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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

A circuit has R1 = 3 Ω, R2 = 10 Ω, L = 2H and C = 1/10F. After the circuit is magnitude-scaled by 100 and frequency-scaled by 106, find the new values of the circuit elements.
In an RLC circuit, R = 20 Ω, L = 4 H and C = 1 F. The circuit is magnitude-scaled by 10 and frequency-scaled by 10 5. Calculate the new values of the elements.
Given a parallel RLC circuit with R = 5 k Ω, L = 10 mH, and C = 20 μF, if the circuit is magnitude-scaled by Km = 500 and frequency-scaled by Kf = 105, find the resulting values of R, L, and C.
A series RLC circuit has R = 10 Ω, ω0 = 40 rad/s, and B = 5 rad/s. Find L and C when the circuit is scaled: (a) In magnitude by a factor of 600, (b) In frequency by a factor of 1,000, (c) In
Redesign the circuit in Fig. 14.85 so that all resistive elements are scaled by a factor of 1,000 and all frequency-sensitive elements are frequency-scaled by a factor of 104.
*Refer to the network in Fig. 14.96.(a) Find Zin (s).(b) Scale the elements by Km = 10 and Kf = 100. Find Zin (s) and Ï‰0.Figure 14.96
Determine the magnitude (in dB) and the phase (in degrees) of H(ω) = at ω = 1 if H(ω) equals (a) 0.05 dB (b) 125 (c) 10 fω/2 + jω (d) 3/1 + j ω + 6/2 + jω
(a) For the circuit in Fig. 14.97, draw the new circuit after it has been scaled by Km = 200 and Kf = 104.(b) Obtain the Thevenin equivalent impedance at terminals a-b of the scaled circuit at
The circuit shown in Fig. 14.98 has the impedanceFind:(a) The values of R, L, C, and G(b) The element values that will raise the resonant frequency by a factor of 10 3 by frequency scalingFigure 14.98
Scale the lowpass active filter in Fig. 14.99 so that its corner frequency increases from 1 rad/s to 200 rad/s. Use a 1-Î¼ F capacitor.Figure 14.99
The op amp circuit in Fig. 14.100 is to be magnitude-scaled by 100 and frequency-scaled by 105. Find the resulting element values.Figure 14.100
Using PSpice, obtain the frequency response of the circuit in Fig. 14.101 on the next page.Figure 14.101
Use PSpice to obtain the magnitude and phase plots of V0 /I s of the circuit in Fig. 14.102.Figure 14.102
Use PSpice to provide the frequency response (magnitude and phase of i) of the circuit in Fig. 14.103. Use linear frequency sweep from 1 to 10,000 Hz.Figure 14.103
In the interval 0.1 Figure 14.104
Use PSpice to generate the magnitude and phase Bode plots of V0 in the circuit of Fig. 14.105.Figure 14.105
Obtain the magnitude plot of the response V0 in the network of Fig. 14.106 for the frequency interval 100 Figure 14.106
A ladder network has a voltage gain of H(ω) = 10/1 + jω) (10 + jω) Sketch the Bode plots for the gain.
Obtain the frequency response of the circuit in Fig. 14.40 (see Practice Problem 14.10). Take R1 = R2 = 100 Ω, L = 2 mH. Use 1 < f < 100,000 Hz.
For the "tank" circuit of Fig. 14.79, obtain the frequency response (voltage across the capacitor) using PSpice. Determine the resonant frequency of the circuit.
Using PSpice, plot the magnitude of the frequency response of the circuit in Fig. 14.85.
For the phase shifter circuit shown in Fig. 14.107, find H = V o /V s .Figure 14.107
For an emergency situation, an engineer needs to make an RC highpass filter. He has one 10-pF capacitor, one 30-pF capacitor, one 1.8-k Ω resistor, and one 3.3-k Ω resistor available. Find the
A series-tuned antenna circuit consists of a variable capacitor (40 pF to 360 pF) and a 240-μ H antenna coil that has a dc resistance of 12 Ω. (a) Find the frequency range of radio signals to which
The crossover circuit in Fig. 14.108 is a lowpass filter that is connected to a woofer. Find the transfer function H(Ï‰) = Vo (Ï‰ )/Vi (Ï‰)Figure 14.108
The crossover circuit in Fig. 14.109 is a highpass filter that is connected to a tweeter. Determine the transfer function H(Ï‰) = Vo (Ï‰)/Vi (Ï‰).Figure 14.109
A certain electronic test circuit produced a resonant curve with half-power points at 432 Hz and 454 Hz. If Q = 20, what is the resonant frequency of the circuit?
