Basic Engineering Circuit Analysis
11th Edition
ISBN: 9781118539293
Author: J. David Irwin, R. Mark Nelms
Publisher: WILEY

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Textbook Question
Chapter 3, Problem 1P

Use nodal analysis to find V 1 in the circuit in Fig. P3.l.

To determine

The value of voltage V1 by use of nodal analysis.

The value of voltage V1 is 35V.

### Explanation of Solution

Calculation:

The circuit diagram is redrawn as shown in Figure 1.

Write the expression for KCL at node A in Figure 1.

i1+V1R2+V1vBR3=0   ..... (1)

Here, i1 is the current in the circuit, V1 is the voltage at node A, vB is the voltage at node B and R2, R3 are the resistances in the circuit.

Substitute 12mA for i1, 5kΩ for R2 and 5kΩ for R3 in equation (1).

12mA+V15kΩ+V1vB5kΩ=0( 5kΩ)( 12mA)+V1+V1vB5kΩ=0( 5× 10 3 Ω)( 12× 10 3 A)+2V1vB5kΩ=060V+2V1vB=0

Rearrange further.

2V1vB=60V   ..... (2)

Write the expression for KCL at node B in Figure 1.

vBV1R3+vBR4+vBR5=0   ..... (3)

Here, R4 and R5 are the resistances in the circuit.

Substitute 5kΩ for R3, 4kΩ for R4 and 4kΩ for R5 in equation (3).

vBV15kΩ+vB4kΩ+vB4kΩ=04( v B V 1 )+5vB+5vB20kΩ=04vB4V1+10vB=04V1+14vB=0

Rearrange for vB.

vB=4V114

Simplify further.

vB=0.286V1

Substitute 0.286V1 for vB in equation (2).

2V10.286V1=60V1.714V1=60VV1=60V1.714=35V

Conclusion:

Thus, the value of voltage V1 is 35V.

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