable and unsustainable economic growth may be one of the greatest modelling challenges of the future." (Solow Growth Model) 6. In countries like Australia and Netherlands, the growth dynamics were determined predominantly by European integration. A broader study on the effect of convergence will

Research Paper About The Business And Operations Of Fedex

About The Business And Operations Of Fedex - Research Paper Example In addition to that, FedEx bought Kinko’s in 2004 and rebranded the offering into FedEx Office. With this brand, the company provides office supplies and printing services to consumers including computer use products, USBs, paper, business and greeting cards, stationery, mailing boxes and supplies, etc. b. Role of technology FedEx uses topnotch technology and MIS in everyday business that allows tracking of big and small packages across the globe. With the most advanced telecommunications and computer networks in place, a customer is able to log into the FedEx online website and track the exact location of the shipment and have an accurate understanding of when the product will reach destination. FedEx also offers FedEx Ship Manager at fedex.com, FedEx WorldTM Shipping Software and well staffed call centers (fedex.com) for the help of customers in tracking their shipments. In addition to that, FedEx utilizes advanced software and programs to assist employees in their everyday work and to be more efficient. For corporate clients, the company has innovative products such as Critical Inventory Logistics service through FedEx Supply Chain. c. Product life cycle FedEx is a mature company that has been in business since 1973. FedEx is in the maturity stage, as shown in the diagram1. However, the company has managed through innovation, new product development, increased customer outreach and efficient business practices to expand this cycle with higher sales volume. d. Price elasticities The logistics industry is highly competitive with not only international players such as DHL, FedEx and Maersk but also an abundance of local (domestic) players in various countries. This means high price elasticity for some of FedEx products. In the U.S. market alone, the two biggest players are UPS and FedEx and customers switch between the two based on the product and service prices. e. Substitute products and service The logistics industry is directly related to businesses and consumer demand for their products. A logistics company is run on a huge investment and requires use of infrastructure. The occurrence of FedEx substitutes is limited to competition such as UPS and DHL; there are no real substitute options for logistics companies that can service the customer need satisfactorily. Market trends Economic activity has a direct impact on the demand for logistics and transport. The logistics industry sees a boom when economies are robust and active: businesses have consumer demand for their products and the timely delivery of the products is based on the performance of the transport company. Conversely, a slow or bad economy shows a sluggish demand for logistics services. The economic downturn of 2007 impacted the logistics industry in a negative way. With a recessing global economy, trade slowdown and conservative consumer demand, logistics industry also faced scarce demand. a. Consumer behavior FedEx has individual customers as well as business or corporate customers. Both types of consumers have a few definite needs. They want specialized, customized products that target their specific needs. While creating a customized product for a corporate customer is more feasible and cost effective than creating one

Prison life and strategies to decrease recidivism upon an inmates Essay

Prison life and strategies to decrease recidivism upon an inmates release from prison - Essay Example In the US, the rate of recidivism is estimated to be approximately two-thirds of all released inmates (Andrews & Bonta, 1994). This means that at least two-thirds of prisoners released will ultimately be re-imprisoned within a period of three years. High recidivism rates impose immense costs with regard to public safety, as well as tax dollars utilized in arresting, prosecuting and imprisoning re-offenders. Due to these high costs, programs for inmates, as well as released prisoners, which reduce recidivism, can prove cost effective, even in the event of modest success (Perkinson, 2010). This paper will consider the US prison system, describing its aspects such as prison life, the existence and effectiveness of programs that reduce recidivism and programs aimed at reintroducing released prisoners into society. Purpose for Prisons in the US As an institution, the prison plays a critical role in the society. The US justice system bestows on prisons various roles. The first essential ro le is rehabilitation; prisons provide convicts with second chances to appreciate and learn from their misconducts and change. In essence, prisons help inmates reflect on their lives and search for ways through which they can coexist peacefully within the society. In addition, prisons offer inmates with learning environments in which they acquire new skills essential in enabling them earn decent livelihoods after their release (Armitage, 2002). Another critical role of prisons is deterrence and punishment aimed at discouraging inmates and others within the society from committing similar crimes. Forms of punishment vary contingent on the crimes committed, ranging from hard labor to the death penalty. Such punishment deters others in the society from committing