(a) To determine Calculate the branch currents i 1 , i 2 , i 3 , i 4 , i 5 , and i 6 in the given circuit using node-voltage method in PSPICE. Explanation The given circuit is redrawn with reference node and the node voltages v 1 , v 2 and v 3 as shown in Figure 1. Apply Kirchhoff’s current law at node v 1 in Figure 1. v 1 − 125 1 + v 1 − v 2 6 + v 1 − v 3 24 = 0 ( 1 + 1 6 + 1 24 ) v 1 − v 2 6 − v 3 24 = 125 1.2083 v 1 − 0.1667 v 2 − 0.0417 v 3 = 125 (1) Apply Kirchhoff’s current law at node v 2 in Figure 1. v 2 2 + v 2 − v 1 6 + v 2 − v 3 12 = 0 − 1 6 v 1 + ( 1 2 + 1 6 + 1 12 ) v 2 − v 3 12 = 0 − 0.1667 v 1 + 0.75 v 2 − 0.0833 v 3 = 0 Rearrange the equation as follows, 0.1667 v 1 = 0.75 v 2 − 0.0833 v 3 v 1 = 0.75 v 2 − 0.0833 v 3 0.1667 v 1 = 4.4991 v 2 − 0.4997 v 3 (2) Apply Kirchhoff’s current law at node v 3 in Figure 1. v 3 + 125 1 + v 3 − v 1 24 + v 3 − v 2 12 = 0 − 1 24 v 1 − 1 12 v 2 + ( 1 + 1 24 + 1 12 ) v 3 = − 125 − 0.0417 v 1 − 0.0833 v 2 + 1.125 v 3 = − 125 (3) Substitute equation (2) in equation (3). − 0.0417 ( 4.4991 v 2 − 0.4997 v 3 ) − 0.0833 v 2 + 1.125 v 3 = − 125 − 0.1876 v 2 + 0.0208 v 3 − 0.0833 v 2 + 1.125 v 3 = − 125 − 0.2709 v 2 + 1.1458 v 3 = − 125 Rearrange the equation as follows, 0.2709 v 2 = 1.1458 v 3 + 125 v 2 = 1.1458 v 3 + 125 0.2709 v 2 = 4.2296 v 3 + 461.4249 (4) Substitute equation (4) in equation (2). v 1 = 4.4991 ( 4.2296 v 3 + 461.4249 ) − 0.4997 v 3 = 19.0294 v 3 + 2075.9968 − 0.4997 v 3 v 1 = 18.5297 v 3 + 2075.9968 (5) Substitute equation (4) and (5) in equation (1). 1.2083 ( 18.5297 v 3 + 2075.9968 ) − 0.1667 ( 4.2296 v 3 + 461.4249 ) − 0.0417 v 3 = 125 22.3894 v 3 + 2508.4269 − 0.7049 v 3 − 76.9195 − 0.0417 v 3 = 125 22.3894 v 3 − 0.7049 v 3 − 0.0417 v 3 = − 2508.4269 + 125 + 76.9195 21.6428 v 3 = − 2306.5074 Rearrange the equation as follows, v 3 = − 2306.5074 21.6428 = − 106.5715 V ≅ − 106.57 V Substitute − 106.57 for v 3 in equation (5) to find the voltage v 1 in volts. v 1 = 18.5297 ( − 106.5715 ) + 2075.9968 = − 1974.7379 + 2075.9968 = 101.2589 V ≅ 101.25 V Substitute − 106.57 for v 3 in equation (4) to find the voltage v 2 in volts. v 2 = 4.2296 ( − 106.57 ) + 461.4249 = 10.67 V In Figure 1, the current i 1 through the 1 Ω resistor is calculated as follows. i 1 = 125 V − v 1 1 Ω Substitute 101.25 V for v 1 to find the current i 1 in amperes. i 1 = 125 V − 101.25 V 1 Ω = 23 (b) To determine Prove that the total power dissipated in the circuit is equal to the power developed by the circuit using PSPICE.

Electrical Circuits and Modified MasteringEngineering - With Access

10th Edition

ISBN: 9780133992793

Author: NILSSON

Publisher: PEARSON

See similar textbooks

Concept explainers

Transmission Line Parameters

The performance of a power system is mostly determined by the producing stations and transmission lines in the system which can be studied with the help of transmission line parameters.

Videos

Question

Chapter 4, Problem 15P

(a)

To determine

Calculate the branch currents i1, i2, i3, i4, i5, and i6 in the given circuit using node-voltage 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

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 14P

Chapter 4, Problem 16P

Students have asked these similar questions

Compute the thevenin equivalent between the two terminals a-b zeq and veq show all your steps and explain clearly what you did.

I need help with this problem and an explanation of the solution for the image described below. (Introduction to Signals and Systems)

Chapter 4 Solutions

Electrical Circuits and Modified MasteringEngineering - With Access

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.