Parallel Plate Capacitance

Question

Capacitance of parallel plate capacitor (area A, separation d, vacuum) is?

RankGuru · Accepted Answer

1. **Definition of Capacitance**: $C = Q/V$.
2. **Field in Capacitor**: For parallel plates, the electric field between them is $E = \frac{\sigma}{\epsilon_0} = \frac{Q}{A \epsilon_0}$.
3. **Potential Difference**: $V = E \cdot d = \frac{Q d}{A \epsilon_0}$.
4. **Isolate C**: $C = \frac{Q}{V} = Q \div \frac{Q d}{A \epsilon_0} = \frac{A \epsilon_0}{d}$.
5. **Result**: The capacitance is directly proportional to plate area and inversely proportional to separation: **$C = \frac{\epsilon_0 A}{d}$**.

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Parallel Plate Capacitance

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