crimes, thus ensuring peace and harmony within the society (Andrews & Bonta, 1994). Moreover, prisons provide justice to victims of crimes. Because law centers on justice and equity, victims of crimes receive justice through th e incarceration of those that harmed them. The incarceration of a wrongdoer provides closure to the victim of the crime. Lastly, prisons in the US protect the public from threats to security and safety as incarceration deters criminals such as serial killers and rapists from committing crimes within the society. Current conditions in US prisons The present condition of US prisons is less than ideal. Prisoners presently live in deplorable conditions characterized by extreme overcrowding. The situation in US prisons provides a viable environment for crime to thrive within prison boundaries. Perkinson (2010) poises that the California and Texas prisons, which are the biggest in the US, have, in the last thirty years, experienced an eight fold increase in the number of prisoners incarcerated. Despite the growing number of inmates, funding for prisons has barely increased, making it difficult to meet the needs of prisoners (Armitage, 2002). Inadequate funding makes it difficult for priso ns to teach prisoners effective skills to enhance their re-introduction into society. Although the US encompasses 5% of the global population, its prisons encompass 25% of the global prisoner population; this indicates the enormity of the issue. Increased congestion in US prisons is also attributable to increased levels of crime and recidivism in the US. This congestion diminishes the rehabilitative role of prisons as congestion makes it difficult

Designing women art Essay Example | Topics and Well Written Essays - 500 words

Designing women art - Essay Example The characters include Dixie Carter, Annie Pott, Jean Smatt and Starring Delta Burke. The narrative and dialog is very articulated and passes the information in very sober manner. The sole information being adopted in the move is the role of women in the church. The role that they are being given in their capacity to serve. This role according to the movie is measured against the quality they possess (Alsup & Wendy, 2008 pg.30). A good example of the role that women get in church against the quality that they possess is when one of Jean Smatt who it is said that she has a good voice that can be productive in ministering the word of God, she is relegated to only singing. One of the male chauvinist does not by the idea and says that women used to minister a long time ago but not in the modern time. The field of ministering the word is dominated by men, unlike the past. On that note, it can clearly be seen due gender profiling and overlooking the capability of women is the main cause of subordinating women in active roles (Alsup & Wendy, 2008 pg.46). Most importantly, in the movie is when female character shows their importance biblically. First, women were missionaries and they helped to many people through their mission. This show the role of women in the church has been helpful and diverse to the extent that they went the far places as the missionaries for the outreach programs of the other people in the far places to help them see the light. On note, its important to remember that in church, women right away from history to the modern time, the role of women in the growth of the church cannot be underestimated. Interestingly, in the movie another role of the movie has been well illustrated by use one Starring Delta Burke and other women in conversation with one of the men. In the conversation, from a biblical point of view, the role of women and how they need to be represented is brought out from a much

Legalism, Taoism and Confucianism Essay Example for Free

Legalism, Taoism and Confucianism Essay All three most influential philosophical schools of thought i.e. legalism, Taoism and Confucianism originate from the same tenet of peace and accord in the Chinese society in particular and in world in general. But their methodologies and philosophical routes to achieve this objective are different. Legalism suggest a strong and central political body as remedy for all the maladies of contemporary Chinese society whereas Taoism and Confucianism do not favor a strong political entity   and reinforce the ideas of individual freedom and social cohesion.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   The doctrine of legalism believes that strict laws and punitive measures are preconditions for a strong central government that can bring peace and prosperity in the society. This doctrine is based on the assumption that human nature is irredeemably malicious and is prone to produce conflicts. These conflicts harm the social cohesion and generate panic and disorder in the community. That is the reason that strong laws and punishments can make them (people) in alignment with needs of the political entity.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In total contrast to Legalism, Taoism and Confucianism are of the view that human nature is constituted of moral virtues. Taoism was directly opposed to the tenets of Legalism and believed in a close association between man and nature. They further reinforce that nature is virtuous in essence and intend at achieving greater unity and universal organization. They view man-made laws as artificial and transient that has limited life. So Taoist are against Legalism and believed that these were fabricated to serve the vested interest of the rulers and they have nothing to do with the common good of the people. This basic difference between the philosophical principles leads the Taoist to rebel against the established social patterns as they considered it a tool to perpetuate the regime of the despotic rulers.