First slide

Capacitance

Question

The dielectrics $K_{1} and K_{2}$ are filled between the plates of a capacitor as shown in Fig. 3.57 (A). The capacity of the system is :

Easy

A

$\frac{2 ε_{0} A (K_{1} K_{2})}{(K_{1} + K_{2}) d}$
B

$\frac{ε_{0} A}{d} [\frac{K_{1} + K_{2}}{2}]$
C

$\frac{ε_{0} {AK}_{1} K_{2}}{(K_{1} + K_{2}) d}$
D

$\frac{ε_{0} A}{d} (K_{1} + K_{2})$

Solution

Where $C_{1} = \frac{{Aε}_{0} K_{1}}{\frac{d}{2}} and C_{2} = \frac{{Aε}_{0} K_{2}}{\frac{d}{2}}$
$C_{effective} = \frac{C_{1} C_{2}}{C_{1} + C_{2}} = \frac{2 ε_{0} {AK}_{1} K_{2}}{(K_{1} + K_{2}) d}$

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