Question

The parallel combination of two air filled parallel plate capacitors of capacitance $C$ and $nC$ is connected to a battery of voltage, $V$. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant $K$ is placed between the two plates of the first capacitor. The new potential difference of the combined system is-

• A. $V$
• B. $\frac{V}{K+n}$
• C. $\frac{(n+1)V}{(K+n)}$
• D. $\frac{nV}{K+n}$

Answer 1

The correct option is C $\frac{(n+1)V}{(K+n)}$

Here,
$C_1=C;C_2=nC;C_1^{\prime }=KC$

Using, conservation of charge

$Q^{{}^{\prime }}=Q_1+Q_2$
$(C_1^{\prime }+C_2)V^{{}^{\prime }}=C_1{V}_1+C_2{V}_2$
$\Rightarrow V^{\prime }=\frac{CV+\left(nC\right)V}{KC+nC}$
$\Rightarrow V^{\prime }=\frac{(n+1)V}{K+n}$
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.