CBSE Class 12-science Answered
Derive an Expression for capacity of a parallel plane capacitor with dielectric medium?
Asked by Manishbhola4436 | 11 Mar, 2019, 01:14: PM
Expert Answer
The capacitor is a component which has the ability or “capacity” to store energy in the form of an electrical charge producing a potential difference (Static Voltage) across its plates, much like a small rechargeable battery.
Answered by Ankit K | 11 Mar, 2019, 08:48: PM
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The generalised equation for the capacitance of a parallel plate capacitor is
C =εA/d
Where € is the permittivity of vacuum, A is the area of the plate and d is the distance between the plate.
In the above case, the medium between the two parallel plates is air.
The capacitance of capacitor can be changed by introducing a dielectric material that means by changing the (€)
If dielectric material is placed between the two parallel plates of capacitor then it's capacity of storing energy in the form of charge increases and it increases by a factor k( which is also known as dielectric constant)
The permittivity of dielectric is
ε(s)=ε(r) * ε(0)
Where,
ε(r) is the realtive permittivity,ε(s) is the permittivity of the medium, ε(0) is the permittivity of vaccumm.
Hence,
The capacitance of parallel plate capacitor filled with dielectric is C=ε(s)A/d
C=ε(r) * ε(0)*A/d
Now €(r) can be written as dielectric constant k
k =ε(r)= ε(s)/ε(0)
Hence C=kε(0)A/d