To determine Find the value of current and power supplied by the 40 V source in the given circuit. Explanation Given data: Replace the right side Y ( 25 Ω , 37.5 Ω , 125 Ω ) to its Δ equivalent. Formula used: Write a general expression to transform the three Y connected resistors into an equivalent Δ connection. R a = R 1 R 2 + R 2 R 3 + R 3 R 1 R 1 (1) R b = R 1 R 2 + R 2 R 3 + R 3 R 1 R 2 (2) R c = R 1 R 2 + R 2 R 3 + R 3 R 1 R 3 (3) Calculation: The given circuit is redrawn as shown in Figure 1. Transform the left side Y ( 25 Ω , 37.5 Ω , 125 Ω ) to its Δ equivalent. Substitute 25 Ω for R 1 , 37.5 Ω for R 2 and 125 Ω for R 3 in equation (1) to find R a . R a = ( 25 Ω ) ( 37.5 Ω ) + ( 37.5 Ω ) ( 125 Ω ) + ( 125 Ω ) ( 25 Ω ) 25 Ω = 937.5 Ω 2 + 4687.5 Ω 2 + 3125 Ω 2 25 Ω = 8750 Ω 2 25 Ω = 350 Ω Substitute 25 Ω for R 1 , 37.5 Ω for R 2 and 125 Ω for R 3 in equation (2) to find R b . R b = ( 25 Ω ) ( 37.5 Ω ) + ( 37.5 Ω ) ( 125 Ω ) + ( 125 Ω ) ( 25 Ω ) 37.5 Ω = 937.5 Ω 2 + 4687.5 Ω 2 + 3125 Ω 2 37.5 Ω = 8750 Ω 2 37.5 Ω = 233.33 Ω Substitute 25 Ω for R 1 , 37.5 Ω for R 2 and 125 Ω for R 3 in equation (3) to find R c . R c = ( 25 Ω ) ( 37.5 Ω ) + ( 37.5 Ω ) ( 125 Ω ) + ( 125 Ω ) ( 25 Ω ) 125 Ω = 937.5 Ω 2 + 4687.5 Ω 2 + 3125 Ω 2 125 Ω = 8750 Ω 2 125 Ω = 70 Ω The transformation of Y − Δ is shown in Figure 2. Now, the Figure 1 is reduced as shown in Figure 3. Refer to Figure 3, the resistors R b and R 4 are connected in parallel and the resistors R a and R 5 are connected in parallel. Write a general expression to calculate the equivalent resistance of parallel connected resistors R b and R 4 . R eq1 = ( R b ) ( R 4 ) R b + R 4 (4) Substitute 233.33 Ω for R b and 100 Ω for R 4 in equation (4) to find R eq1 . R eq1 = ( 233.33 Ω ) ( 100 Ω ) 233.33 Ω + 100 Ω = 23333 Ω 2 333.33 Ω = 70 Ω Write a general expression to calculate the equivalent resistance of parallel connected resistors R c and R 5 . R eq2 = ( R c ) ( R 5 ) R c + R 5 (5) Substitute 70 Ω for R c and 40 Ω for R 5 in equation (5) to find R eq2

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Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 3, Problem 57P

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Electric Circuits (10th Edition)

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