To determine Calculate the total power developed in the circuit. Explanation The given circuit is redrawn as shown in Figure 1. Apply Kirchhoff’s Voltage law for loop current i 1 in Figure 1. 0 = 4 ( i 1 − i Δ ) + 6.5 i Δ + 20 ( i 1 − 20 ) 0 = 4 i 1 − 4 i Δ + 6.5 i Δ + 20 i 1 − 400 400 = 24 i 1 + 2.5 i Δ (1) Apply Kirchhoff’s voltage law for Loop current i Δ in Figure 1. 0 = 4 ( i Δ − i 1 ) + 1 i Δ + 5 ( i Δ − 20 ) 0 = 4 i Δ − 4 i 1 + 1 i Δ + 5 i Δ − 100 100 = − 4 i 1 + 10 i Δ (2) Rearrange the equation (2) as follows, 4 i 1 = 10 i Δ − 100 i 1 = 10 i Δ − 100 4 i 1 = 2.5 i Δ − 25 (3) Substitute equation (3) in equation (1). 400 = 24 ( 2.5 i Δ − 25 ) + 2.5 i Δ 400 = 60 i Δ − 600 + 2.5 i Δ 400 + 600 = 62.5 i Δ 1000 = 62.5 i Δ Rearrange the equation as follows, i Δ = 1000 62.5 = 16 A Substitute 16 for i Δ in equation (3) to find the current i 1 in amperes. i 1 = 2.5 ( 16 ) − 25 = 15 A In Figure 1, the voltage v 20 A across the current source 20 A is calculated as follows, v 20 A = 1 i Δ + 6.5 i Δ v 20 A = 7.5 i Δ (4) Substitute 16 for i Δ in equation (4) to find the voltage v 20 A in volts. v 20 A = 7.5 ( 16 ) = 120 V In Figure 1, the power due to current source is, p 20 A = − v 20 A ( 20 A ) Substitute 120 V for v 20 A to find the power p 20 A in watts

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ISBN: 8220100801792

Author: Riedel

Publisher: YUZU

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Chapter 4, Problem 46P

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Calculate the total power developed in the circuit.

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Chapter 4, Problem 45P

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