Table 1: Laplace Transform PropertiesLinearity L {af(t)} = aF(s)SuperpositionModulation L {e-at f(t)} = F(s + a)Time-Shifting L{f(t-7)u(t-7)} = e-TF(s)Scaling L{f(at)} = F(2)| L { $(10)} = 8= 8F(s)-f(0)L{f(t)} = F(s)L {fi(t) + f₂(t)} = F₁(s) + F₂(s)Real Differentiation LReal IntegrationComplex DifferentiationL {tf(t)}-F(s)dsComplex Integration {f} = f* F(®)LConvolution L {f(t) *g(t)} = F(s). G(s)Table 2: Common Laplace Transform Pairsf(t)F(s)8(t)u(t)tu(t)e-atu(t)te-atu(t)cos(wt)u(t)sin(wt)u(t)11s+a1(s + a)²88² +w²8² +w² (c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function,i. Calculate the time constant T.ii.111.Calculate vc (t) at t = ∞.Obtain an expression for vc (t) valid for all values of t.4u(t) V+3 ΚΩMwww1 ΚΩ .Figure Q2-24 μF+VC

We need to find out the voltage across capacitor for given circuit.

Answered: (c) Consider the circuit shown in…

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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(c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function, i. Calculate the time constant T. ii. 111. Calculate vc (t) at t = ∞. Obtain an expression for vc (t) valid for all values of t. 4u(t) V + 3 ΚΩ M www 1 ΚΩ . Figure Q2-2 4 μF + VC