First slide

Capacitance

Question

A parallel plate capacitor with air as dielectric is charged to a potential V. It is then connected to an uncharged parallel plate capacitor filled with wax of dielectric constant K. The common potential of both capacitor is

Moderate

A

V
B

KV
C

(1+K)V
D

V/(1+K)

Solution

Before connection, the charge Q on the plates of air filled capacitor is C V. After it is connected with an uncharged capacitor, let y' be the common potential. Let Q₁ and Q₂
be the charges on charged and uncharged capacitor respectively. Then
$\begin{array}{ll} Q_{1} = V^{'} C and Q_{2} = V^{'} (KC) \\ ∴ CV = V^{'} C + V^{'} (KC) = (1 + K) V^{'} C \\ or V^{'} = (\frac{V}{1 + K}) \end{array}$

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