Find the vab Voltage when the given Circuit 1 is connected to the Circuit 2 through their a and bterminals. To do this, find the Thevenin equivalents of circuits. Then, combine them and find thevoltage between a and b terminals.0.75va3Ω3Ω8Ω6 VVa12 V()3 A+b

Answered: Find the vab Voltage when the given…

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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Question

Find the vab Voltage when the given Circuit 1 is connected to the Circuit 2 through their a and b
terminals. To do this, find the Thevenin equivalents of circuits. Then, combine them and find the
voltage between a and b terminals.
0.75va
3Ω
3Ω
8Ω
6 V
Va
12 V
()3 A
+
b

Expert Solution

Step 1

consider first

Step 2

to find thvenins equivalent V_th =V_ab and R_th =R_ab

$0.75 v_{a} + \frac{v_{x}}{8} + \frac{v_{x} + 6}{4} = 0 6 v_{a} + v_{x} + 2 v_{x} + 12 = 0 6 v_{a} + 3 v_{x} + 12 = 0 . . . . . . . . . . (1) n o w f r o m c i r c u i t v_{x} = - v_{a} - 6 f r o m e q u a t i o n 1 6 v_{a} + 3 (- v_{a} - 6) + 12 = 0 v_{a} = 2 V V_{a b} = - v_{a} = - 2 V = V_{o c}$

Step 3

$I_{s c} = \frac{6}{8} = 0.75 A R_{t h} = \frac{V_{o c}}{I_{s c}} = \frac{2}{0.75} = 2.66 Ω$

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