# 8 sin 3 V. For the circuit given, determine the voltage v for all time t. Assume that no energy is stored in the circuit before t = 0.

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1 For the circuit given, determine the voltage v for all time t. Assume that no energy is stored in the circuit before t = 0. Spring 2015, Exam #5, Problem #1 4t Answer: e tut 8 sin 3 V 1

2 For the circuit given, determine i(t) for t 0. Spring 2015, Exam #5, Problem #2 Answer: 2t 8e u t A 2

3 Using Laplace analysis, determine if this circuit is overdamped or underdamped. Spring 2015, Exam #5, Problem #3 Answer: overdamped 3

4 (a) Determine the transfer function of this circuit, H(s), as a factored numerator divided by a factored denominator. (b) Continuing from part (a), determine v out (t) for v t t Assume that transients are negligible. in 2cos 3 10 V. Spring 2015, Exam #5, Problem #4 120 Answers: (a) s4 s5, (b) 8.2cos 3t 78 V 4

5 For the ideal op-amp circuit given, determine v o if v ut i 7 9 mv. Spring 2015, Exam #5, Problem #5 Answer: 400 t9 21e u t 9 mv 5

6 The switch has been in its original position (to the left) for a long time before t = 0. At t = 0, the switch moves (to the right). Determine v R (t) for t > 0 using s-domain analysis. Spring 2014, Exam #3, Problem #1 Answer: 40 80e t V 6

7 Parts (a) and (b) refer to the RC circuit depicted. (a) Determine v out (t) for v in (t) = 20u(t 7) V. (b) Determine v out (t) for v in (t) = 16t u(t) V. Spring 2014, Exam #3, Problem #2 Answers: (a) 8 t7 20e u t 7 V 8t, (b) ut e ut 2 2 V 7

8 The RLC circuit has been connected for a long time and both the 500-mH inductor and 250-mF capacitor have been discharged completely prior to t = 0. Determine i(t) for all time t > 0. Spring 2015, Quiz, Problem #1 2 4 Answer: 5 t t e 5e ut A 8

9 Determine the output voltage in the s domain, V out (s). Spring 2015, Quiz, Problem #3 Answer: 1 1 3s e s 2 s 4 s s 2 9

10 At t = 0, the inductor and capacitor are completely discharged. Determine the voltage across the capacitor, v C (t), using s-domain analysis. Spring 2014, Quiz #2, Problem #1 2 4 Answer: t t e 10e ut V 10

11 The initial capacitor voltage (at t = 0 ) is v(t) = 12 V. Determine both v(t) and i(t) for t > 0. Spring 2014, Quiz #2, Problem #2 v t e i t e 2 2t 12 V, 4 A Answers: t 11

12 The switch has been connected to 2 for a very long time (prior to t = 0). At t = 0, the switch connects the 8 and 4 H (series combination) to the voltage source. Determine both v(t) and i(t) for t > 0. Spring 2014, Quiz #2, Problem #3 v t e i t e 2 2t 24 V, 3 3 A Answers: t 12

13 In the circuit below, determine the voltage v C (t) for t > 0. Spring 2015, Final exam, Problem #12 Answer: t 3e 3e 5t 13

14 Obtain an expression for G(s) if g(t) is given by (a) [5u(t)] 2 u(t) (b) 2u(t) 2u(t 2) (c) tu(2t) (d) 2e t u(t) + 3u(t) Spring 2014, Homework #6, Problem #1 Answers: (a) 24 s 2 1 s 1, (c) 2 s s 2, (b) e, (d) 2 3 s1 s 14

15 Obtain a time-domain expression which corresponds to each of the following s-domain functions: 1 3s (a) s 2, (b) s 3s s s s 4s 6 2, 2 14 s1 s1 s 1 2 s 4 s 5 (c), (d) Spring 2014, Homework #6, Problem # , 3 3t Answers: (a) e u t 8t 1 (b) sinh cosh 2 10 (c) t t t e u t 10 t 2te u t t t 4t 5t, (d) te e e e u t, 15

16 For the circuit below, draw an s-domain equivalent and analyze it to obtain an expression for v(t) if i(0) is equal to (a) 0, (b) 3 A. Spring 2014, Homework #6, Problem #3 Answers: (a) t t e 4.53e ut V, (b) t 2.5t e e ut V 16

17 With respect to the s-domain circuit drawn below, (a) calculate V C (s), (b) determine v C (t) for t > 0, and (c) draw the time-domain equivalent circuit. Spring 2014, Homework #6, Problem #4 Answers: (a) 6 5s 1 s 10s 3 3t 10, (b) e ut 2 V, (c) v C (0 + ) = 3 V 17

18 If the current source in the circuit below is 1.5e 2t u(t) A, and i L (0 ) = 1 A, determine i x (t) for t > 0. Spring 2014, Homework #7, Problem #1 Answer: 2t 0.78t 0.53e 0.60e A 18

19 s If a network is found to have the transfer function Hs, determine the s-domain 2 s 8s7 output voltage for v in equal to (a) 3u(t) V, (b) 25e 2t u(t) V, (c) 4u(t + 1) V, (d) 2sin(5t)u(t) V. Spring 2014, Homework #7, Problem #2 3 Answers: (a) 2 s 8s7 25s, (b) s 2 s 2 8s 7 s 4e, (c) 2 s 8s7 10s, (d) s 2 25s 2 8s 7 19

