The current applied to a 10μF capacitor is i=0.01 sin100t. If the capacitor was initially discharged, what is the voltage across the capacitor at time t= pi/200sec?

Question

The current applied to a 10μF capacitor is i=0.01 sin100t. If the capacitor was initially  discharged, what is the voltage across the capacitor at time t= pi/200sec?

anonymous · Answer

The current of a capacitor is related to the voltage as follows:
$$
i(t) = C\frac{dv}{dt}
$$
Thus, we can get an equation for voltage:
$$
\begin{align*}
v(t) &= C\int i(t) dt \
v(t) &= C\int0.01\sin(100t) + K\
v(t) &= \frac{-0.01C}{100}\cos(100t) + K
\end{align*}
$$
Solve for the constant of integration with the initial condition, and then plug in $t = \frac{\pi}{200}$.