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Confucianism is considered a rationalization of these two extremes i.e. legalism and Taoism. Confucianism neither believed in the idea of harsh punishments, impersonal laws and inhuman rules toward the mass nor it gave approval to absolute individual freedom of thought and action as it would lead to utter anarchy. Confucianism adopted an equidistant approach between the two extremes and propagated a philosophy based on the beautiful combination of individual needs and social needs. Confucianism served as a balance between the extreme centralization of power and subjugation of masses as embodied in Legalism and the utter chaos created by the absolute individualistic approach of Taoism.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Legalism was an advanced political system whereas Taoism was inclined toward primitivism. Taoism reinforced the idea of a personal and individual reaction to the mundane and complex social problems. According to its basic precept of Tao (way), human nature can find its own way out of many. So it negated the formulated laws and established social patterns. Subjective judgments were made according to the needs of the occasions. Mostly these judgments were based on the ancient teachings and traditional principles with outsized personal discretion. In complete contrast to Taoism, Legalism established a complete code of laws and they (Legalists) were strictly adhered to these laws. Instead of personal discretion or subjective interpretation, judgments were made according to written laws. This characteristic of Legalism made it the most advanced philosophy of ancient China as compared with Taoism.   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In contrast to abovementioned ways, Confucianism suggested another way i.e. to get social harmony through social cohesion of individuals with the society itself. It took care of individuals’ needs as well as the socio-political needs. To Confucius, society was not a mere collection of individual but is has other internal and external dimensions. Internally, it is the substantial device that moulds our beliefs and attitudes while on the external horizon, it exerts and maintains pressures from the society to facilitate conformity to the above-mentioned collective beliefs and attitudes. Confucius perceived society as a separate and distinguished unit. It is an entity independent of individuals. This argument clearly manifests that social facts i.e. norms, values and institutions, have their independent existence and are not sustained by individual actions but individuals react to them. Confucius also suggests that individual desires are cravings are unlimited and individual hankers after more and more. This natural insatiability produces individual propensities in humans. In order to control these propensities society works as a regulative force. Frederick Cheung has comprehensively summed up the differences and similarities in the doctrines of these major philosophies of Chinese history in this way; If we compare and contrast the three schools of thoughts on individual freedom and control; we would find that Taoism was extremely free, while Legalism was extremely strict (a kind of totalitarian control) with Confucianism in the middle (the golden means or moderation).   On political theory and concepts of progress, Legalism was the most advanced and directing to the future; while Taoism was reactionary and returning to the primitive nature; with again Confucianism in the middle.   Indeed, moderation and balance were perhaps the major reasons for the eventual triumph of Confucianism in traditional Chinese history.   (p.3) References Cheung, Frederick. (2006). The Legacy of Ancient China: The Intellectual Foundations Legalism, Taoism, and Confucianism. The Chinese University of Hong Kong. Website: http. ihome.cuhk.edu.hk/~s050326/legalismtaoismconf.doc

Electric Filed Strength And Electric Flux Density

Electric Filed Strength And Electric Flux Density All bodies are made up of atoms, which consist of a nucleus containing protons (+ve) and neutrons (neutral) and surrounding the nucleus are orbiting electrons (-ve). When a body is uncharged it is electrically neutral, it has the same negative charge as positive charge. If a conductor had a deficit of electrons it would exhibit a net positive charge and if it was to have a surplus of electrons it would exhibit a net negative charge (remember the previous study of the atom reference +ve/-ve ions). An imbalance in charge can be produced by friction (removing or depositing electrons using materials such as silk and fur, respectively) or induction (by attracting or repelling electrons using a second body which is, respectively, positively or negatively charged). Coulombs Law states that if charged bodies exist at two points, the force of attraction (if the charges are of opposite polarity) or repulsion (if the charges have the same polarity) will be proportional to the product of the magnitude of the charges divided by the square of their distance apart. Thus: + + + Direct Inverse Proportionality Maths Q1 and Q2 are the charges present at the two points (in Coulombs), d is the distance separating the two points (in metres), F is the force (in Newtons), and k is a mathematical constant depending upon the medium in which the charges exist. In a vacuum or free