A capacitor is filled with two dielectrics of the same dimensions but of dielectric constants 2 and 3 as shown in figure (a) and in figure (b); the ratio of the capacitances in the two arrangements is

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21 : 25

13 : 12

25 : 24

17 : 13

answer is A.

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Detailed Solution

$\begin{array}{l} C_{1} = C_{0} (\frac{K_{1} + K_{2}}{2}) = C_{0} (\frac{2 + 3}{2}) = 2 .5 C_{0} \\ C_{2} = C_{0} (\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}) = C_{0} (\frac{2 \times 2 \times 3}{5}) = 2 .4 C_{0} \\ \Rightarrow \frac{C_{1}}{C_{2}} = \frac{2 .5 C_{0}}{2 .4 C_{0}} = \frac{25}{24} \end{array}$

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