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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

Find the trigonometric Fourier series for
Obtain the complex Fourier coefficients of the signal in Fig. 17.62.
The spectra of the Fourier series of a function are shown in Fig. 17.84. (a) Obtain the trigonometric Fourier series. (b) Calculate the rms value of the function.
The amplitude and phase spectra of a truncated Fourier series are shown in Fig. 17.85.(a) Find an expression for the periodic voltage using the amplitude-phase form. See Eq.(17.10).(b) Is the voltage
Plot the amplitude spectrum for the signal f2(t) 2 f t in Fig. 17.56(b). Consider the first five terms.
Design the LC ladder network terminated with a 1-Ω resistor that has the normalized transfer function (This transfer function is for a Butterworth lowpass filter.)
Given thatplot the first five terms of the amplitude and phase spectra for the function.
Determine the Fourier coefficients for the waveform in Fig. 17.48 using PSpice.
Calculate the Fourier coefficients of the signal in Fig. 17.58 using PSpice.
Use PSpice to find the Fourier components of the signal in Prob. 17.7.
Use PSpice to obtain the Fourier coefficients of the waveform in Fig. 17.55(a).
Determine the Fourier series of the periodic function in Fig. 17.50.
Rework Prob. 17.40 using PSpice.Rework prob. 17.40* The signal in Fig. 17.76(a) is applied to the circuit in Fig. 17.76(b). Find vo(t).
The signal displayed by a medical device can be approximated by the waveform shown in Fig. 17.86. Find the Fourier series representation of the signal.
A spectrum analyzer indicates that a signal is made up of three components only: 640 kHz at 2 V, 644 kHz at 1 V, 636 kHz at 1 V. If the signal is applied across a 10- Ω resistor, what is the average
A certain band-limited periodic current has only three frequencies in its Fourier series representation: dc, 50 Hz, and 100 Hz. The current may be represented as I(t) = 4 + 6 sin 100πt + 8
Design a lowpass RC filter with a resistance R = 2 k Ω. The input to the filter is a periodic rectangular pulse train (see Table 17.3) with A = 1 V, T = 10 ms, and τ = 1 ms. Select C such that the
A periodic signal given by v (t) = 10 Vs for 0
The voltage across a device is given by V(t) = -2 + 10 cos 4t + 8 cos 6t + 6 cos 8t -5 sin 4t - 3 sin 6t - sin 8t V Find: (a) The period of v(t), (b) The average value of v(t), (c) The effective
A certain band-limited periodic voltage has only three harmonics in its Fourier series representation. The harmonics have the following rms values: fundamental 40 V, third harmonic 20 V, fifth
Write a program to compute the Fourier coefficients (up to the 10th harmonic) of the square wave in Table 17.3 with A = 10 and T = 2.
Obtain the exponential Fourier series of the function in Fig. 17.51.
Write a computer program to calculate the exponential Fourier series of the half-wave rectified sinusoidal current of Fig. 17.82. Consider terms up to the 10th harmonic.
Consider the full-wave rectified sinusoidal current in Table 17.3. Assume that the current is passed through a 1- Ω resistor. (a) Find the average power absorbed by the resistor. (b) Obtain cn for n
A band-limited voltage signal is found to have the complex Fourier coefficients presented in the table below. Calculate the average power that the signal would supply a 4- Î© resistor.
Determine the Fourier coefficients an and bn of the first three harmonic terms of the rectified cosine wave in Fig. 17.52.
Obtain the Fourier transform of the function in Fig. 18.26.
Obtain the Fourier transforms of the signals shown in Fig. 18.35.
Find the Fourier transform of the "sine-wave pulse" shown in Fig. 18.36.
Find the Fourier transform of the following signals. (a) f1 (t) = e−3t sin(10t)u(t) (b) f2 (t) = e−4t cos(10t)u(t)
Find the Fourier transform of the following signals: (a) f(t) = cos(at - π /3), - ∞ < t < ∞ (b) g(t) = u(t + 1)sinπ t, - ∞ < t < ∞ (c) h(t) = (1 + A sin at) cos bt, - ∞ < t < ∞ ,
Find the Fourier transforms of these functions: (a) f(t) = e−t cos(3t + π )u(t) (b) g(t) = sin π t[u(t + 1) - u(t - 1)] (c) h(t) = e−2t cos π tu(t - 1) (d) p(t) = e−2t sin 4tu(-t) (e) q(t) =
Find the Fourier transforms of the following functions: (a) f(t) = δ (t +3) - δ (t - 3) (b) f(t) = ∫∞−∞ 2δ (t −1) dt (c) f(t) = δ (3t) - δ'(2t)
Determine the Fourier transforms of these functions: (a) f(t) = 4/t2 (b) g(t) = 8/(4 + t2)
Find the Fourier transforms of: (a) cos 2tu(t) (b) sin 10tu(t)
Given that F(ω) = F[f(t)], prove the following results, using the definition of Fourier transform: (a) F[f(t - t0)] = e-jωt, F(ω) (b) F[df(t)/dt] = jω F(ω) (c) F[f(-t) = F(-ω) (d) F[tf(t)] = j
Find the Fourier transform of f(t) = cos 2 π t[u(t) - u(t - 1)]
What is the Fourier transform of the triangular pulse in Fig. 18.27?
