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 168: 4.14


$i = -13.667 mA$

Work Step by Step

To start this problem, turn the graph into a piecewise function with $(7*10^5 )t$ defined from 0 to 5 us and -1.9 defined from 5 to infinity. To find the current through a 0.75mH inductor, integrate the equation $v = L*\frac{di}{dt} $ to get $ i(t) = 1/L * \int^{t}_{t_0} {v(t')*dt' + i(0)}$ Apply this equation to the piecewise defined function at $t=15*10^{-6} s$ $i = 1333.333*(3.5*10^5 * t^2|^{5*10^{-6}}_{0} - (1.9*t)|^{15*10^{-6}}_{5*10^{-6}})$ $i = -13.667 mA$ Be sure to convert from micro seconds to seconds, and from mH to H before integrating to avoid any wrong units.
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