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526 For the circuit of Figure P526, determine the time
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constants and before and after the switch opens, respectively RS = 4 k , R1 = 2 k , R2 = R3 = 6 k , and C = 1 F
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Figure P526
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527 For the circuit of Figure P527, nd the initial
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current through the inductor, the nal current through the inductor, and the expression for iL (t) for t 0
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1000 10 t=0 100 V + _ 5 01 H t = 0 iL 5A 10 k + L1 vL1(t) L2 L1 = 1 H L2 = 5 H iL(t) 25
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Figure P529
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530 At t = 0, the switch in the circuit of Figure P530
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closes Assume that iL (0) = 0 A For t 0, a Find iL (t) b Find vL1 (t)
Figure P527
528 At t = 0, the switch in the circuit of Figure P528
opens At t = 10 s, the switch closes
Figure P530
Part I
Circuits
Section 2: Second-Order Transients 531 In the circuit shown in Figure P531:
VS1 = 15 V RS1 = 130 R1 = 11 k L = 17 mH VS2 = 9 V RS2 = 290 R2 = 700 C = 035 F
Determine the current through the inductor and the voltage across the capacitor and across R1 after the circuit has returned to a steady state
t=0 R1 L + + V _ _ S R2
Assume that DC steady-state conditions exist for t < 0 Determine the voltage across the capacitor and the current through the inductor and RS2 as t approaches in nity
t=0 RS1
+ + V _ _S1
Figure P534
535 If the switch in the circuit shown in Figure P535 is
closed at t = 0 and: VS = 12 V R1 = 31 k L = 09 mH
C RS2
+ + V _ _S2
R1 R2
C = 05 F R2 = 22 k
Figure P531
532 In the circuit shown in Figure P531:
VS1 = 12 V RS1 = 50 R1 = 22 k L = 78 mH VS2 = 12 V RS2 = 50 R2 = 600 C = 68 F
Determine the current through the inductor and the voltage across the capacitor after the circuit has returned to a steady state
t=0 + + V _ S _ L R1 C R2
Assume that DC steady-state conditions exist at t < 0 Determine the voltage across the capacitor and the current through the inductor as t approaches in nity Remember to specify the polarity of the voltage and the direction of the current that you assume for your solution
Figure P535
533 If the switch in the circuit shown in Figure P533 is
closed at t = 0 and: VS = 170 V R1 = 23 k L = 30 mH RS = 7 k R2 = 7 k C = 130 F
536 At t < 0, the circuit shown in Figure P536 is at
steady state and the voltage across the capacitor is +7 V The switch is changed as shown at t = 0 and: VS = 12 V R1 = 91 k R3 = 43 k C = 3300 F R2 = 43 k L = 16 mH
determine, after the circuit has returned to a steady state, the current through the inductor and the voltage across the capacitor and R1
t=0 RS L + + VS _ _ R1 C R2
Determine the initial voltage across R2 just after the switch is changed
t=0 + + V R1 _ _S C L R2 + V _C R3
Figure P533
534 If the switch in the circuit shown in Figure P534 is
closed at t = 0 and: VS = 12 V R1 = 23 k L = 30 mH C = 130 F R2 = 7 k
Figure P536
537 In the circuit shown in Figure P537, assume that
DC steady-state conditions exist for t < 0 Determine at t = 0+ , just after the switch is opened, the current
5
Transient Analysis
through and voltage across the inductor and the capacitor and the current through RS2 VS1 = 15 V RS1 = 130 R1 = 11 k L = 17 mH VS2 = 9 V RS2 = 290 R2 = 700 C = 035 F
t=0 RS 1 + + V _ _ S1 L R1 R2 RS2 + + V _ _ S2
541 Assume the circuit of Figure P541 initially stores
no energy Switch S1 is open, and S2 is closed Switch S1 is closed at t = 0, and switch S2 is opened at t = 5 s Determine an expression for the capacitor voltage for t 0
4F t=0 3
S1 6V + _ 2 t=5S S2 5H
Figure P537
538 In the circuit shown in Figure P537:
VS1 = 12 V RS1 = 50 R1 = 22 k L = 78 mH VS2 = 12 V RS2 = 50 R2 = 600 C = 68 F
Figure P541
542 Assume that the circuit shown in Figure P542 is
underdamped and that the circuit initially has no energy stored It has been observed that, after the switch is closed at t = 0, the capacitor voltage reaches an initial peak value of 70 V when t = 5 /3 s, a second peak value of 532 V when t = 5 s, and eventually approaches a steady-state value of 50 V If C = 16 nF, what are the values of R and L
Assume that DC steady-state conditions exist for t < 0 Determine the voltage across the capacitor and the current through the inductor as t approaches in nity Remember to specify the polarity of the voltage and the direction of the current that you assume for your solution
t=0 R L
539 Assume the switch in the circuit of Figure P539
has been closed for a very long time It is suddenly opened at t = 0, and then reclosed at t = 5 s Determine an expression for the inductor current for t 0
4F 3 V + _
Figure P542
543 Given the information provided in Problem 542,
6V + _
explain how to modify the circuit so that the rst two peaks occur at 5 s and 15 s Assume that C cannot be changed
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