A parallel plate capacitor is of area $6 c m^{2}$ and separation $3 m m$ . The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant $K_{1}, = 10$ , $K_{2} = 12$ and, $K_{3} = 14$ . The dielectric constant of a material which when fully inserted in above capacitor gives same capacitance would be

12

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4

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36

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14

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Solution

The correct option is B $12$
Let the dielectric constant of material used be $K$ .
$C_{1} + C_{2} + C_{2} + C_{3} = C_{e q}$
$∴ \frac{10 ϵ_{0} A / 3}{d} + \frac{12 ϵ_{0} A / 3}{d} + \frac{14 ϵ_{0} A / 3}{d} = \frac{K ϵ_{0} A}{d}$
On solving
$\Rightarrow K = 12$ .

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