Fundamentals of Electrical Engineering

Published by McGraw-Hill Education
ISBN 10: 0073380377
ISBN 13: 978-0-07338-037-7

Chapter 4 - AC Network Analysis - Part 1 Circuits - Homework Problems - Page 171: 4.33


$P = 37.5W$

Work Step by Step

Start by setting up the integral to solve for rms. We want rms current because it will give us the same average power. $i_{rms} = \sqrt {100/ \pi * \int^{\pi}_0 sin^4 (t) *dt } $ Use a trig identity to simplify the sin term into terms of cosine with different frequencies. Then integrate to get: $i_{rms} = \sqrt {100/ \pi *(3*t/8 - \frac{1}{4}*sin(2x) + \frac{1}{32}*sin(4x)|^{\pi}_0 } $ $ i_{rms}= \sqrt {\frac{3*100}{8}} $ Now calculate power using $P = i^2 *R$ $P = (6.1237)^2 *1$ $P = 37.5W$
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