space, ÃŽÂ µ0 is the permittivity of free space (8.854 x 10-12 F/m Farad per meter). The force exerted on a charged particle is a manifestation of the existence of an electric field. The electric field defines the direction and magnitude of a force on a charged object. The field itself is invisible to the human eye but can be drawn by constructing lines which indicate the motion of a free positive charge within the field; the number of field lines in a particular region being used to indicate the relative strength of the field at the point in question. The figure above shows the electric fields between charges of the same and opposite polarity. The figure below shows the field which exists between two charged parallel plates. B A As illustrated above, plates A and B are doped and charged to different potentials. If an electron that has a negative charge is placed between the plates, a force will act on the electron tending to push it away from the negative plate B and towards the positive plate A. Similarly, a positive charge would be acted on by a force tending to move it toward the negative plate. The region between the plates in which an electric charge experiences a force, is called an electrostatic field. The direction of the field is defined by the force acting on a positive charge placed in the field, i.e. the direction of the force is from the positive plate to the negative plate. Such a field may be represented in magnitude and direction by lines of electric force drawn between the charged surfaces. The closeness of the lines is an indication of the field strength. Whenever a p.d. is established between two points, an electric field will always exist. The figure above shows two parallel conducting plates separated from each other by air, and are connected to opposite terminals of a battery of voltage V volts. There is therefore an electric field in the space between the plates. If the plates are close together, the electric lines of force will be straight and parallel and equally spaced, except near the edge where fringing will occur (see previous figure). Over the area in which there is negligible fringing, E is the electric field strength (V/m), V is the applied potential difference across the parallel plates (V) and d is the distance (m). **Note: Electric Field Strength is also called Potential/Voltage Gradient. A unit electric flux is defined as emanating from a positive charge of 1 coulomb. Thus electric flux à Ã‹â€  is measured in coulombs, and for a charge of Q coulombs, the electric flux à Ã‹â€  is equal to Q coulombs. Electric flux density D is the amount of flux passing through a defined area A that is perpendicular to the direction of the flux: à Ã‹â€  is the electric flux measured in coulombs, Q is the electric charge also measured in coulombs, and A is the area in m2 over which the flux is distributed. Problem 1: Two parallel rectangular plates measuring 20cm by 40cm carry an electric charge of 0.2  µC. (a) Calculate the electric  ¬Ã¢â‚¬Å¡ux density. (b) If the plates are spaced 5mm apart and the voltage between them is 0.25 kV determine the electric field strength. Solution 1: PERMITTIVITY At any point in an electric field, the electric field strength E maintains the electric flux and produces a particular value of electric flux density D at that point. For a field established in vacuum (or for practical purposes in air), the ratio D/E is a constant ÃŽÂ µ0, i.e. ÃŽÂ µ0 is called the permittivity of free space or the free space constant. The value of ÃŽÂ µ0 is 8.854 x 10-12 F/m Farad per meter. When a dielectric (i.e. insulating medium separating charged surfaces), such as mica, paper, plastic or ceramic is introduced into the region of an electric field, the ratio of D/E is modified. ÃŽÂ µr is called the relative permittivity of the insulating material and indicates its insulating power compared with that of vacuum. ÃŽÂ µr has no units and typical properties of some common insulating dielectric materials are shown below. The product of ÃŽÂ µ0 ÃŽÂ µr is called the absolute permittivity, ÃŽÂ µ, i.e. As discussed earlier, the dielectric is an insulating medium separating charged surfaces and has the property of very high resistivity. They are therefore used to separate conductors at different potentials, such as capacitor plates or electric power lines. The dielectric strength of an insulating dielectric is the maximum electric field strength that can safely be applied to it before breakdown (conduction) occurs. The amount of charge produced for a given applied voltage on the two parallel plates shown earlier will depend not only on the physical dimensions but also on the insulating dielectric material that appears between the plates. Such materials need to have a very high value of resistivity (i.e. they must not conduct charge) coupled with an ability to withstand high voltages without breaking down. A more practical arrangement of parallel plates with an insulating dielectric material is shown. In this arrangement the ratio of charge, Q, to the potential difference, V, is given by the following relationship. A = area of one on the plates, in m2 D = thickness of the dielectric in m ÃŽÂ µ = absolute permittivity of the dielectric material *Later learning, i.e. the parallel plate capacitor/capacitance and physical dimensions. à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦ single pair of plates à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦ arrangement of n plates Problem 1: The  ¬Ã¢â‚¬Å¡ux density between two plates separated by mica of relative permittivity 5 is 2 µC/m2. Find the