energy stored capacitor

Question

Energy stored in capacitor with capacitance C and potential V?

RankGuru · Accepted Answer

1. **Charging Work**: Work is done in transferring small amounts of charge $dq$ against a growing potential $v = q/C$.
2. **Integral**: $U = \int_0^Q v \cdot dq = \int_0^Q \frac{q}{C} dq = \frac{1}{C} [\frac{q^2}{2}]_0^Q = \frac{Q^2}{2C}$.
3. **Using V**: Substitute $Q = CV \implies U = \frac{1}{2C} (CV)^2 = \frac{1}{2} C V^2$.
4. **Location**: This energy is stored in the **electric field** between the plates.

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