Question

Derive an expression for the capacitance of a parallel capacitor when the space between the plates is partailly filled with a die;ectric

Answer 1

Explanation:

Let us consider a parallel plate capacitor having plate charge (Q) , plate area (A) and plate separation (d) . Suppose a slab of dielectric material of dielectric constant (K) and thickness (t) is greater than (d) is introduced between the plates . Then , the distance between the plates is (t) in the dielectric and (d - t) in vacuum (or air) .

If σ be the surface charge density on the plates , then the electric field in air between the plates is

Eo = σ / εo = Q / εo A. [ -.- σ = Q/A ]

and that in the dielectric slab is

E = Eo / K = Q / K εo A

The field Eo between the plates is in the distance (d-t) and E is the distance t . Hence , if the potential difference between the plates be V , then

V = E0 (d - t) + E t

= Q / εo A (d-t) + Q / K εo A × t

So , capacitance of the capacitor is

C = Q / V

C = Q / V ÷ εo A [ (d -t) + t/k ]

C = εo A / d-t + t/ k

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