Name: Equipotential Surfaces and Its Properties
Uploaded: 2019-07-19
Duration: 7 min 22 s
Description: The surface over which the electric potential is the same everywhere is called an equipotential surface. Let's more about it and its properties in this video.

Question

On which factors, does the capacitance of a parallel plate capacitor depend ? A parallel plate air capacitor is of

3 pF

capacitance. When a plate of dielectric constant

k

and thickness

\frac{3 d}{4}

is placed between the plates of the capacitors the capacitance of the capacitor becomes

6 pF

. Find the magnitude of

k

, where

d

is

the distance between the plates of the capacitor.

Accepted Answer

The capacitance of a parallel plate capacitor depends on area of each plate, dielectric medium between the plates and distance between the plates.

The capacitance of a parallel plate capacitor is given by the formula $= C = \frac{ϵ_{\circ} A }{d}$

Where, $A$ is the area of each plate, $is$ is the distance between the plates and, $ϵ$ is the permittivity of the space between the plates

$C = \frac{ε_{\circ} A}{d}$ $= 3 μ = \frac{ε_{\circ} A}{d} . . . . . . . . . . . . . . . . . . . . (i)$

$C' = \frac{ε_{\circ} A}{d - t + \frac{t}{k}}$

$= 6 μ = \frac{ε_{\circ} A}{d - \frac{3 d}{4} + \frac{3 d}{4 k}}$

$6 μ = \frac{ε_{\circ} A}{(\frac{dk + 3 d}{4 k})} . . . . . . . . . . . . . . . (ii)$

Dividing $(i)$ from $(ii)$ We get.

$\frac{1}{2} = \frac{dk + 3 d}{4 kd}$

$∴ 4 kd = 2 dk + 6 d$

$2 kd = 6 d$

$k = 3$

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