Which equation calculates the total energy stored in a capacitor?

The equation that calculates the total energy stored in a capacitor is given by the formula ( \text{energy} = \frac{1}{2} CV^2 ). In this context, ( C ) represents the capacitance of the capacitor in farads, and ( V ) denotes the voltage across the capacitor in volts. This relationship describes how the energy is stored based on the amount of charge the capacitor can hold (determined by its capacitance) and the voltage that creates the electric field within it.

Essentially, the factor of ( \frac{1}{2} ) arises from integrating the work done to charge the capacitor, which varies linearly from zero voltage (when the capacitor is uncharged) to the applied voltage ( V ). As the voltage increases while charging, the energy stored accumulates, resulting in this specific relationship.

Other equations provided serve different contexts; for instance, the equation relating to inductance is applicable to inductors rather than capacitors, and those involving charge and capacitance also offer alternative ways to express energy but are rearrangements or derivations connected to the same fundamental capacitive behavior. In essence, option B directly captures the essence of how energy is stored in a capacitor, making it