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New Capacitance in Dielectric

A parallel pl...

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?

A

12

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B

24

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C

6

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D

3

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Solution

The correct option is C 6
$C = \frac{ϵ_{0} A}{d}; C^{1} = \frac{k ϵ_{0} A}{(\frac{d}{2})}$
$\frac{C^{1}}{C} = 2 k;$
$12 = 2 k; k = \frac{12}{2} = 6$

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