Expression of energy stored in a capacitor in terms of capacitance and potential difference between its plate
Answers
Energy stored in a capacitor
Suppose a conductor of capacity C is at a potential V0 and let q0 be the charge on the conductor at this instant. The potential of the conductor when (during charging) the charge on it was q (< q0) is,
V ∝ q or V = Cq; where ‘C’ is a constant of proportionality that depends on the nature of the material of the conductor. This constant is known as the capacitance.
If we wish to transfer more charge to this conductor, work has to be done against the repulsive forces of the charges already present on the conductor. Let us say that we have to transfer a small charge ‘dq’ which takes a small amount of work ‘dW’. Then work done in bringing a small charge dq at this potential (V) is =
Energy stored in capacitor
The total work done in charging it from 0 to q0 is now easy to calculate. All we have to do is to take an integral of the above equation between the relevant limits as shown below:
Energy stored in capacitor
This work is stored as the potential energy and we have:
Energy stored in capacitor
Further by using q0 = CV0 we can write this expression also as,
Energy stored in capacitor
In general, if a conductor of capacity C is charged to a potential V by giving it a charge q, then
Energy stored in capacitor
Hope this helps you ☺️☺️✌️✌️❤️❤️
Storing Energy in a Capacitor. The energy stored on a capacitor can be expressed in terms of the work done by the battery. Voltage represents energy per unit charge, so the work to move a charge element dq from the negative plate to the positive plate is equal to V dq, where V is the voltage on the capacitor.