A parallel plate condenser initially has air as a medium between the plates

Question

A parallel plate condenser initially has air as a medium between the plates. If a slab of dielectric constant 5 having thickness half the distance of separation between the plates is introduced, the percentage increase in its capacity will be ___

Options:

A . 33.3%

B . 66.7%

C . 50%

D . 75%

Answer: Option B
:
B

C_{1} = \frac{ϵ_{0} A}{d}; C_{2} = \frac{ϵ_{0} A}{d - t + \frac{t}{k}} = \frac{ϵ_{0} A}{\frac{d}{2} + \frac{d}{10}}

C_{2} = \frac{10}{6} \frac{ϵ_{0} A}{d} = \frac{5 ϵ_{0} A}{3 d}

\frac{C_{2}}{C_{1}} = \frac{5}{3}; (\frac{C_{2}}{C_{1}} - 1) 100 % = (\frac{5}{3} - 1) 100 %

= 2 \times 33.3 %

= 66.67 %

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