Consider the circuit below with I$1=10$ A$,$ R$1=50$ ohms, R$2=75$ ohms, and C $=200$ mF$.$ Assume the initial energy stored in the capacitor is zero.

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Find the differential equation for the voltage across the capacitor for t greater than zero.$($This should be similar in form to equation $7\mathrm{.}18$ in your book. Hint: Find the Norton equivalent with respect to the capacitor.$)$

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Find the voltage across the capacitor v$($t$)$ based on the solution to the differential equation.

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Find the current through the capacitor i$($t$)$ using the voltage you found in b$.$

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Using Laplace transforms, find the current through the capacitor.

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Now instead of having a constant current $($step function$),$ assume that the input current is i$($t$)=18$ cos$(0\mathrm{.}5$ t$).$ Find the steady state current through the capacitor.

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