20 Determine the Laplace transform of the following functions: (a) f t 3u t 2 (b) 2t f t 3e ut 5u t (c) t f t e ut 0.5 (d) f t t 1 ut 1 (e) f t cos 100t ut (f) 2t f t e sin 5t ut Spring 2015, Homework #6, Problems #1-6 Answers: (a) 3 2s e s, (b) 3 5 s 2 s, (c) e s s s e, (d) 2 s s, (e) 2 4 s 10 5, (f) 2 s 4s29 20

21 Determine the inverse Laplace transform of (a) F s 2 s 2s s s s, (b) Fs 2s 6 s 1 s 2 2s 5 Spring 2015, Homework #7, Problems #1,2 Answers: (a) 5 t t e cos t 127 4e ut, (b) t t e e cos 2t e t sin 2t ut 21

22 The input to the circuit shown below is the voltage source, 12 V. The output of this circuit is the current i(t) in the inductor. Determine i(t) for t > 0. Spring 2015, Homework #7, Problem #3 0.8t Answer: e 3 1 A 22

23 Determine the capacitor voltage v(t) in the circuit shown below. Spring 2015, Homework #7, Problem # V t 0 Answer: 1.67t e V t 0 23

24 Using Laplace transforms, find v o (t) for t > 0 for the circuit below. Spring 2015, Homework #7, Problem #5 Answer: 2t 3t 24 54e 36e V 24

25 The input to the circuit shown below is the voltage source v i (t) and the output is the capacitor voltage v o (t). Determine the step response of this circuit. Spring 2015, Homework #7, Problem #7 2t Answer: e t cos mv 25

26 4 Determine the Laplace transform of t 5t f t e e ut Express the result as N D s s where N and D are polynomials with integer coefficients.. Spring 2016, Homework #7, Problem #1 10 Answer: 3 2 s 9s 27s 27 26

27 2 3t Determine the Laplace transform of g t 5t e ut Ns Express the result as Ds. where N and D are polynomials with integer coefficients. Spring 2016, Homework #7, Problem #2 1 Answer: 2 s 9s20 27

28 t 6t 9t Determine the Laplace transform of xt e e e u t Express the result as N D s s where N and D are polynomials with integer coefficients.. Spring 2016, Homework #7, Problem #3 8 Answer: 3 2 s 17s 84s

29 2 Determine the Laplace transform of t 2 2t y t te t e ut Express the result as N D s s where N and D are polynomials with integer coefficients.. Spring 2016, Homework #7, Problem #4 s Answer: 3 2 s 6s 12s 8 29

30 2s 6 F. s 3s 7s 5 Determine the inverse transform of s 3 2 Spring 2016, Homework #7, Problem #5 t Answer: e 4 3cos t 4sin tut 30

31 Determine the inverse transform of s 2 G 16s 32 s 8s16. Spring 2016, Homework #7, Problem #6 t Answer: e 1 cos 2t sin 2t ut 31

32 Determine the inverse transform of 2 s 2s1 K s. 3 2 s 3s 4s 2 Spring 2016, Homework #7, Problem #7 4t Answer: 16e 1 2t ut 32

33 In the circuit below, determine i 2 (t) using Laplace transforms. Spring 2016, Homework #8, Problem #1 Answer: t t e 38e u t ma 33

34 In the circuit below, determine v(t) using Laplace transforms. Assume that the switch has been open for a long time before it closes at t = 0. Spring 2016, Homework #8, Problem #2 Answer: 100t e u t V 34

35 In the circuit below, determine i c (t) for (a) R = 3, C = 1/24 F, and (b) R = 10, C = 1/40 F. Assume that the switch has been open for a long time before it closes at t = 0. Spring 2016, Homework #8, Problem #3 and #4 Answers: (a) t t 2t e 0.75e ut A, (b) e t ut 0.75 sin 4 A 35

36 Vo s A circuit is described by the transfer function Vi Determine the output v o (t) for the input v t ut 2 s s s i 6 mv. 80s Spring 2016, Homework #8, Problem #5 4t Answer: e t ut 160 sin 3 mv 36

37 In the circuit below, determine (a) the response v o (t) when the input is v t ut (b) the steady-state response v o (t) when the input is v t t. i 4cos V i 20 mv, and Spring 2016, Homework #8, Problem #5 and #6 Answers: (a) t e ut mv, (b) t 5.8cos V 37

38 Use Laplace analysis to determine v R (t). Write a complete expression for v R (t) for all time t. Spring 2016, Exam #4, Problem #1 Answer: 40t 6 6e u t V 38

39 In the circuit given, the switches transition simultaneously, at t = 0. Use Laplace analysis to determine v C (t). Write an expression for v C (t) for t > 0. Spring 2016, Exam #4, Problem #2 Answer: e t V 39

40 For the circuit given, assume an ideal op amp. (a) Determine the transfer function H(s) for the following element values: R 1 = 5 k, R 2 = 20 k, R 3 = 50 k, C = 25 F. (b) Determine v out (t) for v in = 4cos(10t) V. Assume that transients are negligible. Spring 2016, Exam #4, Problem #4 Answers: (a) 28, 8 j (b) 8.7 cos 10t 51 V 40

41 The switch in the circuit below has been open for a long time. At t = 0, the switch closes. Determine the voltage v(t) for t > 0. Spring 2016, Final exam, Problem #6 300t Answer: e t 60 sin 100 V 41

42 For the circuit given, assume an ideal op amp. (a) Determine the transfer function H(s) for the following element values: R 4 = 10 k, R 5 = 5 k, R 6 = 25 k, C 2 = 50 nf. (b) Determine v out (t) for v in = 40cos(3000t + 20) mv. Assume that transients are negligible. Spring 2016, Final exam, Problem #7 6s Answers: (a), s 2000 (b) 200cos 3000t 54 mv 42

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