P:18) j1012/90ofwww The circuit of Fig. contains a single current source l=12L90°A. Determine the voltage V2 atnode 2 apply the reciprocity theorem and compare results using node analysis.wwroww

Answered: 12/90 ww

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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P:18)

The circuit of Fig. contains a single current source l=12L90°A. Determine the voltage V2 at
node 2 apply the reciprocity theorem and compare results using node analysis.
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Expert Solution

Step 1

It is given a circuit :

We need to calculate voltage at node 2.

Step 2

Calculating equivalent resistance at node V₂:

At first we calculate the equivalent resistance at node V₂.

At node V₂ equivalent resistance is given as,

$Z_{1} = [5 | | (2 + j 2)] = \frac{5 \times (2 + j 2)}{5 + (2 + j 2)} = \frac{10 (1 + j)}{7 + j 2} = \frac{10 (1 + j) (7 - j 2)}{(7 + j 2) (7 - j 2)} = \frac{10 (7 + 2 + j 7 - j 2)}{49 + 4} = \frac{90 + j 50}{53} = 1.7 + j 0.94 Ω$

The equivalent circuit is given as:

The equivalent resistance at node V₂ is $1.7 + j 0.94 Ω$ .

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