Question

derive the relation for the capacitance of a capacitor filled with dielectrics

Answer 1

Answer:

The larger the dielectric constant, the more charge can be stored. Completely filling the space between capacitor plates with a dielectric increases the capacitance by a factor of the dielectric constant: C = KCo, where Co is the capacitance with no dielectric between the plates.

Explanation:

E= Eo Ep

The electric field Eo in the outside region of the dielectric will be null. Now the equation of the potential difference between the plates will be :

V=o (d-t) + Et

But Eo= Er or K

Therefore E= Eo / k

So

V= E o (d-t) + Eot / k

V= E o [d-t+t/k]

As we know

Eo =  /  

= Q / A  

V= Q / A  [d-t+t/k]

Capacitance of the capacitor is shown in the equation below:

C= Q / V= A  / (d-t+t/k)

=  A /d-t (1-1/K)

I.e. C=  A/ d-t (1-1/k) - 2.31

So, C > Co

Clearly, it is proved that if a dielectric slab is placed in the plates of a capacitor then its capacitance will increase by some amount.