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A parallel plate capacitor with air between the plates has a capacitance of $8\;pF$ . The separation between the plates is now reduced by half and the space between them is filled with a medium of dielectric constant 5. Calculate the value of capacitance of the capacitor in the second case .

$\begin{array}{1 1}55\;pF \\ 80\;pF \\ 67\;pF \\ 45\;pF\end{array} $

1 Answer

Solution :
Given capacitance of capacitor
$C= \large\frac{\in A}{d} $ -----------(1)
Where A and d are area of each plate and seperation between two plates Now,
$C'= \large\frac{K \in_0 'A}{d'}$
$\qquad= \large\frac{ \times \in_0 A}{(d/2)}$
$\qquad= 10 \bigg( \large\frac{\in_0A}{d}\bigg)$
$\qquad= 10 \times 8 \;pF$
$c= 80\;pF$
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