Capacitors | Sahithyan's Notes

Capacitors

Made of two conductive plates separated by a dielectric layer.

In an ideal capacitor, the charge imbalance $Q$ is proportional to the voltage $V$ across the plates.

Q = CV

The proportionality constant is the capacitance ( $C$ ), in terms of physical dimensions:

C = \frac{\epsilon A}{d}

Here:

v and i

Current $i$ passing through the capacitor and the voltage $v$ across the capacitor are related by:

i = C \frac{\text{d}v}{\text{d}t}

Suppose voltage across an initially uncharged capacitor rises from $0$ to $V$ during a time period of $t$ .

e = \int_{0}^{t} p\,dt = \int_{0}^{t} vi\,dt = C \int_{0}^{v} v\,dv

E = \frac{1}{2}CV^2

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November 3, 2026 1 min read

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