voltage gradient between the plates. Solution 1: Problem 2: Two parallel plates having a p.d. of 200V between them are spaced 0.8mm apart. What is the electric  ¬Ã‚ eld strength? Find also the electric  ¬Ã¢â‚¬Å¡ux density when the dielectric between the plates is (a) air, and (b) polythene of relative permittivity 2.3 Solution 2: SELF ASSESSMENT (1-2) NOTE: Where appropriate take ÃŽÂ µ0 as 8.85 x 10-12 F/m A capacitor uses a dielectric 0.04mm thick and operates at 30V. What is the electric field strength across the dielectric at this voltage? [Answer: 750kV/m] A two-plate capacitor has a charge of 25C. If the effective area of each plate is 5cm2 determine the electric  ¬Ã¢â‚¬Å¡ux density of the electric field. [Answer: 50 kC/m2] A charge of 1.5 µC is carried on two parallel rectangular plates each measuring 60mm by 80mm. (a) Calculate the electric  ¬Ã¢â‚¬Å¡ux density. (b) If the plates are spaced 10mm apart and the voltage between them is 0.5kV determine the electric  ¬Ã‚ eld strength. [Answer: (a) 312.5 µC/m2, (b) 50kV/m] Two parallel plates are separated by a dielectric and charged with 10 µC. Given that the area of each plate is 50cm2, calculate the electric  ¬Ã¢â‚¬Å¡ux density in the dielectric separating the plates. [Answer: 2mC/m2] The electric  ¬Ã¢â‚¬Å¡ux density between two plates separated by polystyrene of relative permittivity 2.5 is 5 µC/m2. Find the voltage gradient between the plates. [Answer: 226kV/m] Two parallel plates having a p.d. of 250V between them are spaced 1mm apart. (a) Determine the electric  ¬Ã‚ eld strength. (b) Find also the electric  ¬Ã¢â‚¬Å¡ux density when the dielectric between the plates is (i) air and (ii) mica of relative permittivity 5. [Answer: (a) 250kV/m (bi) 2.213 µC/m2 (bii) 11.063 µC/m2] CAPACITORS CAPACITANCE A capacitor is a device for storing electric charge. In effect, it is a reservoir into which charge can be deposited and then later extracted. In its simplest form a capacitor consists of two parallel metal plates which are separated by an insulating material known as a dielectric. C:Documents and SettingsHarveyMy DocumentsMy PicturesPicturePicture 028.jpg Because of the dielectric, current cannot flow from one plate to the other. When the capacitor is connected to a dc source, electrons accumulate on the plate connected to the negative supply terminal. The negative charge repels electrons from the atoms of the other plate. These electrons flow away to the positive terminal of the dc source; this leaves the plate positively charged. C:Documents and SettingsHarveyMy DocumentsMy PicturesPicturePicture 032.jpg If the capacitor is disconnected from the supply, the charges remain. The capacitor stores the electric charge indefinitely. The symbols for a fixed capacitor and a variable capacitor used in electrical circuit diagrams are shown below. Typical applications include reservoir and smoothing capacitors for use in power supplies, coupling a.c. signals between the stages of amplifiers, and decoupling supply rails (i.e. effectively grounding the supply rails as far as a.c. signals are concerned). The following figures illustrate what happens to a capacitor when it is charging and discharging. If the switch is left open (position A), no charge will appear on the plates and in this condition there will be no electric field in the space between the plates nor will there be any charge stored in the capacitor. When the switch is moved to position B, electrons will be attracted from the positive plate to the positive terminal of the battery. At the same time, a similar number of electrons will move from the negative terminal of the battery to the negative plate. This sudden movement of electrons will manifest itself in a momentary surge of current (conventional current will flow from the positive terminal of the battery towards the positive terminal of the capacitor). Eventually, enough electrons will have moved to make the e.m.f. between the plates the same as that of the battery. In this state, the capacitor is said to be fully charged and an electric field will be present in the space between the two plates. If, at some later time the switch is moved back to position A, the positive plate will be left with a deficiency of electrons whilst the negative plate will be left with a surplus of electrons. Furthermore, since there is no path for current to flow between the two plates the capacitor will remain charged and a potential difference will be maintained between the plates. Now assume that the switch is moved to position C. The excess electrons on the negative plate will flow through the resistor to the positive plate until a neutral state once again exists (i.e. until there is no excess charge on either plate). In this state the capacitor is said to be fully discharged and the electric field between the plates will rapidly collapse. The movement of electrons during the discharging of the capacitor will again result in a momentary surge of current (current will flow from the positive terminal of the capacitor and into the resistor). The figure below shows the direction of current flow during charging (i.e. the switch in position B) and discharging (i.e. the switch in position C). It should be noted that current flows momentarily in both circuits even though you may think that the circuit is broken by the gap between the capacitor plates! The charge Q (in coulombs) stored in a capacitor is given by: I is the current in amperes and t is the time in seconds. Charge Q on a capacitor is proportional to the applied voltage V, i.e. Q V. Direct Inverse Proportionality Maths Q = CV