Question

A parallel-plate capacitor consists of two parallel conducting plates of area S

separated by a uniform distance d. The space between the plates is filled with a

dielectric of a constant permittivity, ϵ. Determine the capacitance.​

Answer 1

Given:

A parallel-plate capacitor consists of two parallel conducting plates of area S separated by a uniform distance d. The space between the plates is filled with a dielectric of a constant permittivity, ϵ.

To find:

Net capacitance ?

Calculation:

Let capacitance be C :

$\therefore \: C = \dfrac{q}{V}$

$\implies \: C = \dfrac{q}{E \times d}$

$\implies \: C = \dfrac{q}{( \dfrac{ \sigma}{ \epsilon_{0}}) \times d}$

$\implies \: C = \dfrac{q}{( \dfrac{q}{ S \times \epsilon_{0}}) \times d}$

$\implies \: C = \dfrac{S\epsilon_{0}}{d}$

Since , it's filled with dielectric material :

$\implies \: C = k \times \dfrac{S\epsilon_{0}}{d}$

$\implies \: C = \dfrac{ \epsilon}{ \epsilon_{0}} \times \dfrac{S\epsilon_{0}}{d}$

$\implies \: C = \dfrac{S\epsilon}{d}$

Hope It Helps.