First slide

Capacitance

Question

The ratio of capacitance of two capacitors filled with dielectrics of same dimensions but of different values K and K/4 arranged in two ways as shown in Figure-(1) and Figure-(2) is

Difficult

A

5 : 2
B

25 : 16
C

5 : 4
D

2 : 5

Solution

$Here C_{1} = \frac{ε_{0} k_{1} A}{2 d} + \frac{ε_{0} k_{2} A}{2 d} = \frac{5 ε_{0} kA}{8 d} [Given k_{1} = k, k_{2} = k / 4]$
$C_{2} = \frac{ε_{0} A}{d / 2 k_{1} + d / 2 k_{2}} = \frac{2 ε_{0} kA}{5 d} ∴ \frac{C_{1}}{C_{2}} = \frac{25}{16}$

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