Question

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

• A. $2\,C$
• B. $C/2$
• C. $(1+K)C/2$
• D. $2C(1+K)$

Answer 1

Answer: (C)

$(1+K)C/2$

Answer 2

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, $C'=\frac{A \varepsilon_{0}}{2 d}+\frac{K A \varepsilon_{0}}{2 d}$
$C'=\frac{C}{2}(1+K)$