E117CW13 - AP 7.1[a The circuit for t< 0 is shown below...

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Unformatted text preview: AP 7.1 [a] The circuit for t <: 0 is shown below. Note that the inductor behaves like a short circuit, effectively eliminating the 2 Q resistor from the circuit. First combine the 30 Q and 6 fl resistors in parallel: 30||6 = 5 9 Use vol5tage division to find the voltage drop across the parallel resistors: = — 120 ---= ' I v 5 + 3( ) 75V Now find the currernt using Ohm's law: ' v 5 ' ‘ = —- = —--—— = -12.5A- em ) _ 6 6 1 -2 1 #3 2 [b] rum) = 5L: (0) = -2—(8 x 10 )(12.5) = 6251111 [c] To find the time constant, we need to find the equivalent resistance seen by the inductor fort .‘> 0. When the switch opens. only the 2 Q resistor remains connected to the inductor. Thus, L 8 x 10'3 1" = — = -—--———--— R 2 _ [d] i(t) = t(0*)e*f'r = —12.5e“/°m4 = —12.5e"25°‘A, [e] 3*(‘5 ms) = —12.5e-250<m5) = 4253-1-25 = —3.58A =4ms t>0 So to (5 ms) = §Lt2(5 mm) = %(3) x 10-3(3.53)2 = 51.3mJ to (dis) = 625 -~ 51.3 = 573.7mJ 573.7 d' ‘ = —— = _ fl—fl % 1551pated ( 625 ) 100 91 8% AP 7.3 [a] The circuit for t < 0 is shown below. Note that the capacitor behaves like an- open circuit. ‘ Find the voltage drop across the open circuit by finding the voltage drop across the 50 k9 resistor. First use current division to find the current through the 50 k9 resistor: ' 80x103 3 ' .- —“——"‘“——* . " =4 80x103+20><103+50><103(75‘x m ) Use Ohm’s law to find the voltage drop: _ 1.1(0') -= (50 x 103nm = (50 x 103)(o.004) = 200v 3set: = [b] To find the time constant, we need to find the equivalent resistance seen by the capacitor for t > 0. When the switch opens, only the 50 k9 resistor remains connected to the capacitor. Thus, T = R0 = (50 x 103)(0.4 x 10-5) = 20:11.5 [c1 v(t) = v(0")e"m = 2OOe‘t/D'02 = 20:06"50¢ v, t >‘ o [(1] 111(0) = 13—0122 = %(0.4 x 104x200)2 = 8m] 1 [e] w(t) = $0020) = 5(04 >< 10-6)(zoos-50m)2 = sea-1W m] The initial energy is 8 In], so when 75% is dissipated, 2 11]] remains: 8 x 10*33-10‘3‘ = 2 x 10-3, em = 4, t = (In 4)/100 = 13.361115 ...
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E117CW13 - AP 7.1[a The circuit for t< 0 is shown below...

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