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>>Electrostatic Potential and Capacitance
>>Effects of Dielectrics in Capacitors
>> $A parallel plate capacitor is of area 6$

Question

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

1330281

A

$12$

B

$4$

C

$36$

D

$14$

Medium

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Updated on : 2022-09-05

Solution

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Correct option is A)

Let the dielectric constant of material used be $K$ .

$C_{1} + C_{2} + C_{2} + C_{3} = C_{e q}$

$∴ \frac{1 0 ϵ _{0} A / 3}{d} + \frac{1 2 ϵ _{0} A / 3}{d} + \frac{1 4 ϵ _{0} A / 3}{d} = \frac{K ϵ _{0} A}{d}$

On solving
$\Rightarrow K = 12$ .

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