Question

find an expression for a parellel capacitor with compound dielectric​

Answer 1

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.

The generalised equation for the capacitance of a parallel plate capacitor is

C =€A/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

€(s)=€(r) * €(0)

Where,

€(r) is the realtive permittivity,€(s) is the permittivity of the medium, €(0) is the permittivity of vaccumm.

Hence,

The capacitance of parallel plate capacitor filled with dielectric is C=€(s)A/d

C=€(r) * €(0)*A/d

Now €(r) can be written as dielectric constant k

k =€(r)= €(s)/€(0)

Hence C=k€(0)A/d