(a) To determine Calculate the total power developed in the given circuit using mesh-current method in PSPICE. Explanation The given circuit is redrawn as shown in Figure 1. Apply Kirchhoff’s Voltage law for Loop 1 in Figure 1. 230 − 115 = 4 i 1 + 1 ( i 1 − i 2 ) + 2 ( i 1 − i 3 ) 115 = 4 i 1 + i 1 − i 2 + 2 i 1 − 2 i 3 115 = 7 i 1 − i 2 − 2 i 3 (1) Apply Kirchhoff’s voltage law for Loop 2 in Figure 1. 0 = 6 i 2 + 1 ( i 2 − i 1 ) + 3 ( i 2 − i 3 ) 0 = 6 i 2 + i 2 − i 1 + 3 i 2 − 3 i 3 0 = − i 1 + 10 i 2 − 3 i 3 Rearrange the equation as follows, i 1 = 10 i 2 − 3 i 3 (2) Apply Kirchhoff’s voltage law for Loop 3 in Figure 1. − 460 + 115 = 5 i 3 + 3 ( i 3 − i 2 ) + 2 ( i 3 − i 1 ) − 345 = 5 i 3 + 3 i 3 − 3 i 2 + 2 i 3 − 2 i 1 − 345 = − 2 i 1 − 3 i 2 + 10 i 3 (3) Substitute equation (2) in equation (3). − 345 = − 2 ( 10 i 2 − 3 i 3 ) − 3 i 2 + 10 i 3 − 345 = − 20 i 2 + 6 i 3 − 3 i 2 + 10 i 3 − 345 = − 23 i 2 + 16 i 3 23 i 2 = 16 i 3 + 345 Rearrange the equation as follows, i 2 = 16 i 3 + 345 23 i 2 = 0.6957 i 3 + 15 (4) Substitute equation (4) in equation (2). i 1 = 10 ( 0.6957 i 3 + 15 ) − 3 i 3 i 1 = 6.957 i 3 + 150 − 3 i 3 i 1 = 3.957 i 3 + 150 (5) Substitute equation (4) and (5) in equation (1). 115 = 7 ( 3.957 i 3 + 150 ) − ( 0.6957 i 3 + 15 ) − 2 i 3 115 = 27.699 i 3 + 1050 − 0.6957 i 3 − 15 − 2 i 3 115 = 25.0033 i 3 + 1035 25.0033 i 3 = 115 − 1035 Reduce the equation as follows, 25.0033 i 3 = − 920 i 3 = − 920 25.0033 i 3 = − 36.8 A (6) Substitute equation (6) in equation (5) to find the current i 1 in amperes. i 1 = 3.957 ( − 36.8 ) + 150 = 4.4 A Substitute equation (6) in equation (4) to find the current i 2 in amperes. i 2 = 0.6957 ( − 36.8 ) + 15 = − 10.6 A The components that develop power in the circuit are sources. In Figure 1, the power developed in the circuit due to the 230 V voltage source is calculated as follows. p 230 V = − ( 230 V ) i 1 Substitute 4.4 A for i 1 to find the power p 230 V in watts. p 230 V = − ( 230 V ) ( 4.4 A ) = − 1012 W { ∵ 1 W = 1 V ⋅ 1 A } In Figure 1, the power developed in the circuit due to the 460 V voltage source is calculated as follows (b) To determine Prove that the total power dissipated in the circuit is equal to the power developed by the circuit using PSPICE.

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

See similar textbooks

Concept explainers

Nodal Analysis

In the analysis of any electric circuit, nodal analysis is the method of determining the potential difference or voltage between different nodes in an electric circuit. A node is a point where two or more branches connect each other. In the nodal analysi…

Videos

Question

Chapter 4, Problem 37P

(a)

To determine

Calculate the total power developed in the given circuit using mesh-current method in PSPICE.

(b)

To determine

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

Expert Solution & Answer

Chapter 4 Solutions

Electric Circuits. (11th Edition)

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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.