Questions and Answers of Schaum S Outline Of Electric Circuits

Find the Laplace transform of each of the following functions.(a) f(t) = At(b) f(t) = te−at(c) f(t) = e−at sin ωt(d) f(t) = sinh ωt(e) f(t) = cosh ωt(f) f(t) = e−at sinh ωt
Find the Laplace transform of e−at cosω t, where a is a constant.
Find the Laplace transform of x(t) = 3e2tu(t) and show the region of convergence. 100 3 X(s) = e Nd dt 3 = [[³0²³²0 * d₁ = [[^³x²=²2³4r = _ _ yle=" -²=² ¹dt (x-2)t S- -2 0 s-2' Re[s]> 2
In Example 16.1,Data from Example 16.1Consider a series RL circuit, with R = 5 Ω and L = 2.5 mH. At t = 0, when the current in the circuit is 2 A, a source of 50 V is applied. The time-domain
If L [f(t)] = F(s), show that L = [e−atf(t)] = F(s + a). Apply this result to Problem 16.1.Data from problem 16.1Find the Laplace transform of e−at cosω t, where a is a constant.
A series RL circuit, with R = 10 Ω and L = 0.2 H, has a constant voltage V = 50 V applied at t = 0. Find the resulting current using the Laplace transform method.
Find न g 1 _s(sa)
Find the Laplace transform of f(t) = 1 − e−at, where a is a constant.
In the series RL circuit of Fig. 16-19, the switch is in position 1 long enough to establish the steady state and is switched to position 2 at t = 0. Find the current. 50 V (+ N Fig. 16-19 ' 10
Find the time-domain current i(t) if its Laplace transform is I(s) = s-10 s+ + s² 4 2 S
Find L-¹ s +1 s(s² + 4s + 4)
In the circuit shown in Fig. 16-20, switch 1 is closed at t = 0 and then, at t = t′ = 4 ms, switch 2 is opened. Find the current in the intervals 0 t′. 100 V (+ 50 Ω 100 Ω U. Fig. 16-20 0.1
In the circuit shown in Fig. 16-4(a) an initial current i1 is established while the switch is in position 1.At t = 0, it is moved to position 2, introducing both a capacitor with initial charge Q0
In the series RL circuit shown in Fig. 16-21, the switch is closed at position 1 at t = 0 and then, at t = t′ = 50 μs, it is moved to position 2. Find the current in the intervals 0 t′. 100 V
In the series RC circuit of Fig. 16-5, the capacitor has an initial charge of 2.5 mC. At t = 0, the switch is closed and a constant-voltage source V = 100 V is applied. Use the Laplace transform
Find the current developed in a series RLC circuit in response to the following two voltage sources applied to it at t = 0:(a) A unit-step,(b) A unit-impulse.
A series RC circuit, with R = 10 Ω and C = 4 μF, has an initial charge Q0 = 800 μC on the capacitor at the time the switch is closed, which results in applying a constant-voltage source V = 100 V.
Find the voltage across the terminals of a parallel RLC circuit in response to the following two current sources applied at t = 0:(a) A unit-step,(b) A unit-impulse.
In the RL circuit shown in Fig. 16-6, the switch is in position 1 long enough to establish steady-state conditions, and at t = 0 it is switched to position 2. Find the resulting current. +1 50 V
In the series RL circuit of Fig. 16-7, an exponential voltage v = 50 e−100t (V) is applied by closing the switch at t = 0. Find the resulting current. Ο Fig. 16-7 10 Ω 0.2 Η
A series RC circuit, with R = 1 kΩ and C = 20 μF, has an initial charge Q0 on the capacitor at the time the switch is closed, which results in applying a constant-voltage source V = 50 V. If the
In the RC circuit shown in Fig. 16-22, the switch is closed at position 1 at t = 0 and then, at t = t′ = τ (the time constant), is moved to position 2. Find the transient current in the intervals
The series RC circuit of Fig. 16-8 has a sinusoidal voltage source v = 180 sin (2000t + Φ) (V) and an initial charge on the capacitor Q0 = 1.25 mC with polarity as shown. Determine the current if
In the circuit of Fig. 16-23, Q0 = 300 µC at the time the switch is closed. Find the resulting current transient. 6 μF Qo ww 20 Ω Fig. 16-23 3 μF
In the series RL circuit of Fig. 16-9, the source is u = 100 sin (500t + Φ) (V). Determine the resulting current if the switch is closed at a time corresponding to Φ = 0°. 2 Fig. 16-9 5 Ո 0.01 H
In the circuit shown in Fig. 16-24, the capacitor has an initial charge Q0 = 25 µC and the sinusoidal voltage source is v = 100 sin (1000t + Φ) (V). Find the resulting current if the switch is
Rework Problem 16.10 by writing the voltage function asData from Problem 16.10In the series RL circuit of Fig. 16-9, the source is u = 100 sin (500t + Φ) (V). Determine the resulting current if the
In the series RLC circuit shown in Fig. 16-10, there is no initial charge on the capacitor. If the switch is closed at t = 0, determine the resulting current. 50 V + 202 Fig. 16-10 1 H 0.5 F
A series RLC circuit, with R = 5 Ω, L = 0.1 H, and C = 500 µF, has a constant voltage V = 10 V applied at t = 0. Find the resulting current.