(a) Show that a periodic signal with exponential Fourier serieshas the Fourier transformwhere Ï‰0 = 2Ï€ /T.(b) Find the Fourier transform of the signal in Fig. 18.37.
Show that
Prove that if F(ω ) is the Fourier transform of f(t), F[f (t)sin ω0 t] = j/2 [F(ω + ω0) - F(ω - ωo)]
If the Fourier transform of f(t) isdetermine the transforms of the following:(a) f(-3t)(b) f(2t - 1)(c) f(t) cos2t(d) d/dt f(t)
Given that F[ f (t)] = ( j /Ï‰)(eˆ’jÏ‰ - 1), find the Fourier transforms of:(a) x(t) = f ( t) + 3(b) y(t) = f ( t - 2)(c) h(t) = f ' ( t)(d)
Obtain the inverse Fourier transform of the following signals. (a) F(ω) = 5/jω - 2 (b) H()ω) = 12/ ω2 + 4 (c) X(ω) = 10/(jω - 1) (jω - 2)
Determine the inverse Fourier transforms of the following: (a) F(ω) = e-j2ω/1 + jω (b) H(ω) = 1/(jω + 4)2 (c) G(ω) = 2u (ω + 1) - 2u(ω - 1)
Find the inverse Fourier transforms of the following functions:(a)(b) (c) (d)
Find the inverse Fourier transforms of:(a)(b)(c)(d)
Determine the inverse Fourier transforms of: (a) F(ω) = 4δ (ω + 3) + δ (ω) + 4δ (ω − 3) (b) G(ω) = 4u(ω + 2) - 4u(ω - 2) (c) H(ω) = 6 cos 2ω
Calculate the Fourier transform of the signal in Fig. 18.28.
For a linear system with input x(t) and output y(t) find the impulse response for the following cases: (a) x(t) = e−at u(t), y(t) = u(t) - u( - t) (b) x(t) = e−t u(t), y(t) = e−2t u(t) (c) x(t)
Given a linear system with output y(t) and impulse response h(t), find the corresponding input x(t) for the following cases: (a) y(t) = te−at u(t), h(t) = e−at u(t) (b) y(t) = u(t + 1) - u(t -
Determine the functions corresponding to the following Fourier transforms:(a)(b) F2 (Ï‰) = 2e|Ï‰|(c)(d)
Find f(t) if: (a) F(ω) = 2sinπω[u(ω +1) − u(ω −1)] (b) F(ω) = 1/ω (sin 2 ω - sin ω) + j/ω (cos 2 ω - cos ω)
Determine the signal f(t) whose Fourier transform is shown in Fig. 18.38. (Hint: Use the duality property.)
A signal f(t) has Fourier transform F(ω) = 1 / 2+ j ω Determine the Fourier transform of the following signals: (a) x(t) = f(3t - 1) (b) y(t) = f(t) cos 5t (c) z(t) = d / dt f(t) (d) h(t) = f(t) *
The transfer function of a circuit is H(ω) = 2/jω + 2 If the input signal to the circuit is vs (t) = e−4t u(t) V find the output signal. Assume all initial conditions are zero.
Find the transfer function Io(Ï‰) / Is (Ï‰ ) for the circuit in Fig. 18.39.
Suppose vs (t) = u(t) for t > 0. Determine i(t) in the circuit of Fig. 18.40, using the Fourier transform.
Given the circuit in Fig. 18.41, with its excitation, determine the Fourier transform of i(t).
Find the Fourier transform of the waveform shown in Fig. 18.29.
Determine the current i(t) in the circuit of Fig. 18.42(b), given the voltage source shown in Fig. 18.42(a).
Determine the Fourier transform of v(t) in the circuit shown in Fig. 18.43.
Obtain the current io(t) in the circuit of Fig. 18.44.(a) Let i(t) = sgn(t) A.(b) Let i(t) = 4[u(t) - u(t - 1)] A.
