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A linear system is described by the circuit shown below. L R₁ м i(t) x(t) R₂. y(t) = ve(t) (a) Find the differential equation that relates the output y(t) (the voltage across the capacitor) and the input voltage x(t) in terms of R1, R2, L and C. (b) For R₁ =100, R₂ = 20, L = 2H and C = F, and given the initial conditions y(0) : dy(0)=0, find the output y(t) for each of the following inputs, dt (i) x(t) = 24, t≥0 (ii) x(t)=(6+2+13 + 10.5), t≥0 (iii) x(t)=10e5t, t≥0 (iv) x(t) = 10e-4, t≥0 (v) x(t) = 12 cos(√12t+45°), t≥ 0 = 2,

A linear system is described by the circuit shown below. L R₁ м i(t) x(t) R₂. y(t) = ve(t) (a) Find the differential equation that relates the output y(t) (the voltage across the capacitor) and the input voltage x(t) in terms of R1, R2, L and C. (b) For R₁ =100, R₂ = 20, L = 2H and C = F, and given the initial conditions y(0) : dy(0)=0, find the output y(t) for each of the following inputs, dt (i) x(t) = 24, t≥0 (ii) x(t)=(6+2+13 + 10.5), t≥0 (iii) x(t)=10e5t, t≥0 (iv) x(t) = 10e-4, t≥0 (v) x(t) = 12 cos(√12t+45°), t≥ 0 = 2,

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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A linear system is described by the circuit shown below. L R₁ м i(t) x(t) R₂. y(t) = ve(t) (a) Find the differential equation that relates the output y(t) (the voltage across the capacitor) and the input voltage x(t) in terms of R1, R2, L and C. (b) For R₁ =100, R₂ = 20, L = 2H and C = F, and given the initial conditions y(0) : dy(0)=0, find the output y(t) for each of the following inputs, dt (i) x(t) = 24, t≥0 (ii) x(t)=(6+2+13 + 10.5), t≥0 (iii) x(t)=10e5t, t≥0 (iv) x(t) = 10e-4, t≥0 (v) x(t) = 12 cos(√12t+45°), t≥ 0 = 2,
Transcribed Image Text:A linear system is described by the circuit shown below. L R₁ м i(t) x(t) R₂. y(t) = ve(t) (a) Find the differential equation that relates the output y(t) (the voltage across the capacitor) and the input voltage x(t) in terms of R1, R2, L and C. (b) For R₁ =100, R₂ = 20, L = 2H and C = F, and given the initial conditions y(0) : dy(0)=0, find the output y(t) for each of the following inputs, dt (i) x(t) = 24, t≥0 (ii) x(t)=(6+2+13 + 10.5), t≥0 (iii) x(t)=10e5t, t≥0 (iv) x(t) = 10e-4, t≥0 (v) x(t) = 12 cos(√12t+45°), t≥ 0 = 2,
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