The constant of proportionality C is the capacitance. The unit of capacitance C is the farad F (or more usually  µF =10-6F or pF =10-12F), and is defined as the capacitance when a p.d. of one volt appears across the plates when charged with one coulomb. Capacitance is the ability of a circuit or object (i.e. in this case a capacitor) to store electric charge. Problem 1: (a) Determine the p.d. across a 4  µF capacitor when charged with 5 mC (b) Find the charge on a 50 pF capacitor when the voltage applied to it is 2 kV. Solution 1: Problem 2: A direct current of 4A flows into a previously uncharged 20  µF capacitor for 3 ms. Determine the p.d. between the plates. Solution 2: Problem 3: A 5 µF capacitor is charged so that the p.d. between its plates is 800V. Calculate how long the capacitor can provide an average discharge current of 2 mA. Solution 3: SELF ASSESSMENT (3) Find the charge on a 10  µF capacitor when the applied voltage is 250 V. (Answer: 2.5 mC) Determine the voltage across a 1000à Ã‚ F capacitor to charge it with 2  µC. (Answer: 2 kV) The charge on the plates of a capacitor is 6 mC when the potential between them is 2.4 kV. Determine the capacitance of the capacitor. (Answer: 2.5  µF) For how long must a charging current of 2 A be fed to a 5  µF capacitor to raise the p.d. between its plates by 500V. (Answer: 1.25 ms) A direct current of 10 A flows into a previously uncharged 5  µF capacitor for 1 ms. Determine the p.d. between the plates. (Answer: 2 kV) A 16  µF capacitor is charged at a constant current of 4  µA for 2 minutes. Determine the final p.d. across the capacitor and the corresponding charge in coulombs. (Answer: 30V, 480  µC) A steady current of 10 A flows into a previously uncharged capacitor for 1.5 ms when the p.d. between the plates is 2 kV. Find the capacitance of the capacitor. (Answer: 7.5 µF) CAPACITANCE AND PHYSICAL DIMENSIONS (Conventional Parallel Plate Capacitor) The capacitance of a capacitor depends upon the physical dimensions of the capacitor (i.e. the size of the plates and the separation between them) and the dielectric material between the plates. The capacitance of a conventional parallel plate capacitor is given by: Where, C = Capacitance, unit of measure farads (F) ÃŽÂ µ0 = Permittivity of free space or the free space constant (8.85 x 10-12 F/m) ÃŽÂ µr = Relative permittivity of the dielectric medium between the plates (ÃŽÂ µr has no units as it is a ratio of density material/vacuum) A = Area of one of the plates (m2) d = Thickness of the dielectric or separation between the plates (m) In order to increase the capacitance of a capacitor, many practical components employ multiple plates as shown. Ten plates are shown, forming nine capacitors with a capacitance nine times that of one pair of plates. Such an arrangement has n plates then capacitance C à ¢Ã‹â€ Ã‚  (n -1). Thus capacitance is then given by: Problem 1: A ceramic capacitor has an effective plate area of 4cm2 and separated by 0.1 mm of ceramic of relative permittivity 100. Calculate the capacitance of the capacitor in picofarads (à Ã‚ F). If the capacitor in part (a) is given a charge of 1.2 µC what will be the p.d. between the plates? Solution 1: Problem 2: A waxed paper capacitor has two parallel plates, each of effective area 800 cm2. If the capacitance of the capacitor is 4425 pF determine the effective thickness of the paper if its relative permittivity is 2.5. Solution 2: Problem 3: A parallel plate capacitor has nineteen interleaved plates each 75 mm by 75 mm and separated by mica sheets 0.2 mm thick. Assuming that the relative permittivity of the mica is 5, calculate the capacitance of the capacitor. Solution 3: n = 19, thus (n 1) = 18 A = 75 x 75 = 5625mm2 ÃŽÂ µr = 5, ÃŽÂ µ0 = 8.85 x 10-12 F/m d = 0.2mm = 0.2 x 10-3m SELF ASSESSMENT (4) ** Where appropriate take ÃŽÂ µ0 as 8.85 x 10-12 F/m. A capacitor consists of two parallel plates each of area 0.01 m2, spaced 0.1 mm in air. Calculate the capacitance in picofarads (pF). [Answer: 885 pF] A waxed paper capacitor has two parallel plates, each of effective area 0.2m2. If the capacitance is 4000 pF determine the effective thickness of the paper if its relative permittivity is 2. [Answer: 0.885 mm] Calculate the capacitance of a parallel plate capacitor having 5 plates, each 30 mm by 20 mm and separated by a dielectric 0.75 mm thick having a relative permittivity of 2.3. [Answer: 65.14 pF] How many plates does a parallel plate capacitor have if its capacitance is 5nF, each plate is 40mm by 40mm and each dielectric is 0.102mm thick with a relative permittivity of 6? [Answer: 7] A parallel plate capacitor is made from 25 plates, each 70mm by 120mm interleaved with mica of relative permittivity 5. If the capacitance of the capacitor is 3000pF determine the thickness of the mica sheet. [Answer: 2.97mm] The capacitance of a parallel plate capacitor is 1000pF. It has 19 plates, each 50mm by 30mm separated by a dielectric of thickness 0.40mm. Determine the relative permittivity of the dielectric. [Answer: 1.67] CAPACITORS CONNECTED IN PARALLEL AND SERIES CAPACITORS CONNECTED IN PARALLEL The figure above shows three capacitors, C1, C2 and C3 connected in parallel with a supply voltage V applied across the arrangement. (Note: just like resistors in parallel, the supply voltage V is the same across each parallel capacitor) V = V1 = V2 = V3 When the charging current I reaches point A it divides, some flowing into C1, some flowing into C2 and some into C3. Hence the total charge QT (i.e. QT= I x t) is divided between the three capacitors. The capacitors each store a