1 problem 216 10 2 14 4 req 5 8 figure 21 carefully

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Unformatted text preview: terminals. PRESENT everything you know about the problem. To find equivalent resistance, the resistor network must be reduced using series combinations, parallel combinations, and conversions between wye and delta connected resistors. We know that series resistances are added to obtain the equivalent resistance and the inverse of parallel resistances are added to obtain the inverse of the equivalent resistance; i.e. R eq = R 1 + R 2 1 R eq = 1 R 1 + 1 R 2 and We also know how to convert between wye and delta connected loads, as seen previously in this section. Establish a set of ALTERNATIVE solutions and determine the one that promises the greatest likelihood of success. The set of alternatives to reducing resistor networks involves the various ways that resistors can be combined. In this case, we will convert the lower ∆ connection to a Y connection. Then, we will combine parallel resistors (two series resistors are in parallel with two series resistors) to get a series combination. This will produce the equivalent resistance of the resistor network. ATTEMPT a problem solution. 10 Ω 2Ω 4Ω Req v v 5Ω | | 14 Ω e-Text Main Menu 8Ω | Textbook Table of Contents | R a + R b + R c = 8 + 5 + 4 = 17 (4)(5) R1 = = 1.1765 17 (4)(8) R2 = = 1.8824 17 (5)(8) R3 = = 2.353 17 Problem Solving Workbook Contents 10 Ω 2Ω 14 Ω 2 + 1.1765 = 3.177 14 + 1.8824 = 15.882 Req 3.177 15.882 1.1765 Ω 1.8824 Ω (3.177)(15.882) 3.177 + 15.882 50.46 = = 2.647 19.059 = 2.353 Ω 10 Ω 2.647 Ω Req 10 + 2.647 + 2.353 = 15 2.353 Ω Req Therefore, R eq = 15 ohms. 15 Ω EVALUATE the solution and check for accuracy. To check for accuracy, reduce the resistor network by converting the upper ∆ connection to a Y connection. Then, combine parallel resistors (two series resistors are in parallel with two series resistors) to get a series combination. This will produce the equivalent resistance of the resistor network. It can be shown that 10 Ω 2Ω 4Ω Req v v 5Ω | | e-Text Main Menu 14 Ω 8Ω | Textbook Table of...
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