In an electronic device, a series circuit is employed that has a resistance of 100 Ω, a capacitive reactance of 5 k Ω , and an inductive reactance of 300 Ω when used at 2 MHz. Find the resonant
Find the Laplace transform of: (a) Cosh at (b) Sinh at
In two different ways, find the Laplace transform of G(t) = d/dt (te-t cost)
Find F(s) if: (a) f (t) = 6e−t cosh 2t (b) f (t) = 3te−2t sinh 4t (c) f (t) = 8e−3t cosh tu(t − 2)
Find the Laplace transform of the following functions: (a) t cos t u (t) (b) e-t t sin t u (t) (c) sin βt/t u(t)
Find the Laplace transform of the signal in Fig. 15.26.
Determine the Laplace transform of the function in Fig. 15.27.
Find the Laplace transform of f(t) shown in Fig. 15.29.
Obtain the Laplace transforms of the functions in Fig. 15.30.
Determine the Laplace transform of: (a) Cos(ωt +θ) (b) Sin(ωt +θ)
The periodic function shown in Fig. 15.32 is defined over its period asFind G(s)
Obtain the Laplace transform of the periodic waveform in Fig. 15.33.
Find the Laplace transforms of the functions in Fig. 15.34.
Determine the Laplace transforms of the periodic functions in Fig. 15.35.
Given that F(s) = s2 + 10s + 6 / s(s + 1)2 (s + 3) Evaluate f(0) and f (∞) if they exist.
Let F(s) = 5(s + 1)/(s + 2) (s + 3) (a) Use the initial and final value theorems to find f(0) and f (∞). (b) Verify your answer in part (a) by finding f(t), using partial fractions.
Determine the initial and final values of f(t), if they exist, given that:(a)(b)
Determine the inverse Laplace transform of each of the following functions: (a) F(s) = 1/s + 2/s + 1 (b) G(s) = 3s + 1/s + 4 (c) H(s) = 4/(s + 1) (s + 3) (d) J(s) = 12/(s + 2)2(s + 4)
Find the inverse Laplace transform of the following functions: (a) F(s) = 20(s + 2)/s(s2 + 6s + 25) (b) P(s) = 6s2 + 36s + 20/(s + 1) (s + 2)(s + 3)
Find the inverse Laplace transform of: V(s) = 2s + 26/s(s2 + 4s + 13)
Obtain the Laplace transform of each of the following functions: (a) e−2t cos3tu(t) (b) e−2t sin 4tu(t) (c) e−3t cosh 2tu(t) (d) e−4t sinh tu(t) (e) te−t sin 2tu(t)
Find the inverse Laplace transform of: (a) F1(s) = 6s2 + 8s + 3/s(s2 + 2s + 5) (b) F2(s) = s2 + 5s + 6/(s + 1)2 (s + 4) (c) F3(s) = 10/(s + 1) (s2 + 4s + 8)
Find f(t) for each F(s): (a) 10s/(s + 1) (s + 2) (s + 3) (b) 2s2 + 4s + 1 / (s + 1) (s + 2)3 (c) s + 1 / (s + 2) (s2 + 2s + 5)
Determine the inverse Laplace transform of each of the following functions:(a)(b)(c)
Calculate the inverse Laplace transform of: (a) 6(s-1)/s4 - 1 (b) se- πt / s2 + 1 (c) 8 / s(s + 1)3
Find the time functions that have the following Laplace transforms:(a)(b)(c)
Obtain f(t) for the following transforms:(a)(b)(c)
Obtain the inverse Laplace transforms of the following functions:(a)(b) Y(s) = 1/s(s + 1)2(c) Z(s) 1/s(s + 1) (s2 + 6s + 10)
Find the inverse Laplace transform of:(a)(b)(c)(d)
Find f(t) given that: (a) F(s) = S2 + 4s/s2 + 10s+ 26 (b) F(s) = 5s2 + 7s + 29 / s(s2 + 4s + 29)
*Determine f(t) if:(a)(b)
Find the Laplace transforms of the following: (a) g(t) = 6cos(4t −1) (b) f (t) = 2tu(t)+ 5e−3(t−2)u(t − 2)
* Let x(t) and y(t) be as shown in Fig. 15.36. Find z(t) = x(t)* y(t).
Suppose that f (t) = u(t)− u(t − 2). Determine f (t)* f (t).
Find y(t) = x(t)* h(t) for each paired x(t) and h(t) in Fig. 15.37.
Obtain the convolution of the pairs of signals in Fig. 15.38.
