Derive an expression for the energy stored in a capacitor
Answers
Answer:
Let us consider a capacitor of capacitance C and potential difference V between the plates.
Let the charge on one plate be +q and -q on the other.
Suppose the capacitor is being charged gradually.
Now,at any stage the charge on capacitor is q.
Therefore, the potential difference =
C
q
Small amount of work doe in giving n additional charge dq to the capacitor is
dW=
C
q
∗dq
Total work done in giving a charge Q to the capacitor is
W=∫dW
W= ∫
0
Q
C
Q
dq
W =
C
Q
2
Energy = E
E=
2C
Q
2
=
2
CV
2
=
2
QV
The energy is stored in the form of potential energy.
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Explanation:
Let us consider a capacitor of capacitance C and potential difference V between the plates.
Let the charge on one plate be +q and -q on the other.
Suppose the capacitor is being charged gradually.
Now,at any stage the charge on capacitor is q.
Therefore, the potential difference =
C
q
Small amount of work doe in giving n additional charge dq to the capacitor is
dW=
C
q
∗dq
Total work done in giving a charge Q to the capacitor is
W=∫dW
W= ∫
0
Q
C
Q
dq
W =
C
Q
2
Energy = E
E=
2C
Q
2
=
2
CV
2
=
2
QV
The energy is stored in the form of potential energy.