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engineering
schaum s outline of electric circuits

ISE Fundamentals Of Electric Circuits 7th Edition Charles K. Alexander, Matthew Sadiku - Solutions

Determine the trigonometric Fourier series of the signal in Fig. 17.59. f(t) 2 -5-4-3-2-1 0 1 2 3 4 5 t Figure 17.59
Find the Fourier series for the signal in Fig. 17.58.Evaluate f(t) at t = 2 using the first three nonzero harmonics. f(t) 4 -4-2 -202 0 2 4 4 6 8 t Figure 17.58
Obtain the Fourier series for the periodic waveform in Fig. 17.57. f(t) 10 -4 -3-2-10 12 Figure 17.57 3 4 5 6 t
Determine the fundamental frequency and specify the type of symmetry present in the functions in Fig. 17.56. f(t) 2 -2 -1 0 1 2 3 t -2 (a) 12(t) 2 1 -2-1 0 1 2 3 4. 5 t (b)
Determine if these functions are even, odd, or neither.(a) 1 + t (b) t 2 − 1 (c) cos nπt sin nπt (d) sin2 πt (e) e−t
The waveform in Fig. 17.55(a) has the following Fourier series: v4-(ous+cos 3 + + 25 cos 5x + ...) V Obtain the Fourier series of v2(t) in Fig. 17.55(b). V(t) -2 -10 1 2 3 4 t v2(t) 1 (a) -1 0 1 2 3 4 t (b)
Express the Fourier series(a) in a cosine and angle form,(b) in a sine and angle form. 4 f(t)=10+ cos 10nt+sin 10nt = n+1 n
Find the quadrature (cosine and sine) form of the Fourier series f(t)=5+ 25 cos n=1 n + 1 is (2nt + M/T) 4
Design a problem to help other students better understand obtaining the Fourier series from a periodic function.
A voltage source has a periodic waveform defined over its period asv(t) = 10t(2π − t) V, 0 < t < 2π Find the Fourier series for this voltage.
Obtain the exponential Fourier series for the signal in Fig. 17.54. y(t) 10 -101 2 3 4 5 t
Find the exponential Fourier series for the waveform in Fig. 17.53. v(t) Vo 0 k 2 3 t
Determine the Fourier coefficients an and bn of the first three harmonic terms of the rectified cosine wave in Fig. 17.52. f(t) 10 8 10 t -202 4 6 8
Using Fig. 17.51, design a problem to help other students better understand how to determine the exponential Fourier series from a periodic wave shape. f(t) f(0) 0 t t t3 t4 t5 t
Determine the Fourier series of the periodic function in Fig. 17.50. f(t) 2 -1 0 1 2 3 t(s)
17.6 Find the trigonometric Fourier series for f(t) = {1 50 < < and f(t+2) = f(t). 10, <
17.5 Obtain the Fourier series expansion for the waveform shown in Fig. 17.49. z(t) 2 -I 0 2 3 t -4 (a)
Find the Fourier series expansion of the backward sawtooth waveform of Fig. 17.48. Obtain the amplitude and phase spectra. f(t) 10 -4 -2 0 2 4 6 t
Give the Fourier coefficients a0, an, and bn of the waveform in Fig. 17.47. Plot the amplitude and phase spectra. g(t) 10 5 -4-3-2-1 0 1 2 3 4 5 6 t
Using MATLAB, synthesize the periodic waveform for which the Fourier trigonometric Fourier series is f(1) = 12 - 11 (cos 1 + 1/1 cos COS cos 31+ 25 cos 5t + ...)
