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24. (a) An electrical load requires a sinusoidal voltage v(t), as shown in Fig. 24(a)(i), to operate. However, an AC supply is not readily available and so a squarewave û(t) is generated from a DC supply as shown in Fig. 24(a)(ii) to approximate the desired signal v(t) and drive the load. Af 10 20 30 40 v(t) 6v+- 3 V -4 V →t (ms) Fig. 24(a)(i): A sinusoidal signal. û (t) hr 10 20 30 40 Vp -4 V- t (ms) Fig. 24(a)(ii): A discrete sinusoidal signal. (i) Determine the equation describing the voltage signal v(t) in Fig. 24(a)(i) and express it in the form v(t) = A cos(Bt+C) + D for some constants A > 0, B > 0, C > 0, and D > 0. (ii) If the RMS value of the squarewave signal û(t) in Fig. 24(a)(ii) and the sinusoidal signal v(t) in Fig. 24(a)(i) are to be equal, briefly explain whether the peak voltage V₂ of the squarewave signal should be larger, smaller, or equal in value compared to the peak voltage of the sinusoidal signal v(t). Note: It is not necessary to determine the exact value of V.

24. (a) An electrical load requires a sinusoidal voltage v(t), as shown in Fig. 24(a)(i), to operate. However, an AC supply is not readily available and so a squarewave û(t) is generated from a DC supply as shown in Fig. 24(a)(ii) to approximate the desired signal v(t) and drive the load. Af 10 20 30 40 v(t) 6v+- 3 V -4 V →t (ms) Fig. 24(a)(i): A sinusoidal signal. û (t) hr 10 20 30 40 Vp -4 V- t (ms) Fig. 24(a)(ii): A discrete sinusoidal signal. (i) Determine the equation describing the voltage signal v(t) in Fig. 24(a)(i) and express it in the form v(t) = A cos(Bt+C) + D for some constants A > 0, B > 0, C > 0, and D > 0. (ii) If the RMS value of the squarewave signal û(t) in Fig. 24(a)(ii) and the sinusoidal signal v(t) in Fig. 24(a)(i) are to be equal, briefly explain whether the peak voltage V₂ of the squarewave signal should be larger, smaller, or equal in value compared to the peak voltage of the sinusoidal signal v(t). Note: It is not necessary to determine the exact value of V.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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24. An electrical load requires a sinusoidal voltage v(t), as shown in Fig. 24(a)(i), to operate. However, an AC supply is not readily available and so a squarewave û(t) is generated from a DC supply as shown in Fig. 24(a)(ii) to approximate the desired signal v(t) and drive the load. v(t) 6vf- DE HE 10 20 30 40 10 20 30 40 3 V û (t) t (ms) Vp -4 V-₁ t (ms) Fig. 24(a)(i): A sinusoidal signal. Fig. 24(a)(ii): A discrete sinusoidal signal. (i) Determine the equation describing the voltage signal v(t) in Fig. 24(a)(i) and express it in the form v(t) = A cos(Bt + C) + D for some constants A > 0, B > 0, C > 0, and D > 0. (ii) If the RMS value of the squarewave signal û(t) in Fig. 24(a)(ii) and the sinusoidal signal v(t) in Fig. 24(a)(i) are to be equal, briefly explain whether the peak voltage V₂ of the squarewave signal should be larger, smaller, or equal in value compared to the peak voltage of the sinusoidal signal v(t). Note: It is not necessary to determine the exact value of Vp.
Transcribed Image Text:24. An electrical load requires a sinusoidal voltage v(t), as shown in Fig. 24(a)(i), to operate. However, an AC supply is not readily available and so a squarewave û(t) is generated from a DC supply as shown in Fig. 24(a)(ii) to approximate the desired signal v(t) and drive the load. v(t) 6vf- DE HE 10 20 30 40 10 20 30 40 3 V û (t) t (ms) Vp -4 V-₁ t (ms) Fig. 24(a)(i): A sinusoidal signal. Fig. 24(a)(ii): A discrete sinusoidal signal. (i) Determine the equation describing the voltage signal v(t) in Fig. 24(a)(i) and express it in the form v(t) = A cos(Bt + C) + D for some constants A > 0, B > 0, C > 0, and D > 0. (ii) If the RMS value of the squarewave signal û(t) in Fig. 24(a)(ii) and the sinusoidal signal v(t) in Fig. 24(a)(i) are to be equal, briefly explain whether the peak voltage V₂ of the squarewave signal should be larger, smaller, or equal in value compared to the peak voltage of the sinusoidal signal v(t). Note: It is not necessary to determine the exact value of Vp.
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