In the series RLC circuit of Fig. 16-25, the capacitor has an initial charge Q0 = 1 mC and the switch is in position 1 long enough to establish the steady state. Find the transient current which
In the two-mesh network of Fig. 16-11, the two loop currents are selected as shown. Write the s-domain equations in matrix form and construct the corresponding circuit. i₁ 50 2 F Fig. 16-11 2
In the two-mesh network of Fig. 16-13, find the currents which result when the switch is closed. 100 V (+ 10 Ω Fig. 16-13 0.02 H 50
A series RLC circuit, with R = 5 Ω, L = 0.2 H, and C = 1 F has a voltage source v = 10e−100t (V) applied at t = 0. Find the resulting current.
Apply the initial- and final-value theorems to Problem 16.14.Data from problem 16.14In the two-mesh network of Fig. 16-13, find the currents which result when the switch is closed. 100 V (+ 10
A series RLC circuit, with R = 200 Ω, L = 0.5 H, and C = 100 µF has a sinusoidal voltage source u = 300 sin (500t + f) (V). Find the resulting current if the switch is closed at a time
Solve for i1 in Problem 16.14 by determining an equivalent circuit in the s-domain.Data from problem 16.14In the two-mesh network of Fig. 16-13, find the currents which result when the switch is
A series RLC circuit, with R = 5 Ω, L = 0.1 H, and C = 500 µF has a sinusoidal voltage source u = 100 sin 250t (V). Find the resulting current if the switch is closed at t = 0.
In the two-mesh network of Fig. 16-26, the currents are selected as shown in the diagram. Write the time-domain equations, transform them into the corresponding s-domain equations, and obtain the
In the two-mesh network shown in Fig. 16-15 there is no initial charge on the capacitor. Find the loop currents i1 and i2 which result when the switch is closed at t = 0. 50 v + 10 i Fig.
Referring to Problem 16.17, obtain the equivalent impedance of the s-domain network and determine the total current and the branch currents using the current-division rule.Data from Problem 16.17In
For the two-mesh network shown in Fig. 16-27, find the currents i1 and i2 which result when the switch is closed at t = 0. 50 V (+ 5 Ω i₁ 20 μF Fig. 16-27 5 Ω 0.1 H
In the network of Fig. 16-18 the switch is closed at t = 0 and there is no initial charge on either of the capacitors. Find the resulting current i. 50 V (+ 10 (2 Fig. 16-18 1 F 5 Ω 0.5 F {50
In the network shown in Fig. 16-28, the 100-V source passes a continuous current in the first loop while the switch is open. Find the currents after the switch is closed at t = 0. 100 V (+ US i₁ 10
Apply the initial- and final-value theorems to the s-domain current of Problem 16.19.Data from Problem 16.19In the network of Fig. 16-18 the switch is closed at t = 0 and there is no initial charge
The two-mesh network shown in Fig. 16-29 contains a sinusoidal voltage source v = 100 sin (200t + Φ) (V). The switch is closed at an instant when the voltage is increasing at its maximum rate. Find
In the circuit of Fig. 16-30, v(0) = 1.2 V and i(0) = 0.4 A. Find v and i for t > 0. 1Η Μ ww 3Ω ΖΩ Fig. 16-30 1F ν
In the circuit of Fig. 16-31, Find v and i for t > 0 and compare with results of Problems 16.41 and 16.42.Data from problem 16.41In the circuit of Fig. 16-30, v(0) = 1.2 V and i(0) = 0.4 A. Find
In the circuit of Fig. 16-31, ig(t) = cos tv(t). Find v and i. 1Η ww 3 Ω Ω Ο ΖΩ Fig. 16-31 1F = + U
Find capacitor voltage v(t) in the circuit shown in Fig. 16-32. i, (A). 10 5 V + is Fig. 16-32 292 -14 0.1 F
Find inductor current i(t) in the circuit shown in Fig. 16-32. i, (A) 4 10 ν + εἰς Fig. 16-32 200 m ΖΩ 01 F
