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: P1.80

Answer

$I = 1.5A $ $V = 52.5V$

Work Step by Step

First, we apply Kirchhoff's junction rule to obtain: $I = .5I_x + I_x \\ I = 1.5I_x$ We now use Ohm's law to find $I_x$: $ I_x = \frac{V}{R} = \frac{20V}{20\Omega} = 1A$ Thus, we find $I$: $ I = 1.5 I_x = 1.5(1) = \fbox{1.5A}$ We now use Kirchhoff's Voltage Law, which states that the voltage around any closed loop in a circuit is 0, to find: $-v + (15\Omega)(1.5A)+20V + (10\Omega)(1A) = 0 \\ v = (15\Omega)(1.5A)+20V + (10\Omega)(1A)\\ v = \fbox{52.5V} $
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