Question

In a parallel plate air capacitor of capacitance $4F$, if the lower half of air space is filled with a material of dielectric constant 3, its capacitance changes to

• A. $\frac{4}{3}F$
• B. $\frac{8}{3}F$
• C. $8F$
• D. $12F$

Answer 1

Answer: (C)

$8F$

Initial capacitor $C=\frac{{ϵ}_{0}A}{d}=\Delta F$
$C_{eff}$ is parallel combination of $\frac{{ϵ}_{0}A}{2d}$ and $\frac{k{ϵ}_{0}A}{2d}$
The area has become half of original for each capacitor in parallel
$C_{eff}=\frac{{ϵ}_0(1+k)}{2d}$
$C_{eff}=\frac{{ϵ}_{0}A}{d}\left(\frac{1+3}{2}\right)$
$C_{eff}=4\times 2$
$C_{eff}=8F$