Find the trigonometric Fourier series for the square wave shown in Fig. 17-18 and plot the line spectrum. ( -V TT 2п Fig. 17-18 3п шт
Synthesize the waveform for which the trigonometric Fourier series is f(t)=- sincor-sin 3eur+sin 50or - sin 7eur + 70t ++...} 49 8V π
Find the Fourier series for the waveform shown in Fig. 17-2. 10 0 2πT Fig. 17-2 4T wt
Find the trigonometric Fourier series for the triangular wave shown in Fig. 17-20 and plot the line spectrum. - п 0 2п Fig. 17-20 TT Зп cot
Synthesize the waveform if its Fourier series is 40 1 1 f(1) = 5-4 (cosat +cos 3wt +- cos 50t +...) 25 I 20 1 1 1 + (sin cotsin 20t+ sin 30t-sin. sin 40t +...) T
Derive the exponential series (9) from the trigonometric series (1). f(t) = a + a, cosat +a, cos 2t + a cos 3wt + + b, sinoot + b₂ sin 200t + b3 sin 300t +... .. (1)
Synthesize the waveform for the given Fourier series. 1 V(ZT 1 2π Л f(t) = V +sin -sin cot -cos@t - 2 3π 1 377 cos 20t + -sin 200t + 4 15 1 2π -sin 40t cos 30t ..) 1 15 cos 40t 1 бл -cos60t +..
Find the trigonometric Fourier series for the sawtooth wave shown in Fig. 17-22 and plot the line spectrum. TT на TT 2п Fig. 17-22 Зп wf
Find the exponential Fourier series for the waveform shown in Fig. 17-2. Using the coefficients of this exponential series, obtain an and bn of the trigonometric series and compare with Example
Find the trigonometric Fourier series for the sawtooth wave shown in Fig. 17-39 and plot the line spectrum. Compare with Example 17.1.Data from Example 17.1Find the Fourier series for the waveform
Find the trigonometric Fourier series for the waveform shown in Fig. 17-24 and sketch the line spectrum. И V TT 2п Зп Fig. 17-24 4 п wl
In Fig. 17-8, the sawtooth wave of Example 17.1 and its line spectrum are shown. Since there were only sine terms in the trigonometric series, the harmonic amplitudes are given directly by 1/2 a0 and
Find the trigonometric Fourier series for the sawtooth wave shown in Fig. 17-40 and plot the spectrum. Compare with the result of Problem 17.3.Data from problem 17.3Find the trigonometric Fourier
Find the trigonometric Fourier series for the half-wave-rectified sine wave shown in Fig. 17-26 and sketch the line spectrum. 0 TT 2п Fig. 17-26 Зп cut
A series RL circuit in which R = 5 Ω and L = 20 mH (Fig. 17-11) has an applied voltage v = 100 + 50 sin ωt + 25 sin 3ωt (V), with ω = 500 rad/s. Find the current and the average power.Compute the
Find the trigonometric Fourier series for the waveform shown in Fig. 17-41 and plot the line spectrum. 0 -v- П Сп Fig. 17-41 3п шу
A voltage represented by the triangular wave shown in Fig. 17-12 is applied to a pure capacitor C. Determine the resulting current. TT Vmax 0 - Vmax Fig. 17-12 ㅠ ان
Find the trigonometric Fourier series for the half-wave-rectified sine wave shown in Fig. 17-28, where the vertical axis is shifted from its position in Fig. 17-26. 0 ก TT 2π Fig. 17-26 3π ال
Find the trigonometric Fourier series of the square wave shown in Fig. 17-42 and plot the line spectrum. Compare with the result of Problem 17.1.Data from problem 17.1Find the trigonometric Fourier
Obtain the trigonometric Fourier series for the repeating rectangular pulse shown in Fig. 17-29 and plot the line spectrum. 0 -π/6 7/6 TT Fig. 17-29 1. 2 TT 3
Find the trigonometric Fourier series for the waveforms shown in Fig. 17-43. Plot the line spectrum of each and compare. 10 TT/12 (a) L. 2π ال 10 Fig. 17-43 5π/3 2π (b) I 4T wt
Find the Fourier transform of x(t) = e−atu(t), a > 0. Plot X( f ) for −∞ < f < +∞.
