ECE๎202๎(Fall๎2007)๎
Homework๎No.๎9๎
Due:๎Friday,๎11/9/2007๎
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Instructions:๎๎Draw๎a๎box๎around๎to๎indicate๎each๎answer.๎๎Failure๎to๎do๎so๎will๎cost๎you๎2๎pts๎per๎
offence.๎
๎
Total๎=๎100๎pts๎
๎
(P.1)๎[13๎pts]๎The๎switch๎in๎Figure๎1๎has๎been๎in๎position๎b๎for๎a๎long๎time.๎๎It๎is๎moved๎to๎position๎a๎at๎
t=0.๎๎Determine๎v(t)๎for๎t>0.๎๎What๎is๎the๎time๎constant๎of๎this๎circuit?๎
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Figure๎1๎Circuit๎for๎Problem๎1๎
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(P.2)๎[50๎pts]๎Consider๎the๎circuit๎in๎Figure๎2.๎๎The๎input๎signal๎is๎vs(t) = 10 u(t)๎V๎and๎assume๎that๎at๎t =๎
0,๎โ1๎A๎flows๎through๎the๎inductor๎and๎+5๎V๎is๎across๎the๎capacitor.๎
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Figure๎2๎Circuit๎for๎Problem๎2๎
(a) [14๎pts]๎Draw๎the๎sโdomain๎circuit๎incorporating๎the๎initial๎conditions.๎
(b) [11๎pts]๎What๎is๎the๎voltage๎across๎the๎capacitor๎for๎t๎>๎0?๎
(c) [5๎pts]๎What๎is๎the๎network๎function,๎T1(s),๎of๎this๎circuit?๎(Caution:๎recall๎how๎a๎network๎
function๎is๎defined.)๎Express๎the๎denominator๎of๎T1(s)๎as๎a๎polynomial๎with๎an๎unity๎coefficient๎
for๎the๎highest๎order๎of๎s.๎
(d) [10๎pts]๎What๎is๎the๎impulse๎response๎of๎the๎circuit๎in๎the๎time๎domain?๎
(e) [10๎pts]๎What๎is๎the๎step๎response๎of๎the๎circuit๎in๎the๎time๎domain?๎
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v1(t)
