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  4. A dielectric of dielectric constant K is introduced such that half of its area of a capacitor of capacity C is occupied by it. The new capacity is

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Q. A dielectric of dielectric constant $K$ is introduced such that half of its area of a capacitor of capacity $C$ is occupied by it. The new capacity is

J & K CETJ & K CET 2007Electrostatic Potential and Capacitance

Solution:

The dielectric is introduced such that, half of its area is occupied by it. In the given case the two capacitors are in parallel.
$\therefore C'=C_{1}+C_{2}$
$C_{1}=\frac{A \varepsilon_{0}}{2 d}$
and $C_{2}=\frac{K A \varepsilon_{0}}{2 d}$
Thus, $C'=\frac{A \varepsilon_{0}}{2 d}+\frac{K A \varepsilon_{0}}{2 d}$
$C'=\frac{C}{2}(1+K)$

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