Question

A capacitor stores $40$ $\mu$C charge when connected across a battery. When the gap between the plates is filled with a dielectric a charge of $80$ $\mu$C flows through the battery. The dielectric constant of dielectric inserted is?

• A. $2$
• B. $3$
• C. $1$
• D. $4$

Answer 1

Answer: (B)

$\because C_0=\frac{{\epsilon }_{0}A}{d}$ and $C=\frac{\epsilon A}{d}=\frac{K{\epsilon }_{0}A}{d}$
So, $q_0=C_{0}V=\frac{\epsilon A}{d}V$
and $q=CV=\frac{K{\epsilon }_{0}A}{d}V$
$\therefore \frac{q}{q_0}=K$
Given $q_0=40\mu C$
On inserting a dielectric, an additional charge of $80\mu C$ also flows through the battery.
So, total charge $=q_0+80=40+80=120\mu C$
$\therefore K=\frac{q}{q_0}=\frac{120}{40}=3$.