Find the exponential Fourier series for the square wave shown in Figs. 17-18 and 17-31, and sketch the line spectrum. Obtain the trigonometric series coefficients from those of the exponential series
Find the trigonometric Fourier series for the half-wave-rectified sine wave shown in Fig. 17-44 and plot the line spectrum. Compare the answer with the results of Problems 17.5 and 17.6.Data from
Find the Fourier transform of the square pulse x(t) = [1 for-T
Find the Fourier transform of x(t) = eatu(−t), a > 0.
Find the exponential Fourier series for the triangular wave shown in Figs. 17-20 and 17-33 and sketch the line spectrum. TT 0 2 п Fig. 17-20 П Зп wt
Find the inverse Fourier transform of X( f ) = 2a/(a2 + 4π2 f2), a > 0.
Find the trigonometric Fourier series for the full-wave-rectified sine wave shown in Fig. 17-45 and plot the spectrum. 0 T Fig. 17-45 27 ال
Find the exponential Fourier series for the half-wave rectified sine wave shown in Figs. 17-26 and 17-34 and sketch the line spectrum. V 0 TT 2п Fig. 17-26 3п cut
Find the spectrum of x(t) = e−atu(t) − eatu(−t), a > 0, shown in Fig. 17-17. -1 -ear 4x(1) Fig. 17-17 1 e-at t
The waveform in Fig. 17-46 is that of Fig. 17-45 with the origin shifted. Find the Fourier series and show that the two spectra are identical. mm. Fig. 17-45 TT Fig. 17-46 3 πT
Find the average power in a resistance R = 10 Ω, if the current in Fourier series form is i = 10 sin ωt + 5 sin 3ωt + 2 sin 5ωt (A).
Find the trigonometric Fourier series for the waveform shown in Fig. 17-47. ДА. 2п Fig. 17-47 1 27T TT Зп wt
Find and compare the energy contents W1 and W2 of y1(t) = e−|at| and y2(t) = e−atu(t) − eatu(−t), a > 0, within the band 0 to 1 Hz. Let a = 200.
Find the average power supplied to a network if the applied voltage and resulting current are v = 50 + 50 sin5 × 10³t+ 30 sin 10ft +20 sin 2 × 10¹t (V) i = 11.2 sin (5 × 10³ t + 63.4°) + 10.6
Find the trigonometric Fourier series for the waveform shown in Fig. 17-48. Add this series termwise to that of Problem 17.27, and compare the sum with the series obtained in Problem 17.5.Data from
The voltage wave shown in Fig. 17-35 is applied to a series circuit with R = 2 kΩ and L = 10 H. Use the trigonometric Fourier series to obtain the voltage across the resistor. Plot the line spectra
Obtain the constants of the two-element series circuit with the applied voltage and resultant current given in Problem 17.12.Data from problem 17.12Find the average power supplied to a network if the
Find the exponential Fourier series for the waveform shown in Fig. 17-49 and plot the line spectrum. Convert the coefficients obtained here into the trigonometric series coefficients, write the
The current in a 10-mH inductance has the waveform shown in Fig. 17-37. Obtain the trigonometric series for the voltage across the inductance, given that ω = 500 rad/s. 10 0 - 10 Fig. 17-37 2π wl
Find the exponential Fourier series for the waveform shown in Fig. 17-50 and plot the line spectrum. 0 П 2п Fig. 17-50 3п wl
Find the exponential Fourier series for the square wave shown in Fig. 17-51 and plot the line spectrum. Add the exponential series of Problems 17.29 and 17.30 and compare the sum to the series
Find the exponential Fourier series for the sawtooth waveform shown in Fig. 17-52 and plot the spectrum. Convert the coefficients obtained here into the trigonometric series coefficients, write the
Find the exponential Fourier series for the waveform shown in Fig. 17-54 and plot the spectrum. Convert the coefficients to trigonometric series coefficients, write the trigonometric series, and
Find the exponential Fourier series for the waveform shown in Fig. 17-53 and plot the spectrum. Convert the trigonometric series coefficients found in Problem 17.20 into exponential series
Find the exponential Fourier series for the waveform shown in Fig. 17-56 and plot the line spectrum. - 17/6 0 7/6 TT Fig. 17-56 21 ان
Find the exponential Fourier series for the full-wave rectified sine wave shown in Fig. 17-58 and plot the line spectrum. m TT Fig. 17-58 2π 3 ال
A voltage v = 50 + 25 sin 500t + 10 sin 1500t + 5 sin 2500t (V) is applied to the terminals of a passive network and the resulting current is i = 5 + 2.23 sin (500t - 26.6°) + 0.556 sin (1500t -
Find the effective voltage, effective current, and average power supplied to a passive network if the applied voltage is v = 200 + 100 cos (500t + 30°) + 75 cos (1500t + 60°) (V) and the resulting

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