Evaluate each of the following functions and see if it is periodic. If periodic, find its period.(a) f(t) = cos πt + 2 cos 3πt + 3 cos 5πt (b) y(t) = sin t + 4 cos 2 π t (c) g(t) = sin 3t cos 4t (d) h(t) = cos2 t (e) z(t) = 4.2 sin(0.4πt + 10°)+ 0.8 sin(0.6πt + 50°)(f) p(t) = 10(g)
17.10 The instrument for displaying the spectrum of a signal is known as:(a) oscilloscope(b) spectrogram(c) spectrum analyzer(d) Fourier spectrometer
17.9 When the periodic voltage 2 + 6 sin ω0t is applied to a 1-Ω resistor, the integer closest to the power (in watts)dissipated in the resistor is:(a) 5(b) 8(c) 20(d) 22(e) 40
17.8 The plot of ∣cn∣ versus nω0 is called:(a) complex frequency spectrum(b) complex amplitude spectrum(c) complex phase spectrum
17.7 The function in Fig. 17.14 is half-wave symmetric.(a) True(b) False
17.6 If f(t) = 10 + 8 cos t + 4 cos 3t + 2 cos 5t + …, the angular frequency of the 6th harmonic is(a) 12(b) 11(c) 9(d) 6(e) 1
17.5 If f(t) = 10 + 8 cos t + 4 cos 3t + 2 cos 5t + …,the magnitude of the dc component is:(a) 10(b) 8(c) 4(d) 2(e) 0
17.4 Which of the following are odd functions?(a) sin t + cost (b) t sin t (c) t ln t (d) t 3 cos t (e) sinh t
17.3 Which of the following are even functions?(a) t + t 2(b) t 2 cost (c) e t 2(d) t 2 + t 4(e) sinh t
17.2 If f(t) = t, 0 < t < π, f(t + nπ) = f(t), the value of ω0 is(a) 1(b) 2(c) π (d) 2π
17.1 Which of the following cannot be a Fourier series? (a)1-+-+ 5 (b) 5 sint + 3 sin 2t - 2 sin 31 + sin 4t (c) sint-2 cos 3t+4 sin 4t + cos 4t (d) sin + 3 sin 2.71-cos t +2 tant -2x (e) 1+e+ e -j3xt e 2 3
16.105 If the input voltage in the circuit of Fig. 17.24 is determine the response io(t). COS nt - sin nt) V (0) n +1 + = (D)a
16.105 If the sawtooth waveform in Fig. 17.9 (see Practice Prob. 17.2) is the voltage source vs(t) in the circuit of Fig. 17.22, find the response vo(t). vs(t) ( Figure 17.22 202 ww + 1F vo(t)
16.105 Determine the Fourier series of the function in Fig. 17.12(a). TakeA = 5 and T = 2π.
16.105 Calculate the Fourier series for the function in Fig. 17.17. f(t) A 1 -1 0 1 2 3 4 t -1 Figure 17.17
16.105 Find the Fourier series expansion of the function in Fig. 17.16. f(t) A 8 -2x 0 2 4x t
16.105 Determine the Fourier series of the sawtooth waveform in Fig. 17.9. f(t) im. -2 -1 0 1 2 3 t
16.105 A gyrator is a device for simulating an inductor in a network. A basic gyrator circuit is shown in Fig. 16.113. By finding Vi(s)∕Io(s), show that the inductance produced by the gyrator is L = CR2 . R R ww +1 ww R ww C + tio R
16.104 A certain network has an input admittance Y(s). The admittance has a pole at s = −3, a zero ats = −1, and Y(∞) = 0.25 S.(a) Find Y(s).(b) An 8-V battery is connected to the network via a switch. If the switch is closed at t = 0, find the current i(t) through Y(s) using the Laplace
16.103 Obtain the transfer function of the op amp circuit in Fig. 16.112 in the form ofwhere a, b, and c are constants. Determine the constants. V(s) as V(s) s+bs+c
16.101 Realize the transfer functionusing the circuit in Fig. 16.110. Let Y1 = sC1,Y2 = 1∕R1, Y3 = sC2. Choose R1 = 1 kΩ and determine C1 and C2. Vo(s) S V(s) s+ 10
16.102 Synthesize the transfer functionusing the topology of Fig. 16.111. Let Y1 = 1∕R1,Y2 = 1∕R2, Y3 = sC1, Y4 = sC2. Choose R1 = 1 kΩand determine C1, C2, and R2. Vo(s) Vin(S) 106 +100s+106
16.100 Design an op amp circuit, using Fig. 16.109, that will realize the following transfer function: V(s) s+ 1000 V(s) 2(s + 4000)
16.99 It is desired to realize the transfer functionusing the circuit in Fig. 16.108. Choose R = 1 kΩ and find L and C. V(s) 2s V(s)+2s+6
16.98 Determine whether the op amp circuit in Fig. 16.107 is stable. C R R ww ww + (+1) S Vs o + -
16.97 A system is formed by cascading two systems as shown in Fig. 16.106. Given that the impulse responses of the systems areh1(t) = 3e−t u(t), h2(t) = e−4t u(t)(a) Obtain the impulse response of the overall system.(b) Check if the overall system is stable. h(t) h(t) Vo
16.96 Show that the parallel RLC circuit shown in Fig. 16.105 is stable. R www C L HH
16.83 Refer to the RL circuit in Fig. 16.101. Find:(a) the impulse response h(t) of the circuit.(b) the unit step response of the circuit. L ell +1 Vs + R Vo
16.88 Develop the state equations for the circuit shown in Fig. 16.102. V(t) (+1) F + vo(t) 1 H m 292 +1 +v(t)
16.87 Develop the state equations for the problem you designed in Prob. 16.13.
16.86 Develop the state equations for Prob. 16.12.
16.85 A circuit has a transfer functionFind the impulse response. H(s) = S+4 (s + 1)(s + 2)
16.84 A parallel RL circuit has R = 4 Ω and L = 1 H. The input to the circuit is is(t) = 2e−t u(t) A. Find the inductor current iL(t) for all t > 0 and assume that iL(0) = −2 A.
