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

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

• A. 1/2 CV^2
• B. CV
• C. 1/2 LI^2
• D. CVI^2

Answer: (A)

The formula for the average energy stored in a capacitor is \( \frac{1}{2} CV^2 \). This relationship arises from the definition of electric potential energy in the context of capacitors. When a capacitor is charged, the work done to move charge from one plate to the other against the electric field is stored as potential energy. The energy stored can be derived from integrating the work done over the distance moved by the charge in the electric field. As charge \( Q \) accumulates on the plates of the capacitor, the voltage \( V \) across the capacitor is given by \( V = \frac{Q}{C} \). Thus, the energy \( U \) can be expressed in terms of charge: \[ U = \int_0^Q V \, dQ = \int_0^Q \frac{Q}{C} \, dQ = \frac{1}{C} \int_0^Q Q \, dQ \] Evaluating this integral gives: \[ U = \frac{1}{C} \left[ \frac{Q^2}{2} \right]_0^Q = \frac{Q^2}{2C}

The formula for the average energy stored in a capacitor is ( \frac{1}{2} CV^2 ). This relationship arises from the definition of electric potential energy in the context of capacitors.

When a capacitor is charged, the work done to move charge from one plate to the other against the electric field is stored as potential energy. The energy stored can be derived from integrating the work done over the distance moved by the charge in the electric field.

As charge ( Q ) accumulates on the plates of the capacitor, the voltage ( V ) across the capacitor is given by ( V = \frac{Q}{C} ). Thus, the energy ( U ) can be expressed in terms of charge:

[

U = \int_0^Q V , dQ = \int_0^Q \frac{Q}{C} , dQ = \frac{1}{C} \int_0^Q Q , dQ

]

Evaluating this integral gives:

[

U = \frac{1}{C} \left[ \frac{Q^2}{2} \right]_0^Q = \frac{Q^2}{2C}