Question 171 of 180

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 the two plates of the first capacitor. The new potential difference of the combined system is:

A$\dfrac{\left(n+1\right)V}{\left(K+n\right)}$B$\dfrac{nV}{K+n}$C$\dfrac{V}{K+n}$D$V$

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Answer: (A) $\dfrac{\left(n+1\right)V}{\left(K+n\right)}$

i)

ii) Battery disconnected after full charge,
Total charge of the system,
$=CV+nCV$
$=\left(n+1\right)CV$

iii) Inserting dielectric of constant $K$

Common potential, ${V}_{C}=\dfrac{total charge}{total capacitance}$
$=\dfrac{\left(n+1\right)CV}{KC+nC}=\dfrac{\left(n+1\right)V}{K+n}$