Question

A parallel plate capacitor with air between the plates has a capacitance of $10\, pF$. The capacitance, if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant $4$ is

• A. $80\, pF$
• B. $96 \,pF$
• C. $100 \,pF$
• D. $120 \, pF$

Answer 1

Answer: (A)

$80\, pF$

Answer 2

Here, $C_{1}=\frac{\varepsilon_{0}A}{d}=10\,PF \ldots\left(i\right)$ and $C_{2}=k\frac{\varepsilon_{0}A}{d 2}=\frac{4\times2\varepsilon_{0}A}{d} \left(\because k=4\right)$ $=8\times10 \left(using \left(i\right)\right)$ $=80\,PF$