This will produce the equivalent resistance of the

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Unformatted text preview: Contents | Problem Solving Workbook Contents 10 Ω 10 Ω 1.4 Ω Req 0.4 Ω 2.8 Ω 1.4 Ω Req 3.6 Ω 8Ω 5.4 Ω Req Therefore, R eq = 15 ohms. 15 Ω This is the same answer as that obtained above. Our check for accuracy was successful. Has the problem been solved SATISFACTORILY? If so, present the solution; if not, then return to “ALTERNATIVE solutions” and continue through the process again. This problem has been solved satisfactorily. R eq = 15 ohms [2.47] Problem 2.17 Find the equivalent resistance R eq in each of the following circuits where each resistor has a value of 100 Ω. a a Req Req b b | v v (a) | e-Text Main Menu (b) | Textbook Table of Contents | Problem Solving Workbook Contents (a) Begin by combining the series resistors on the rightmost corners of the network. a 200 Ω 100 Ω Req 200 Ω b Now, convert the T (or Y) connection to a ∆ connection. a 100 Ω Rb Req Rc 100 Ω Ra b (200)(200) + (200)(100) + (100)(200) 80000 = = 400 ohms 200 200 80000 Rb = = 400 ohms 200 80000 Rc = = 800 ohms 100 Ra = Notice that R a 100 and R b 100 where 400 || 100 = (400)(100) 40000 = = 80 ohms. 400 + 100 500 100 Ω a Req 100 Ω 100 Ω 80 Ω 800 Ω 80 Ω | v v b | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents Now, convert ∆ connection to a Y connection. 100 Ω R1 100 Ω R3 100 Ω R2 a Req b (80)(800) 64000 200 ohms = = 80 + 80 + 800 960 3 (80)(800) 64000 200 R2 = ohms = = 80 + 80 + 800 960 3 (80)(80) 6400 20 R3 = ohms = = 80 + 80 + 800 960 3 R1 = Now, combine the series resistors. Then, convert the T (or Y) connection to a ∆ connection. 500/3 Ω 500/3 Ω a a 100 Ω Req 100 Ω Ra′ 320/3 Ω Req Rc′ Rb′ 500/3 Ω b 500/3 Ω b (100)(100) + (100)(320 3) + (320 3)(100) = 94000 3 94000 3 940 Ra′ = = = 313.3 ohms 100 3 94000 3 940 Rb′ = = = 313.3 ohms 100 3 94000 3 94000 Rc′ = = = 293.8 ohms 320 3 320 | v v Note that Ra′||500/3 and Rb′||500/3 where | e-Text Main Menu (940 3)(500 3) (940)(500) = = 1...
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This note was uploaded on 07/16/2012 for the course KA KA 2000 taught by Professor Bkav during the Spring '12 term at Cambridge.

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