One Step At a Time
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Consider the circuit below:
where \displaystyle{ I(t) = \begin{cases} I_0\cos(\omega t) & \text{if}~t\leq 0\\ 0 & \text{otherwise} \end{cases}}
This represents an oscillation going on for a long time (long enough to reach sinusoidal steady state), and then suddenly terminating at t=0. This current is sketched below for the neighborhood around t=0:
Find an expression for v_{\rm C}(t) for t\geq 0. For full credit, show your work and describe your process.
Hint: Before time 0, the circuit will be operating in sinusoidal steady state. Can you use this to find the value of v_{\rm C}(0^-)?
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