What is the formula for the average energy stored in a capacitor?

The formula for the average energy stored in a capacitor is derived from its fundamental characteristics of capacitance. The energy (U) stored in a capacitor can be expressed in terms of its capacitance (C) and the voltage (V) across its plates. This relationship is given by the equation:

[ U = \frac{1}{2} C V^2 ]

This formula shows that the energy stored is proportional to both the capacitance and the square of the voltage. The factor of one-half originates from the derivation of the work done to charge the capacitor, as the voltage increases linearly from 0 to V as the capacitor charges. This reflects the cumulative effect of voltage across the charge stored in the capacitor.

In contexts where you're comparing this to the energy stored in inductors, the equivalent formula is ( U = \frac{1}{2} L I^2 ) for inductors, where L is inductance and I is current. The confusion might arise because of the similarity in structure between energy formulas for capacitors and inductors, but in the case of a capacitor, the energy storage depends specifically on capacitance and voltage.

Therefore, the given answer accurately reflects the physical principles governing capacitors and provides a clear