(a) To determine Calculate the branch currents i 1 , i 2 , and i 3 in the given circuit using mesh-current method. Explanation The given circuit is redrawn as shown in Figure 1. Apply Kirchhoff’s voltage law for loop current i a in Figure 1. − 30 = ( 5 k ) i a + 500 ( i a − i c ) − 30 = 5000 i a + 500 i a − 500 i c { ∵ 1 k = 10 3 } − 30 = 5500 i a − 500 i c (1) Apply Kirchhoff’s voltage law for loop current i d in Figure 1. − 80 = ( 4 k ) ( i d − i c ) − 80 = 4 000 ( i d − i c ) { ∵ 1 k = 10 3 } − 80 = − 4000 i c + 4 000 i d (2) From Figure 1 the two supermesh equations are as follows. i c − i b = 10 m i c − i b = 10 × 10 − 3 { ∵ 1 m = 10 − 3 } i c − i b = 0.01 (3) 0 = ( 1 k ) i b + ( 4 k ) ( i c − i d ) + 500 ( i c − i a ) 0 = 1 000 i b + 4 000 i c − 4000 i d + 500 i c − 500 i a { ∵ 1 k = 10 3 } 0 = − 500 i a + 1 000 i b + 4 500 i c − 4000 i d (4) Rearrange the equation (4) as follows, 500 i a = 1 000 i b + 4 500 i c − 4000 i d i a = 1 000 i b + 4 500 i c − 4000 i d 500 i a = 2 i b + 9 i c − 8 i d (5) Rearrange the equation (1) as follows, 500 i c = 5500 i a + 30 i c = 5500 i a + 30 500 i c = 11 i a + 0.06 (6) Rearrange the equation (3) as follows, i c = 0.01 + i b (7) Substitute equation (7) in equation (6). 0.01 + i b = 11 i a + 0.06 i b = 11 i a + 0.06 − 0.01 i b = 11 i a + 0.05 (8) Rearrange the equation (2) as follows;. 4 000 i d = − 80 + 4000 i c i d = − 80 + 4000 i c 4 000 i d = − 0.02 + i c (9) Substitute equation (6) in equation (9). i d = − 0.02 + 11 i a + 0.06 i d = 0.04 + 11 i a (10) Substitute equation (6), (8) and (10) in equation (5) to find the current i a in amperes (b) To determine Prove that the total power dissipated in the circuit is equal to the power developed in the circuit.

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 4, Problem 49P

(a)

To determine

Calculate the branch currents i1, i2, and i3 in the given circuit using mesh-current method.

(b)

To determine

Prove that the total power dissipated in the circuit is equal to the power developed in the circuit.

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