Question

derive an expression for the energy stored in a capacitor.​

Answer 1

Answer:

Ecap=QV2=CV22=Q22C , where Q is the charge,V is the voltage and C is the capacitance of the capacitor.

Answer 2

The energy stored in a capacitor is nothing but the electric potential energy and is related to the voltage and charge on the capacitor. If the capacitance of a conductor is C, then it is initially uncharged and it acquires a potential difference V when connected to a battery. If q is the charge on the plate at that time, then

q
=
C
V
The work done is equal to the product of the potential and charge. Hence, W = Vq

If the battery delivers a small amount of charge dQ at a constant potential V, then the work done is

d
W
=
V
d
q
=
q
C
d
q
Now, the total work done in delivering a charge of an amount q to the capacitor is given by

W
=
∫
q
0
q
C
d
q
=
1
C
q
2
2
=
1
2
q
2
C
Therefore the energy stored in a capacitor is given by

U
=
1
2
q
2
C
Substituting
q
=
C
V
in the equation above, we get

U
=
1
2
C
V
2
The energy stored in a capacitor is given by the equation
U
=
1
2
C
V
2
.

Let us look at an example, to better understand how to calculate the energy stored in a capacitor.

U = 1/2CV^2 = 1/2QV= Q^2/ 2C