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Physics Question on electrostatic potential and capacitance

An uncharged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of V0V_0. lf the common potential after sharing of charges becomes V, then the dielectric constant of the dielectric must be

A

V0/VV_0 / V

B

VV0\frac{V}{V_0}

C

(V0−V)V\frac{(V_0 - V)}{V}

D

(V0−V)V0\frac{(V_0 - V)}{V_0}

Answer

(V0−V)V\frac{(V_0 - V)}{V}

Explanation

Solution

Common potential, V = Total chargeTotal capacitance\frac{Total \, charge}{Total \, capacitance}
\hspace40mm V = \frac{C_1 V_1 + C_2 V_2}{C_1 + C_2}
\hspace40mm = \frac{0 + CV_0}{KC + C}
\hspace40mm = \frac{CV_0}{C(1 + K)}
\hspace40mm V = \frac{V_0}{(1 + K)}
\hspace40mm K = \frac{V_0}{V} - 1
\hspace40mm K = \frac{V_0 - V}{V}