charge and these are shown as Q1, Q2 and Q3 respectively. Hence, But, QT=CV (where C is the total equivalent circuit capacitance) And, Q1=C1V Q2=C2V Q3=C3V Therefore, CV = C1V + C2V + C3V (where C is the total equivalent circuit capacitance) Dividing throughout by the common V giving, C = C1 + C2 + C3 à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦. + Cn The equivalent capacitance of a group of parallel connected capacitors is the sum of the capacitances of the individual capacitors. CAPACITORS CONNECTED IN SERIES The figure above shows three capacitors, C1, C2 and C3 connected in series across a supply voltage V. Let the p.d. across the individual capacitors be V1, V2 and V3 respectively as shown. Let the charge on the plate a of the capacitor C1 be +Q coulombs. This induces and equal but opposite charge of -Q coulombs on plate b. The conductor between plates b and c is electrically isolated from the rest of the circuit so that an equal but opposite charge of +Q coulombs must appear on plate c, which, in turn, induces an equal and opposite charge of -Q coulombs on plate d, and so on. Hence when capacitors are connected in series the charge on each is the same. QT = Q1 = Q2 = Q3 In a series circuit: V = V1 + V2 + V3 (Similar to resistors in series) Since, then (where C is the total equivalent circuit capacitance) Dividing throughout by the common Q giving, (Where C is the total equivalent circuit capacitance) For series connected capacitors, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitance. For special case of two capacitors in series, Hence, i.e. Problem 1: Calculate the equivalent capacitance of two capacitors of 6ÃŽÂ ¼F and 4ÃŽÂ ¼F connected in (a) Parallel (b) Series. Solution 1: Problem 2: What capacitance must be connected in series with a 30ÃŽÂ ¼F capacitor for the equivalent capacitance to be 12ÃŽÂ ¼F? Solution 2: Problem 3: Capacitances of 1ÃŽÂ ¼F, 3ÃŽÂ ¼F, 5ÃŽÂ ¼F and 6ÃŽÂ ¼F are connected in parallel to a direct voltage supply of 100V. Determine (a) the equivalent circuit capacitance, (b) the total charge and (c) the charge on each capacitor. Solution 3: Problem 4: Capacitances of 3ÃŽÂ ¼F, 6ÃŽÂ ¼F and 12ÃŽÂ ¼F are connected in series across a 350V supply. Calculate (a) the equivalent circuit capacitance, (b) the charge on each capacitor, and (c) the p.d. across each capacitor. Solution 4: Problem 5: For the arrangement shown, find (a) the equivalent capacitance of the circuit, (b) the voltage across QR and (c) The charge on each capacitor. Solution 5: SELF ASSESSMENT (5) Capacitors of 2 µF and 6 µF are connected (a) in parallel and (b) in series. Determine the equivalent capacitance in each case. [Answers: (a) 8ÃŽÂ ¼F (b) 1.5ÃŽÂ ¼F] Find the capacitance to be connected in series with a 10 µF capacitor for the equivalent capacitance to be 6 µF. [Answer: 15ÃŽÂ ¼F] What value of capacitance would be obtained if capacitors of 0.15 µF and 0.10 µF are connected in (a) series and (b) parallel? [Answers: (a) 0.06ÃŽÂ ¼F (b) 0.25ÃŽÂ ¼F] Two 6 µF capacitors are connected in series with one having a capacitance of 12 µF. Find the total equivalent circuit capacitance. What capacitance must be added in series to obtain a capacitance of 1.2 µF? [Answers: (a) 2.4ÃŽÂ ¼F (b) 2.4ÃŽÂ ¼F] For the arrangement shown below, find (a) the equivalent circuit capacitance and (b) the voltage across a 4.5ÃŽÂ ¼F capacitor. [Answers: (a) 1.2ÃŽÂ ¼F (b) 100V] Three 12 µF capacitors are connected in series across a 750V supply. Calculate (a) the equivalent capacitance, (b) the charge on each capacitor and (c) the p.d. across each capacitor. [Answers: (a) 4 µF (b) 3mC (c) 250V] If two capacitors having capacitances of 3 µF and 5 µF respectively are connected in series across a 240V supply, determine (a) the p.d. across each capacitor and (b) the charge on each capacitor. [Answers: (a) 150V, 90V (b) 0.45 mC on each] Capacitances of 4 µF, 8 µF and 16 µF are connected in parallel across a 200V supply. Determine (a) the equivalent capacitance, (b) the total charge and (c) the charge on each capacitor. [Answers: (a) 28  µF (b) 5.6mC (c) 0.8mC, 1.6mC, 3.2mC] DIELECTRIC STRENGTH The maximum safe working voltage is the maximum voltage that can be applied to the terminals of a capacitor without causing damage to the capacitor. The manufacturer specifies this voltage. The limit is necessary so that the field strength in the dielectric does not exceed a value that would cause the dielectric to breakdown and loose its insulating properties. The figure quoted by the manufacturer for a capacitor is also known as the dielectric strength and will be in volts per metre. E is the dielectric strength (V/m), V is the applied potential difference across the parallel plates (V) and d is the distance (m). **Note: Equation identical to Electric Field Strength (Potential/Voltage Gradient). Problem1: A capacitor is to be constructed so that its capacitance is 0.2 µF and to take a p.d. of 1.25kV across its terminals. The dielectric is to be mica and has a dielectric strength of 50MV/m. Find (a) the thickness of the mica needed, and (b) the area of a plate assuming a two-plate construction. (Assume ÃŽÂ µr for mica to be 6). Solution 1: ENERGY STORED IN CAPACITORS The energy, W, stored by a capacitor is given by, Where, W is the energy (in Joules), C is the capacitance (in Farads), and V is the potential difference (in Volts). Problem 1: (a) Determine the energy stored in a 3 µF capacitor when charged to 400V. (b) Find also the average power developed if this energy is dissipated in a time of 10 µs. Solution 1: Problem 2: A 12 µF capacitor is required to