A parallel plate air condenser has a capacity ‘C’. When the

Question

A parallel plate air condenser has a capacity ‘C’. When the plate separation is halved and a dielectric of constant k is inserted, new capacitance is found to be 12C. The value of dielectric constant ‘k’ is?

Options:

A . 12

B . 24

C . 6

D . 3

Answer: Option C
:
C

C = \frac{ϵ_{0} A}{d}; C^{1} = \frac{k ϵ_{0} A}{(\frac{d}{2})}

\frac{C^{1}}{C} = 2 k;

12 = 2 k; k = \frac{12}{2} = 6

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