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  4. An air filled parallel plate condenser has a capacity of 2 pF. The separation of the plates is doubled and the interspace between the plates is filled with wax. If the capacity is increased to 6 pF, the dielectric constant of wax is :

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Q. An air filled parallel plate condenser has a capacity of $2\,pF$. The separation of the plates is doubled and the interspace between the plates is filled with wax. If the capacity is increased to $6\,pF$, the dielectric constant of wax is :

BITSATBITSAT 2005

Solution:

$C _{\text {old }}=\frac{\varepsilon_{ 0 } A }{ d }=2 pF \rightarrow$ (i)
$C _{\text {new }}=\frac{ K \varepsilon_{ 0 } A }{2 d }=6 pF \rightarrow$ (ii)
By Equating (i) and (ii)
$\frac{ K }{2}(2) pF =6 pF$
$\Rightarrow K =6$