16.95 Given the following state equation, solve for y1(t)and y2(t). -2 [+] x= 2 -2 -21 y= 1 x+ x+ 2 u(t) 2u(t). u(t) 2u(t).
16.94 Given the following state equation, solve for y(t): x= -4 4 -2 0 y(t)= [10]x x+ [] u(t)
16.93 Develop the state equations for the following differential equation. dy(t) 6dy(t) 11 dy(t) + + dt dr dt +6y(t) = z(t)
16.92 Develop the state equations for the following differential equation. dz(t) +9y(t) = + z(t) dt dt d'y(t) 7 dy(t) dt +
16.91 Develop the state equations for the following differential equation. d'y(t) 6 dy(t) dr + + 7y(t) = z(1) dt
16.82 Calculate the gain H(s) = Vo∕Vs in the op amp circuit of Vs (+1 + R Vo C www
16.81 For the op-amp circuit in Fig. 16.99, find the transfer function, T(s) = I(s)/Vs(s). Assume all initial conditions are zero. Vs(t) + R C + ww 7 lio(t) ell
16.80 Refer to the network in Fig. 16.98. Find the following transfer functions:(a) H1(s) = Vo(s)∕Vs(s)(b) H2(s) = Vo(s)∕Is(s)(c) H3(s) = Io(s)∕Is(s)(d) H4(s) = Io(s)∕Vs(s) Vs 1 192 1H www m + 1 F 1F 192 vo (+1)
16.79 For the circuit in Fig. 16.97, find: (a) I/Vs (b) 12/Vx 302 2 H ww + m 0.5 F Vs Vx +1 4vx
16.78 The transfer function of a certain circuit isFind the impulse response of the circuit. 5 3 6 H(s) = + s+1 s+2 S+4
16.77 Obtain the transfer function H(s) = Vo∕Vs for the circuit of Fig. 16.96. i 0.5 F 1 H m + 2i 3 (+1) S Vs
16.76 For the circuit in Fig. 16.95, find H(s) = Vo(s)∕Vs(s).Assume zero initial conditions. Kvs 202 1 H wwwm + 492 0.1 F
16.75 When a unit step is applied to a system at t = 0, its response isy(t) = [4 + 0.5 e−3t − e−2t (2 cos 4t + 3 sin 4t)]u(t)What is the transfer function of the system?
16.74 Design a problem to help other students better understand how to find outputs when given a transfer function and an input.
16.73 When the input to a system is a unit step function, the response is 10 cos 2tu(t). Obtain the transfer function of the system.
