A parallel plate capacitor with air as medium between the plates has a capacitance of $10 μ F$ . The area of capacitor is divided into two equal halves and filled with two media as shown in the figure having dielectric constant $k_{1} = 2$ and $k_{2} = 4$ . The capacitance of the system will now be

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$10 μ F$

$20 μ F$

$30 μ F$

$40 μ F$

answer is C.

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Detailed Solution

$C_{R} = C_{1} + C_{2} = \frac{k_{1} \in_{0} A_{1}}{d} + \frac{k_{2} \in_{0} A_{2}}{d} = \frac{2 \times \in_{0} \frac{A}{2}}{d} + \frac{4 \times \in_{0} \frac{A}{2}}{d} W i t h o u t d i e l e c t r i c, C_{a i r} = \frac{\in_{0} A}{d} = 10 μ F (g i v e n) = 2 \times \frac{10}{2} + 4 \times \frac{10}{2} = 30 μ F$