First slide

Capacitance

Question

In the circuit shown in figure, magnitude of instantaneous power consumed by the capacitor is

Moderate

A

zero
B

$\frac{V_{0}^{2} ωc}{2} \sin 2 ωt$
C

$\frac{V_{0}^{2} ωt}{\sqrt{2}}$
D

$V_{0}^{2} ωC \cos^{2} ωt$

Solution

If Q be the instantaneous charge, then $\frac{Q}{C} = v$
$∴ Q = Cv = {CV}_{0} cosωt \Rightarrow i = \frac{dQ}{dt} = - {CV}_{0} ωsinωt$
$∴$ Magnitude of instantaneous power
$p = |vi| = V_{0} cosωt \times {CV}_{0} ωsinωt = \frac{V_{0}^{2} ωC}{2} \sin 2 ωt$

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