Given h(t) = 4e−2tu(t) and x(t) = δ (t)− 2e−2tu(t), find y(t) = x(t)* h(t).
Given the following functions x(t) = 2δ (t), y(t) = 4u(t), z(t) = e−2tu(t), evaluate the following convolution operations. (a) x(t)* y(t) (b) x(t)* z(t) (c) y(t)* z(t) (d) y(t)*[y(t)+ z(t)]
A system has the transfer function H(s) = s/(s + 1) (s + 2) (a) Find the impulse response of the system. (b) Determine the output y(t), given that the input is x(t) = u(t)
Find f(t) using convolution given that: (a) F(s) = 4/(s2 + 2s + 5)2 (b) F(s) = 2s / (s + 1) (s2 + 4)
* Use the convolution integral to find: (a) t *eatu(t) (b) cos(t)* cos(t)u(t) * An asterisk indicates a challenging problem.
Find the Laplace transform of each of the following functions: (a) t2 cos (2t + 30°)u(t) (b) 3t4e-2t u(t) (c) 2tu(T) - 4 d/dt δ(t) (d) 2e-(t-1) u(t) (e) 5u(t/2) (f) 6e-t/3 u(t) (g) dn/dtn δ(t)
Use the Laplace transform to solve the differential equation D2v(t)/dt2 + 2dv(t)/dt + 10v(t) = 3 cos 2t subject to v(0) = 1, dv(0)/ dt = −2 .
Given that v(0) = 2 and dv(0)/ dt = 4 , solve
Use the Laplace transform to find i(t) for t > 0 ifi(0) = 0 , i'(0) = 3
* Use Laplace transforms to solve for x(t) in* An asterisk indicates a challenging problem.
Using the Laplace transform, solve the following differential equation forSubject to i(0) = 0,i€²(0) = 2 .
Solve for y(t) in the following differential equation if the initial conditions are zero.
Solve for v(t) in the integrodifferential equationGiven that v(0) = 2.
Solve the following integrodifferential equation using the Laplace transform method:
Given thatwith v(0) = ˆ’1, determine v(t) for t > 0 .
Solve the integrodifferential equation
Find F(s) given that
Solve the following integrodifferential equation
Find the Laplace transform of the following signals: (a) f (t) = (2t + 4)u(t) (b) g(t) = (4 + 3e−2t)u(t) (c) h(t) = (6sin(3t)+ 8cos(3t))u(t) (d) x(t) = (e−2t cosh(4t))u(t)
Find the Laplace transform F(s), given that f(t) is: (a) 2tu(t − 4) (b) 5cos(t)δ (t − 2) (c) e−tu(t − t) (d) sin(2t)u(t −τ )
Determine the Laplace transforms of these functions: (a) f (t) = (t − 4)u(t − 2) (b) g(t) = 2e−4tu(t −1) (c) h(t) = 5cos(2t −1)u(t) (d) p(t) = 6[u(t − 2)− u(t − 4)]
Determine i(t) in the circuit of Fig. 16.35 by means of the Laplace transform.
Use Thevenin's theorem to determine v0 (t), t > 0 in the circuit of Fig. 16.44.
Solve for the mesh currents in the circuit of Fig. 16.45. You may leave your results in the s-domain.
Find vo (t) in the circuit of Fig. 16.46.
Determine i0 (t) in the circuit of Fig. 16.47.
* Determine i0 (t) in the network shown in Fig. 16.48.
Find Vx (s) in the circuit shown in Fig. 16.49.
* Find i0 (t) for t > 0 in the circuit of Fig. 16.50.
Calculate i0 (t) for t > 0 in the network of Fig. 16.51.
(a) Find the Laplace transform of the voltage shown in Fig. 16.52(a).(b) Using that value of vs (t) in the circuit shown in Fig. 16.52(b), find the value of v0 (t).
In the circuit of Fig. 16.53, let i(0) = 1 A, v0 (0) and v s = 4eˆ’2t u(t) V. Find v0 (t) for t > 0.
Find vx in the circuit shown in Fig. 16.36 given vs .= 4u(t)V.
Find v 0 (t) in the circuit of Fig. 16.54 if v x (0) = 2 V and i(0) = 1A.
Find the voltage v 0 (t) in the circuit of Fig. 16.55 by means of the Laplace transform.
Find the node voltages v1 and v2 in the circuit of Fig. 16.56 using the Laplace transform technique. Assume that is = 12eˆ’t u(t) A and that all initial conditions are zero.
Consider the parallel RLC circuit of Fig. 16.57. Find v(t) and i(t) given that v(0) = 5 and i(0) = -2 A.

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