## anonymous 5 years ago The current applied to a10μ F capacitir is i=0.01sin(100t).If the capacitor was initially discharged, what is the voltage across the capacitor at time t=π/200sec?

1. anonymous

The relation between the voltage cross a capacitor and the current through it is given by: $v(t)={1 \over C}\int\limits_{t_0}^{t}i(t)dt +v_0(t) .... (1)$ initial voltage is zero, in this case, since the capacitor was not charged. Hence, $v(t)={1 \over 10\mu}\int\limits_{0}^{\pi/200}0.01\sin (100t)={1 \over 10\mu}\left[ -\cos (100t) \right]_{0}^{\pi/200}={1 \over 10\mu}\left[ -0-(-1) \right]$

2. anonymous

So v(t)=10^6 voltage unit.

3. anonymous

Does that make sense?