Find vo(t) in the circuit of Fig. 18.45, where is = 5eˆ’t u(t) A.
If the rectangular pulse in Fig. 18.46(a) is applied to the circuit in Fig. 18.46(b), find vo at t = 1 s.
Use the Fourier transform to find i(t) in the circuit of Fig. 18.47 if v s (t) = 10eˆ’2t u(t).
Determine the Fourier transform of io(t) in the circuit of Fig. 18.48.
Find the voltage vo(t) in the circuit of Fig. 18.49. Let i s (t) = 8eˆ’t u(t) A.
Find io(t) in the op amp circuit of Fig. 18.50.
Use the Fourier transform method to obtain vo(t) in the circuit of Fig. 18.51.
Obtain the Fourier transform of the signal shown in Fig. 18.30.
Determine vo(t) in the transformer circuit of Fig. 18.52.
Find the energy dissipated by the resistor in the circuit of Fig. 18.53.
Let f(t) = 5e−(t−2) u(t) and use it to find the total energy in f(t).
The voltage across a 1-Ω resistor is v(t) = te−2t u(t) V. (a) What is the total energy absorbed by the resistor? (b) What fraction of this energy absorbed is in the frequency band -2 ≤ ω ≤ 2?
Let i(t) = 2et u(-t)A. Find the total energy carried by i(t) and the percentage of the 1- Ω energy in the frequency range of -5 < ω < 5 rad/s.
An AM signal is specified by f(t) = 10(1 + 4 cos 200 π t)cosπ ×104 t Determine the following: (a) The carrier frequency, (b) The lower sideband frequency, (c) The upper sideband frequency.
For the linear system in Fig. 18.54, when the input voltage is vi (t) = 2Î´ (t) V, the output is v0 (t) = 10eˆ’2t - 6eˆ’4t V. Find the output when the input is v i (t) = 4eˆ’t u(t) V.
Find the Fourier transforms of both functions in Fig. 18.31 on the following page.
A band-limited signal has the following Fourier series representation:is (t) = 10 + 8 cos(2Ï€ t + 30º) + 5 cos(4Ï€ t - 150º)mAIf the signal is applied to the circuit in
In a system, the input signal x(t) is amplitude-modulated by m(t) = 2 + cos ω0t. The response y(t) = m(t)x(t). Find Y(ω ) in terms of X(ω).
A voice signal occupying the frequency band of 0.4 to 3.5 kHz is used to amplitude-modulate a 10-MHz carrier. Determine the range of frequencies for the lower and upper sidebands.
For a given locality, calculate the number of stations allowable in the AM broadcasting band (540 to 1600 kHz) without interference with one another.
A TV signal is band-limited to 4.5 MHz. If samples are to be reconstructed at a distant point, what is the maximum sampling interval allowable?
Given a signal g(t) = sinc(200π t) find the Nyquist rate and the Nyquist interval for the signal.
The voltage signal at the input of a filter is v(t) = 50e−2|t| V What percentage of the total 1- Ω energy content lies in the frequency range of 1 < ω < 5 rad/s?
A signal with Fourier transform F(ω) = 20/4 + jω is passed through a filter whose cutoff frequency is 2 rad/s (i.e., 0 < ω < 2). What fraction of the energy in the input signal is contained in the
Find the Fourier transforms of the signals in Fig. 18.32.
Obtain the Fourier transforms of the signals shown in Fig. 18.33.
Determine the Fourier transforms of the signals in Fig. 18.34.
Obtain the z parameters for the network in Fig. 19.65.
Construct a two-port that realizes each of the following z parameters.a.b.
Determine a two-port network that is represented by the following z parameters:
For the circuit shown in Fig. 19.73, letFind 11, I2, V1, and V2.
Determine the average power delivered to ZL 5 j4 = + in the network of Fig. 19.74. Note: The voltage is rms.
For the two-port network shown in Fig. 19.75, show that at the output terminals,And
For the two-port circuit in Fig. 19.76,(a) Find ZL for maximum power transfer to the load.(b) Calculate the maximum power delivered to the load.
For the circuit in Fig. 19.77, at Ï‰ = 2 rad/s, z11 = 10Î©, z12 = z21 = j 6Î©, z22 = 4Î©. Obtain the Thevenin equivalent circuit at terminals a-b and calculate vo.
Determine the z and y parameters for the circuit in Fig. 19.78.An asterisk indicates a challenging problem.
Calculate the y parameters for the two-port in Fig. 19.79.

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