## Related questions with answers

Question

In a pulse power circuit, the voltage of a 10$\mu$F capacitor is zero for t<0 and $v=5(1-e^{-4000t})$ V for t>0. Determine the capacitor current and the energy stored in the capacitor at t=0ms and t=10ms.

Solutions

VerifiedSolution A

Solution B

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1 of 3Current trough a capacitor is equal to:

$\begin{align*} i_c(t)&=C\dfrac{\partial}{\partial{t}}v_c(t) \end{align*}$

Energy stored in the capacitor:

$\begin{align*} w_c(t)&=\int_{-\infty}^t{v_c\cdot i \ dt}\\ &=\int_{-\infty}^t{v_c\cdot C\dfrac{dv_c}{dt}\ dt}\\ &=C\int_{-\infty}^t{v_cdv}\\ &=\dfrac{C}{2}v_c^2\bigg\vert_{v(-\infty)}^{v(t)} \end{align*}$

From the given voltage we can calculate current:

$\begin{align*} i&=10\cdot 10^{-6}\cdot 5(1-e^{-4000t})'\\ &=50\cdot 10^{-6}(-e^{-4000t})(-4000)\\ &=0.2e^{-4000t} \end{align*}$

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