store 4J of energy. Find the p.d. to which the capacitor must be charged. Solution 2: Problem 3: A capacitor is charged with 10mC. If the energy stored is 1.2J, determine (a) the voltage and (b) the capacitance. Solution 3: SELF ASSESSMENT (6) ** Where appropriate take ÃŽÂ µ0 as 8.85 x 10-12 F/m. When a capacitor is connected across a 200V supply the charge is 4 µC. Find (a) the capacitance and (b) the energy stored. [Answer: (a) 0.02 µF (b) 0.4mJ] Find the energy stored in a 10 µF capacitor when charged to 2kV. [Answer: 20 J] A 3300pF capacitor is required to store 0.5mJ of energy. Find the p.d. to which the capacitor must be charged. [Answer: 550 V] A capacitor is charged with 8mC. If the energy stored is 0.4J, determine (a) the voltage and (b) the capacitance. [Answer: (a) 100V (b) 80  µF] A capacitor, consisting of two metal plates each of area 50 cm2 and spaced 0.2mm apart in air, is connected across a 120V supply. Calculate (a) the energy stored (b) the electric  ¬Ã¢â‚¬Å¡ux density and (c) the potential gradient (i.e. electric field strength). [Answer: (a) 1.593 µJ (b) 5.31 µC/m2 (c) 600kV/m] D.C TRANSIENTS Networks of capacitors and resistors (known as C-R circuits) form the basis of many timing and pulse shaping circuits and are thus often found in practical electronic circuits. When a d.c. voltage is applied to a capacitor C and resistor R connected in series, there is a short period of time immediately after when the voltage is connected that the current flowing in the circuit and voltages across C and R are changing. These changing values are called transients. CHARGING A CAPACITOR The figure above shows a series connected C-R circuit. When the switch S is closed, then by Kirchhoffs valotage law: V = Vc + VR The battery voltage V is constant. The capacitor voltage Vc is given by, The voltage drop across R (i.e. VR) is given by, Hence at all times: At the instant of closing S (i.e. initial circuit condition), assuming there is no initial charge on the capacitor, Q is zero (i.e. Q0), hence Vc is zero (i.e. VC0). (Note: From equation Vc = Q / C). Thus from equation V = Vc + VR, V = 0 + VR (i.e. V = VR = IR) A short time later at time T1 seconds after closing S, the capacitor is partly charged to, say, Q1 coulombs because current has been flowing. The voltage VC1 is now, If the current flowing is I1 amperes, then the voltage drop across R has fallen to VR1 = I1R volts. Thus from equation V = Vc + VR A short time later still, say at time T2 seconds after closing S, the charge has increased to Q2 coulombs and VC has increased to, Since V = VC + VR and V is a constant, then VR decreases to I2R. Thus VC is increasing and I and VR are decreasing as time increases. Ultimately, a few seconds after closing S (i.e. at the final or steady state condition), the capacitor is fully charged to, say Q coulombs, current no longer flows, i.e. I = 0, and hence VR = IR = 0. It follows from equation V = Vc + VR that V = VC. Curves showing the changes in VC, VR and I with time are shown below. The curve showing the variation of VC with time is called an exponential growth curve and the graph is called the capacitor voltage / time characteristic. The curves showing variations of VR and I with time are called exponential decay curves, and the graphs are called resistor voltage / time and current / time characteristics respectively. The name exponential shows that the shape can be expressed mathematically by an exponential mathematical equation, as shown below. Growth of capacitor voltage, Decay of resistor voltage, Decay of resistor current, TIME CONSTANT (à Ã¢â‚¬Å¾ TAU) FOR A C-R CIRCUIT As shown earlier, if a constant d.c. voltage is applied to a series connected C-R circuit, a exponential transient growth curve of capacitor voltage VC results as shown below. With reference to the figure below, the constant voltage supply is replaced by a variable voltage supply at time t1 seconds. The voltage is varied so that the current flowing in the circuit is constant. Since the current flowing is a constant, the curve will follow a tangent, AB, drawn to the curve at point A. Let the capacitor voltage VC reach its final value of V at time t2 seconds. The time corresponding to (t2-t1) seconds is called the time constant of the circuit, denoted by the Greek letter tau, à Ã¢â‚¬Å¾. The value of the time constant is CR seconds, i.e. for a series connected C-R circuit, (seconds) Where C is capacitance (F), R is the resistance (à ¢Ã¢â‚¬Å¾Ã‚ ¦) and à Ã¢â‚¬Å¾ is the time constant (s) DISCHARGING A CAPACITOR When a capacitor is charged (i.e. with the switch in position A), and the switch is then moved to position B, the electrons stored in the capacitor keep the current flowing for a short time. Initially, at the instant of moving from A to B, the current flow is such that the capacitor voltage VC is balanced by equal and opposite voltage (Kirchhoffs 2nd law), i.e. VC = VR = IR. Finally the transients decay exponentially as current is reduced to zero, i.e. VC = VR = 0. The transient curve representing the voltages and current are shown below. The equations representing the transient curves during discharge period of a series connected C-R circuit are: Decay of voltage, Decay of current, When a capacitor has been disconnected from the supply it may still be charged and it may retain this charge for some considerable time. Thus precautions must be taken to ensure that the capacitor is automatically discharged after the supply is switched off. This is done by connecting a high value resistor across the capacitor terminals. Problem 1: A capacitor is charg