- When DC supply is given to capacitor, some energy is stored in the dielectric medium of capacitor.
- When capacitor is discharged, this electrostatic energy released.
- When capacitor is in discharged condition, work done requires transferring charge from one plate to other plate.
- Let a charge transfer from positive plate to negative plate is dq when voltage across capacitor is v.
- Therefore the work done dW = vdq…………….. ( 1 )

Where

dW = Work done
to transfer charge

v = Voltage
across capacitor

dq = Charge
transfer from positive plate to negative plate

As q = Cv

Therefore dq =
Cdv ………………..( 2 )

From equation (
1 ) and ( 2 )

dW = Cvdv

∫ dW = C ∫ vdv

The lower to
upper limit for voltage is 0 to V

W = CV

^{2}/ 2
Energy stored in
the capacitor = ½ CV

^{2}- If capacitance C is given in Farad and V is in voltage, the energy stored is given in Joule.

E = ½ CV

^{2 }Joule
= ½ QV
( As Q = CV )

= ½ Q

^{2 }/ C Joule ( As V = Q / C )
The unit of
energy stored in the capacitor is Joule

E = ½ CV

^{2 }
The unit of
capacitance is Coulomb / voltage

E = ( Coulomb /
voltage ) ( Voltage )

^{2}
= Coulomb × Voltage

= Coulomb × Joule / coulomb

= Joule

Therefore the
unit of E is given in Joule

**Energy stored per unit volume**

E = ½ CV

^{2}/ Ad
Where

A = Plate area
and

d = Distance
between plates

E = ½ [ εAV

^{2}/ Ad^{2}] ( As C = εA / d )
= ½ [ ε ( V

^{2}/ d^{2})]
= ½ [ εE

^{2}] ( Where electric intensity E = V / d )
= ½ [ DE ] ( Where Electrical displacement D = εE )

= ½ [ D

^{2}/ ε ] in Joule / meter^{3}( As E = D / ε )
The unit of
Energy stored per unit volume is Joule / meter

^{3}
E = ½ [ DE
]

= [ Coulomb /
meter

^{2}] [ Voltage / meter ]
= [ Coulomb –
voltage / meter

^{3}]
= [Coulomb ×
Joule / coulomb ] / meter

^{3}
= Joule / meter

^{3}
E = ½ [ D

^{2}/ ε ]
= [ Coulomb

^{2}/ meter^{4}] / [ Farad / meter ]
= [ Coulomb

^{2}/ Farad - meter^{3}]
= [ Coulomb

^{2}- Voltage / Coulomb - meter^{3 }]^{ }[ As C = Q / V ]
= [ Coulomb

^{2}- Joule / Coulomb^{2}- meter^{3 }] [ As voltage = Joule / Coulomb ]
= Joule / meter

^{3}**You may also like :**