Which formula correctly calculates the energy stored in a capacitor?

The formula that correctly calculates the energy stored in a capacitor is based on the relationship between capacitance, voltage, and energy. The correct formula is ( W = 0.5CV^2 ), where ( W ) represents the energy in joules, ( C ) is the capacitance in farads, and ( V ) is the voltage across the capacitor in volts.

This formula arises from the work done to charge a capacitor. As the capacitor charges, the voltage increases, and the amount of energy stored is a function of the voltage squared. The factor of 0.5 appears because the voltage starts at zero and gradually increases to ( V ) as the capacitor charges, effectively averaging the voltage over the charging process.

In contrast, the other formulas do not accurately reflect the energy stored in a capacitor. For instance, ( W = CQ^2 ) incorrectly focuses on charge without taking voltage into account adequately. The formula ( W = CV ) does not consider the relationship between energy and the square of the voltage. Lastly, ( W = V^2/R ) pertains to power dissipation in a resistor rather than energy stored in a capacitor.