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 172: 4.44

Answer

Time domain: $170cos(wt + \pi/3)$ Phasor notation: $V(wt) = 170e^{j\frac{\pi}{3}}$

Work Step by Step

This problem is pretty straightforward, we want to find the amplitude of the sinusoid as well as the phase shift, we don't need to worry about period because the x-axis is left as $wt$ The peak of the sinusoid reaches 170. so $A = 170$ Next look at how far the top peak is shifted from 0. The x-axis is already in radians so it corresponds to the shift value of $\phi$ $\phi = \frac{\pi}{3} $ Now fill in the "template" of a sinusoid using cosine function $v(wt) = 170*cos(wt + \frac{\pi}{3}) $ Next write the function in phasor notation by "picking out" $\phi$ and $A$ $V(wt) = 170e^{j\frac{\pi}{3} }$
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