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## anonymous 5 years ago 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?

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1. anonymous

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 $$t = \frac{\pi}{200}$$.

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