What is the formula for calculating the total energy stored in a capacitor?

The correct formula for calculating the total energy stored in a capacitor is derived from the relationship between the capacitance, voltage, and energy. Specifically, the formula is E = 1/2 C V^2, where E represents the energy in joules, C is the capacitance in farads, and V is the voltage in volts.

This formula reflects the fact that the energy stored in the capacitor is not simply a product of capacitance and voltage; it accounts for how the energy storage varies with the square of the voltage. When voltage is applied across a capacitor, it charges up, and the amount of energy that can be stored increases not linearly, but quadratically with respect to voltage. Therefore, the term V^2 shows that as the voltage is increased, the energy increases exponentially.

This understanding is crucial in circuit design and analysis, as it helps engineers calculate how much energy can be stored in capacitors for various applications, such as power supply smoothing, energy storage, and timing circuits. Other options provided do not accurately reflect the relationship between energy, capacitance, and voltage in a capacitor, as they either misrepresent the dependence on voltage or the concept of energy storage altogether.