First slide

Insertion of dielectric in capacitor

Question

Two square plates $(l \times l)$ and dielectric $(\frac{l}{2} \times \frac{t}{2} \times l)$ arranged as shown in figure. Find the equivalent capacitance of the structure.

Moderate

A

$\frac{ε_{0} A}{t} (\frac{3 K + 1}{2 (K + 1)})$
B

$\frac{2 ε_{0} A}{t} (\frac{K + 1}{K + 3})$
C

$\frac{ε_{0} A}{t} (\frac{K + 1}{K + 3})$
D

$\frac{ε_{0} A}{t} (\frac{2 K + 1}{2 K + 3})$

Solution

We can make equivalent circuit of given system in two ways as in Figs. (a) and (b). But (b) is wrong and (a) is correct.
Here $C_{1} = \frac{ε_{0} A / 2}{t / 2} = \frac{ε_{0} A}{t}$
$C_{2} = \frac{{Kε}_{0} A / 2}{t / 2} = \frac{{Kε}_{0} A}{t} and C_{3} = \frac{ε_{0} A / 2}{t} = \frac{ε_{0} A}{2 t}$
Now, $C_{eq} = \frac{C_{1} C_{2}}{C_{1} + C_{2}} + C_{3}$
$= \frac{ε_{0} A}{t} [\frac{3 K + 1}{2 (K + 1)}]$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App