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 170: 4.29


avg value $ = 2.5$ rms $ = 2.872$

Work Step by Step

Start by writing down $T = 2* \pi /w$ Next use the integral formula for average value on the signal $avg = \frac{w}{2* \pi} * \int ^{(2* \pi/w}_{0} {2*cos(w*t)+2.5)dt}$ Evaluate the integral and see that the values of w cancel out and all that is left is 2.5 $avg = 2.5$ Calculate rms by using the square root of the integral of the signal squared times frequency $rms = \sqrt{ w/(2* \pi) \int ^{\frac{2 \pi}{w}}_0 {(4*cos^2 (wt) + 10*cos(wt) +6.25)dt}}$ Evaluate the integral $rms = \sqrt{33/4}$ rms = 2.872
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