Comprehensive Problems

17.77 The voltage across a device is given by

v(t) = -2 + 10 \cos 4t + 8 \cos 6t + 6 \cos 8t

Find:

(a) the period of v(t),
(b) the average value of v(t),
(c) the effective value of v(t).
17.78 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 harmonic 10 V.
- (a) If the voltage is applied across a 5-Ω resistor, find the average power dissipated by the resistor.
- (b) If a dc component is added to the periodic voltage and the measured power dissipated increases by 5 percent, determine the value of the dc component added.
17.79 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.
17.80 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.

17.81 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 = 1, 2, 3, and 4.
- (c) What fraction of the total power is carried by the dc component?
- (d) What fraction of the total power is carried by the second harmonic (n = 2)?
17.82 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-Ω resistor.

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