Question

The distance between the plates of a parallel plate condenser is $8\, mm$ and potential difference $120$ volts. If a $6\,mm$ thick slab of dielectric constant $6$ is introduced between its plates, then

• A. the charge on the condenser will be doubled
• B. the charge on the condenser will be reduced to half
• C. the potential difference across the condenser will be 320 volts
• D. the potential difference across the condenser will be 45 volts

Answer 1

Answer: (D)

If nothing is said, it is considered that battery is disconnected.
Hence, charge remain the same.
Also, $V_{\text {air }}=\frac{\sigma}{\varepsilon_{0}} \times d$
and $V_{\text {medium }}=\frac{\sigma}{\varepsilon_{0}}\left(d-t+\frac{t}{k}\right)$
$\Rightarrow \frac{V_{\text {medium }}}{V_{\text {air }}}=\frac{\left(d-t+\frac{t}{k}\right)}{d }$
$\Rightarrow \frac{V_{\text {medium }}}{120}=\frac{\left(8-6+\frac{6}{6}\right)}{8}$
$\Rightarrow V_{d i}=45\, V$