(a) To determine Calculate the node voltages v 1 , v 2 , and v 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 1 in Figure 1. 0 = 5 i 1 + 40 ( i 1 − i 2 ) + 20 ( i 1 − 5 i o ) 0 = 5 i 1 + 40 i 1 − 40 i 2 + 20 i 1 − 100 i o 0 = 65 i 1 − 40 i 2 − 100 i o Rearrange the equation as follows, 100 i o = 65 i 1 − 40 i 2 i o = 65 i 1 − 40 i 2 100 i o = 0.65 i 1 − 0.4 i 2 (1) Apply Kirchhoff’s voltage law for Loop current i 2 in Figure 1. 0 = 10 i 2 + 40 ( i 2 − i 1 ) + 5 ( i 2 − i 3 ) + 11.5 i o 0 = 10 i 2 + 40 i 2 − 40 i 1 + 5 i 2 − 5 i 3 + 11.5 i o 0 = − 40 i 1 + 55 i 2 − 5 i 3 + 11.5 i o (2) Substitute equation (1) in equation (2). 0 = − 40 i 1 + 55 i 2 − 5 i 3 + 11.5 ( 0.65 i 1 − 0.4 i 2 ) 0 = − 40 i 1 + 55 i 2 − 5 i 3 + 7.475 i 1 − 4.6 i 2 0 = − 32.525 i 1 + 50.4 i 2 − 5 i 3 32.525 i 1 = 50.4 i 2 − 5 i 3 Reduce the equation as follows, i 1 = 50.4 i 2 − 5 i 3 32.525 i 1 = 1.5496 i 2 − 0.1537 i 3 (3) Apply Kirchhoff’s voltage law for Loop current i 3 in Figure 1. − 96 = 4 i 3 + 5 ( i 3 − i 2 ) − 11.5 i o − 96 = 4 i 3 + 5 i 3 − 5 i 2 − 11.5 i o − 96 = − 5 i 2 + 9 i 3 − 11.5 i o (4) Substitute equation (1) in equation (4). − 96 = − 5 i 2 + 9 i 3 − 11.5 ( 0.65 i 1 − 0.4 i 2 ) − 96 = − 5 i 2 + 9 i 3 − 7.475 i 1 + 4.6 i 2 − 96 = − 7.475 i 1 − 0.4 i 2 + 9 i 3 (5) In Figure 1, the current i o is calculated as follows. i o = i 1 − i 2 (6) Substitute equation (6) in equation (1). i 1 − i 2 = 0.65 i 1 − 0.4 i 2 i 1 − 0.65 i 1 = − 0.4 i 2 + i 2 0.35 i 1 = 0.6 i 2 i 1 = 0.6 0.35 i 2 Simplify the equation as follows, i 1 = 1.7143 i 2 (7) Substitute equation (7) in equation (5). − 96 = − 7.475 ( 1.7143 i 2 ) − 0.4 i 2 + 9 i 3 − 96 = − 12.8144 i 2 − 0.4 i 2 + 9 i 3 − 96 = − 13.2144 i 2 + 9 i 3 Rearrange the equation as follows, 13 (b) To determine Calculate the total power dissipated in the circuit.

ELECTRIC CIRCUITS-W/MASTERINGENGINEERING

11th Edition

ISBN: 9780134894300

Author: NILSSON

Publisher: PEARSON

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Chapter 4, Problem 44P

(a)

To determine

Calculate the node voltages v1, v2, and v3 in the given circuit using mesh-current method.

(b)

To determine

Calculate the total power dissipated in the circuit.

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Chapter 4 Solutions

ELECTRIC CIRCUITS-W/MASTERINGENGINEERING

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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