Question

Two identical parallel plate capacitor A and B are connected to a battery of V volt with the switch S closed. The switch is now opened and the free space between the plates filled with a dielectric constant K. Find the ratio of the total electrostatic energy stored in both the capacitor before and after the introduction of the dielectric.

Answer 1

The ratio of electrostatic energy stored in the capacitor before and after the introduction of the dielectric is 1/K or (K) ^ (-1).

Parallel plate capacitors are used in electronic equipment for the conversion of stored energy into a form such as light, heat or sound. The energy stored in the capacitor is located in the field between both the plates and can be altered by the introduction of a dielectric material in between the plates.

 

Without a dielectric, when the capacitor is connected to a battery, the electrostatic energy stored is given by the formula:

 

U1 = ½ x C x V^2

 

However, when the battery is disconnected from the capacitor with the help of a switch, the stored energy is calculated as follows:  

 

U2 = K x ½ x C x V^2

 

Here, K is the dielectric coefficient or constant of the material that is inserted in between the capacitor plates.

 

Hence, the ratio of electrostatic energy stored in the capacitor before and after the introduction of the dielectric is 1/K or (K) ^ (-1).