A series (R C ) circuit in the zero state with (R 2 mathrm k Omega ) and (C 1 mu mathrm F ) is excited by (v mathrm S (t) 2 left(1 e 1000 t ight) u(t) mathrm V ) (a) Find the differential equation for the capacitor voltage (b) Solve for the capacitor voltage (v mathrm C (t) ) using Laplace transfor...

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A series (R C) circuit in the zero state with (R=2 mathrm{k} Omega) and (C=1 mu mathrm{F})

Question:

A series $R C$ circuit in the zero state with $R=2 \mathrm{k} \Omega$ and $C=1 \mu \mathrm{F}$ is excited by $v_{\mathrm{S}}(t)=2\left(1-e^{-1000 t}\right) u(t) \mathrm{V}$.

(a) Find the differential equation for the capacitor voltage.

(b) Solve for the capacitor voltage $v_{\mathrm{C}}(t)$ using Laplace transformation techniques.

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