Electronic – How to find the voltage across a capacitor at time t= 0 and t = infinity


Here is a diagram of the circuit, I am confused about problems a and b.

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How do I go about solving these two problems? Thanks!

By the way you don't have to tell me the answer, I just want to know how I should think about it, or any helpful hints would be appreciated. Thanks.

Best Answer


A capacitor's voltage-current response is governed by: \begin{equation} I = C \frac{dV_c}{dt} \end{equation}

At \$t = 0\$: think about what happens when you integrate in the limit as \$dt \rightarrow 0\$ (i.e. what is a capacitor unable to do with respect to really fast transients?)

\begin{equation} \lim_{\delta \rightarrow 0^+} \int_{0^-}^{\delta} I dt = \lim_{\delta \rightarrow 0^+} C \int_{0^-}^{\delta} \frac{d V_c}{dt} dt \end{equation} Note that this equation does not imply \$I(0^+) = 0\$; it only provides a mathematical "weak" guarantee that it's integral doesn't change over the infinitesimal.

At \$t \rightarrow \infty\$, think of what happens when all transient behavior goes away (\$\frac{d <value>}{dt} = 0\$).