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 :

Engineering

Physics

Parallel Plate Capacitor

Question

$\frac{nV}{K + n}$

$\frac{(n + 1) V}{(K + n)}$

$\frac{V}{K + n}$

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Total chare of the system = CV + nCV

= (n + 1)CV

After the insertion of dielectric of constant K

New potential (common)

$V_{c} = \frac{Total charge}{Total charge}$

$= \frac{(n + 1) CV}{KC + nC} = \frac{(n + 1) V}{K + n}$

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