Energy stored in a capacitor equation derivation and problems

Energy stored in a capacitor equation

Consider a capacitor with the capacitance ‘C’ ,which is connected to the battery of emf ‘V’ .If ‘dq’ charge is transferred from one plate to other,then the work done ‘dW’ will be:
dW =V dq
This work done is stored in the form of electric potential energy ‘dU’
dU =V dq
When the capacitor is fully charged then the total energy stored is:
Energy stored in capacitor equation
The energy stored in the capacitor is the energy store in the electric field between its plates.So,the energy stored can be expressed in terms of electric field strength ‘E’.

Energy stored in capacitors with dielectric equation

relation of energy

Energy density:

The energy density ‘μ’ is described as the energy stored ‘U’ per unit volume ‘V’ .mathematically it is expressed as:
If any dielectric medium having dielectric constant ‘Ke‘ is placed between the plates of a capacitor,then the expression of energy stored in the electric field of capacitor ‘U’ and energy density ‘μ’ will become:
energy density 2
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