Q2:- For the series-parallel network of Fig. 1: a) Calculate Zr and YT.b) Determine Ir and I. e) FindVXL. VR and Ig.V, VT.VR12 n606ΩVyt 3 1212 2E = 25 sin(377t - 20°)

Answered: Q2:- For the series-parallel network of…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Q2:- For the series-parallel network of Fig. 1: a) Calculate Zr and YT.b) Determine Ir and I. e) Find
VXL. VR and Ig.
V, V
T.
VR
12 n
60
6Ω
Vyt 3 12
12 2
E = 25 sin(377t - 20°)

Expert Solution

Step 1

Given:

Step 2

The two inductors are replaced with

$L \Leftrightarrow j X_{L} L \Leftrightarrow j 12$

The above two inductors are in the parallel combination so the equivalent inductance between them will be:

$j 12 ∥ j 12 = \frac{j 12 \times j 12}{j 12 + j 12} j 12 ∥ j 12 = j 6 Ω$

Two capacitors and a resistor are in parallel as shown above:

$\frac{1}{Z'} = \frac{1}{4} + \frac{1}{- j 12} + \frac{1}{- j 6} \frac{1}{Z'} = \frac{1}{4} + \frac{j}{12} + \frac{j}{6} \frac{1}{Z'} = \frac{3 + j + 2 j}{12} \frac{1}{Z'} = \frac{3 + 3 j}{12} \frac{1}{Z'} = \frac{1 + j}{4} Z' = \frac{4}{1 + j} N o w, r a t i o n a l i z i n g t h e d e n o m i n a t o r, Z' = \frac{4}{1 + j} \times \frac{1 - j}{1 - j} Z' = \frac{4 - 4 j}{2} Z' = 2 - 2 j$

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