An air filled parallel plate capacitor has a capacitance of $10^{- 12} F .$ The separation of plates is doubled and wax is inserted between them, which makes capacitance $2 \times 10^{- 12} F .$ The dielectric constant of wax is

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3.13

2.0

8.0

4.0

answer is C.

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Detailed Solution

$\begin{array}{l} C_{1} = \frac{ϵ_{0} A}{d} = 10^{- 12} . . . . (i) \\ C_{2} = \frac{K \in_{0} A}{2 d} = 2 \times 10^{- 12} . . . (ii) \end{array}$
Divide : $\frac{C_{2}}{C_{1}} = \frac{K}{2} = 2 ∴ K = 4$

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