Name: Dielectrics in a Capacitor
Uploaded: 2019-07-19
Duration: 6 min 3 s
Description: Let us use our knowledge about dielectrics and capacitors to find out how the use of dielectrics can increase the capacitance of a system. Learn through this...

Question

What is the potential energy of a capacitor? Derive its expression. Where and in which form this energy is found?

Accepted Answer

When a capacitor is charged by a battery, charges are transferred from one plate of the capacitor and this work is done by the charging battery at the expense of its chemical energy. The work is stored in the capacitor in the form of electrostatic potential energy.

To derive the expression of the potential energy of a capacitor, consider a capacitor of capacitance $C$ . Let $Q$ be the charge in the capacitor, $V$ be the potential difference across the plates of a parallel plate capacitor. The initial charge on the capacitor is zero. The initial potential difference between plates is zero. When the charge on a capacitor increases, the potential difference between the plates increases.

Potential difference, $V = \frac{Q}{C}$

Work done to give an infinitesimal charge $d Q$ to capacitor is given by,

$d W = V d Q = \frac{Q}{C} d Q$

$W = \int d W = \int_{0}^{Q} \frac{Q}{C} d Q W = \frac{1}{C} {[\frac{Q^{2}}{2}]}_{0}^{Q} W = \frac{Q^{2}}{2 C}$

$W = \frac{{(C V)}^{2}}{2 C} = \frac{1}{2} C V^{2}$

Work done is stored in form of electrostatic potential energy.

$U = \frac{1}{2} C V^{2} = \frac{Q^{2}}{2 C} = \frac{1}{2} Q V$

Energy is stored in the capacitor when work is done to move a positive charge from negative conductor towards the positive conductor against the repulsive force. This energy is stored in the form of electric field energy in the charged capacitor, and it resides in the dielectric medium between the plates.

What is the potential energy of a capacitor? Derive its expression. Where and in which form this energy is found?

Important Questions on Electrostatic Potential and Capacitance

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