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

capacitordctimevoltage

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

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.

A capacitor's voltage-current response is governed by: $$I = C \frac{dV_c}{dt}$$
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?)
$$\lim_{\delta \rightarrow 0^+} \int_{0^-}^{\delta} I dt = \lim_{\delta \rightarrow 0^+} C \int_{0^-}^{\delta} \frac{d V_c}{dt} dt$$ 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\$).