16.72 The transfer function of a system is H(s) = 3s+1 Find the output when the system has an input of 4e-1/u(t).
16.71 For the ideal transformer circuit in Fig. 16.94,determine io(t). 10e-tu(t) V 192 1:2 0.25 F 8
16.70 Using Fig. 16.93, design a problem to help other students better understand how to do circuit analysis with circuits that have mutually coupled elements by working in the s-domain. vs(t) R ww 4 ell M (+1) ell L2 R + vo
16.69 Find I1(s) and I2(s) in the circuit of Fig. 16.92 2 HV m 1H 2H 2 m 10e-3tu(t) V ( 1 1
16.68 Obtain V0/Vs in the op amp circuit in Fig. 16.91. vs(t) 60 www 10 pF +1 60 www + 20 pF vo(t)
16.67 Given the op amp circuit in Fig. 16.90, ifv1(0+) = 2 V and v2(0+) = 0 V, find v0 for t > 0.Let R = 100 kΩ and C = 1 μF. C R www + C V + V2 R www + vo
16.66 For the op amp circuit in Fig. 16.89, find v0(t) fort > 0. Take vs = 3e−5t u(t) V. 20 +1 S 10 ww 50 F
16.65 For the RLC circuit shown in Fig. 16.88, find the complete response if v(0) = 2 V when the switch is closed. 2 cos 4t V(+ t=0 602 1H wwm 619 TI 1 < +
16.64 The switch in Fig. 16.87 moves from position 1 to position 2 at t = 0. Find v(t), for all t > 0. 12 V (+1 t=0 2, 0.25 H 10 mF +
16.63 Consider the parallel RLC circuit of Fig. 16.86. Findv(t) and i(t) given that v(0) = 5 V and i(0) = −2 A. 4u(t) A 10 4H FL -18 m 1+
16.62 Using Fig. 16.85, design a problem to help other students better understand solving for node voltages by working in the s-domain is www V ell 7 m R V2 R C
16.61 Find the voltage v o(t) in the circuit of Fig. 16.84 by means of the Laplace transform. 12 www 1 H m 10u(t) A 0.5 F 202 1F +21
16.60 Find the response vR(t) for t > 0 in the circuit in Fig. 16.83. Let R = 3 Ω, L = 2 H, and C = 1/18 F. 10u(t) V (+ R www + VR C m
16.59 Find vo(t) in the circuit of Fig. 16.82 if vx(0) = 2 V and i(0) = 1 A. e-tu(t) A 1 www + 1x Vx - 1F 192 1H ell
16.58 Using Fig. 16.81, design a problem to help other students better understand circuit analysis in thes-domain with circuits that have dependent sources. Vs +1 R www ki ell C +
16.57 (a) Find the Laplace transform of the voltage shown in Fig. 16.80(a). (b) Using that value of vs(t) in the circuit shown in Fig. 16.80(b), find the value of vo(t). vs(t) 3 V vs(t) +1 1s (a) t 192 m 1F (b) + Vo(t)
16.56 Calculate io(t) for t > 0 in the network of Fig. 16.79. 1F 2e-tu(t) V (+ io 1H m 192 4u(t) A 192
16.55 Obtain i1 and i2 for t > 0 in the circuit of Fig. 16.78. 4u (t) A ww 1 H 302 ww m 12 1 H
16.54 The switch in Fig. 16.77 has been in position 1 fort t = 0, it is moved from position 1 to the top of the capacitor at t = 0. Please note that the switch is a make before break switch; it stays in contact with position 1 until it makes contact with the top of the capacitor and then breaks
16.53 In the circuit of Fig. 16.76, the switch has been in position 1 for a long time but moved to position 2 att = 0. Find:(a) v(0+), dv(0+)/dt (b) v(t) for t ≥ 0. 2 1 8 ww t=0 + 0.25 H 0.5 V 1 F 4 V (+1)
16.52 If the switch in Fig. 16.75 has been closed for a long time before t = 0 but is opened at t = 0, determine ix and vR for t > 0. 16 V Figure 16.75 (+1) t=0 + 8 VR 12 FL -18 ele 1 H
16.51 In the circuit of Fig. 16.74, find i(t) for t > 0. t=0 www 60 492 ww 50 V 114
16.50 For the circuit in Fig. 16.73, find v(t) for t > 0.Assume that v (0+) = 4 V and i(0) = 2 A. 0.1 F +A1 202 www -14 0.5 F
16.49 Find i0(t) for t > 0 in the circuit in Fig. 16.72. 5e-2t u(t) V 202 www +1- ww (+1) 1F 192 0.5% +1 +1 1H m 3[1-u(t)] V
16.48 Find Vx(s) in the circuit shown in Fig. 16.71. 3 0.25 H m 0.2 F 10 www Vx +1 (+1 5e-2t u(t)V
16.47 Determine io(t) in the network shown in Fig. 16.70 5 + 10u(t) V 12 ww 42 ww 2 H F LL -14
16.46 Determine io(t) in the circuit in Fig. 16.69. 202 1 F 2 H m e-2tu(t) A 1
16.45 Find v(t) for t > 0 in the circuit in Fig. 16.68. io R www t=0 -
16.44 For the circuit in Fig. 16.67, find i(t) for t > 0. 30 V + 10 www 6u(t) A 10 mF: www 40 li(t) 4 H
16.43 Determine i(t) for t > 0 in the circuit of Fig. 16.66. 12 V(+ (+1) 492 ww t=0 i(t) 5HF 53
16.42 Given the circuit in Fig. 16.65, find i(t) and v(t)for t > 0. i(t) 1 H m 192 +1 12 V(+ t=0 114 LL + v(t) -
16.41 Find the output voltage vo(t) in the circuit of Fig. 16.64. 3 A 5 t=0 www 10 + 1 H 10 mF Vo

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