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Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square- voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the capacitor voltage vo(1) in the first half-cycle, as shown in Figure 2(a), by following the procedure below: (a) Derive the differential equation (DE) for the capacitor voltage v (t) valid in the interval 0

Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square- voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the capacitor voltage vo(1) in the first half-cycle, as shown in Figure 2(a), by following the procedure below: (a) Derive the differential equation (DE) for the capacitor voltage v (t) valid in the interval 0

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square-wave voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the capacitor voltage vo(t) in the first half-cycle, as shown in Figure 2(a), by following the procedure below: (a) Derive the differential equation (DE) for the capacitor voltage v, (t) valid in the interval 0<t<T/2, where v, (t) = V. Note that the initial condition for this DE is v. (0) = V, which is still unknown. (b) Assume that the solution has the form vo(t) = A + Bea. Then substitute this into the DE and determine the unknown parameters A, B and a. (c) Find the unknown initial condition V (in terms of the parameters R, C, T and V) by imposing the symmetry condition on the solution: v(T/2) = -v(0) = V. (d) Find the time instant t₁ (in terms of R, C, T and V) at which the capacitor voltage becomes zero in the first half-cycle. (e) Calculate the numerical values of V, and t₁ for T=10 ms, Vs = 10 V, R = 10 k2 and C = 0.1 μµF. Figure 1 vs(t) risques bris 20 R = 10 kΩ ww C=0.1 µF + vo(t) -1.0
Transcribed Image Text:Consider the first order RC circuit shown in Figure 1. With v.(1) being a symmetrical square-wave voltage having period T and amplitude V, as shown in Figure 2(a), derive an expression for the capacitor voltage vo(t) in the first half-cycle, as shown in Figure 2(a), by following the procedure below: (a) Derive the differential equation (DE) for the capacitor voltage v, (t) valid in the interval 0<t<T/2, where v, (t) = V. Note that the initial condition for this DE is v. (0) = V, which is still unknown. (b) Assume that the solution has the form vo(t) = A + Bea. Then substitute this into the DE and determine the unknown parameters A, B and a. (c) Find the unknown initial condition V (in terms of the parameters R, C, T and V) by imposing the symmetry condition on the solution: v(T/2) = -v(0) = V. (d) Find the time instant t₁ (in terms of R, C, T and V) at which the capacitor voltage becomes zero in the first half-cycle. (e) Calculate the numerical values of V, and t₁ for T=10 ms, Vs = 10 V, R = 10 k2 and C = 0.1 μµF. Figure 1 vs(t) risques bris 20 R = 10 kΩ ww C=0.1 µF + vo(t) -1.0
V. S V >V, -V. S Figure 2 t₁ T/2 Vi Vo T t
Transcribed Image Text:V. S V >V, -V. S Figure 2 t₁ T/2 Vi Vo T t
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