(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.

Electric Circuits Plus Mastering Engineering with Pearson eText 2.0 - Access Card Package (11th Edition) (What's New in Engineering)

11th Edition

ISBN: 9780134814117

Author: NILSSON, James W., Riedel, Susan

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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Electric Circuits Plus Mastering Engineering with Pearson eText 2.0 - Access Card Package (11th Edition) (What's New in Engineering)

Ch. 4.2 - a) For the circuit shown, use the node-voltage...Ch. 4.2 - Use the node-voltage method to find v in the...Ch. 4.3 - Use the node-voltage method to find the power...Ch. 4.4 - Use the node-voltage method to find vo in the...Ch. 4.4 - Use the node-voltage method to find v in the...Ch. 4.4 - Use the node-voltage method to find v1 in the...Ch. 4.5 - Use the mesh-current method to find (a) the power...Ch. 4.6 - Determine the number of mesh-current equations...Ch. 4.6 - Use the mesh-current method to find vo in the...Ch. 4.7 - Use the mesh-current method to find the power...

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