To determine Find the value of current and power supplied by the 40 V source in the given circuit. Explanation Given data: Replace the lower Δ ( 25 Ω , 37.5 Ω , 40 Ω ) to its Υ equivalent in the figure given in the question. Formula used: Write a general expression to transform the three Δ connected resistors into an equivalent Y connection. R 1 = R b R c R a + R b + R c (1) R 2 = R c R a R a + R b + R c (2) R 3 = R a R b R a + R b + R c (3) Calculation: The given circuit is redrawn as shown in Figure 1. Transform the lower Δ ( 25 Ω , 37.5 Ω , 40 Ω ) to its Υ equivalent. Substitute 37.5 Ω for R a , 40 Ω for R b and 25 Ω for R c in equation (1) to find R 1 . R 1 = ( 40 Ω ) ( 25 Ω ) 37.5 Ω + 40 Ω + 25 Ω = 1000 Ω 2 102.5 Ω = 9.756 Ω Substitute 37.5 Ω for R a , 40 Ω for R b and 25 Ω for R c in equation (2) to find R 2 . R 2 = ( 25 Ω ) ( 37.5 Ω ) 37.5 Ω + 40 Ω + 25 Ω = 937.5 Ω 2 102.5 Ω = 9.1463 Ω Substitute 37.5 Ω for R a , 40 Ω for R b and 25 Ω for R c in equation (3) to find R 3 . R 3 = ( 37.5 Ω ) ( 40 Ω ) 37.5 Ω + 40 Ω + 25 Ω = 1500 Ω 2 102.5 Ω = 14.634 Ω The transformation of Δ − Y is shown in Figure 2. Now, the Figure 1 is reduced as shown in Figure 3. Refer to Figure 3, the resistors R 1 and R e are connected in series and the resistors R 2 and R d are connected in series. Write a general expression to calculate the equivalent resistance of series connected resistors R 1 and R e . R eq1 = R 1 + R e (4) Substitute 9.756 Ω for R 1 and 100 Ω for R e in equation (4) to find R eq1 . R eq1 = 9.756 Ω + 100 Ω = 109.756 Ω Write a general expression to calculate the equivalent resistance of series connected resistors R 2 and R d . R eq2 = R 2 + R d (5) Substitute 9.1463 Ω for R 1 and 125 Ω for R e in equation (5) to find R eq2 . R eq2 = 9.1463 Ω + 125 Ω = 134.1463 Ω Now, the Figure 3 is reduced as shown in Figure 4

10th Edition

ISBN: 9781292060545

Author: James W. Nilsson, Susan Riedel

Publisher: Pearson Education Limited

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Chapter 3, Problem 55P

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