Electrical Engineering: Principles & Applications (6th Edition)

Published by Prentice Hall
ISBN 10: 0133116646
ISBN 13: 978-0-13311-664-9

Chapter 1 - 1.7 - Problems - Introduction to Circuits: P1.71


15 Volts

Work Step by Step

First of all, we need to find the current going through the 3 Ohm resistor. To do this, we first find the current going through the middle branch with no resistors in it. We find the current to be: $I=(4)(.5)=2\ A$ Kirchhoff's junction rule states that the current entering a junction and the current leaving a junction are equal. Thus, since we see that there are $1+2=3\ A$ leaving the junction, it follows that there are 3 Amps going into the junction, meaning that 3 Amps of current are going through the 3 Ohm resistor. Thus, we can find the voltage using Kirchhoff's Voltage Law, which states that the voltage around a complete path is 0. $v_s=(3)(3)+(4)(1)+(2)(1)=\fbox{15 Volts}$
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