Question

An uncharged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of $V_0$. If the common potential after sharing of charges becomes $V$ ,then the dielectric constant of the dielectric must be

• A. $\frac{V_0}{V}$
• B. $\frac{V}{V_0}$
• C. $\frac{V_0-V}{V}$
• D. $\frac{V_0-V}{V_0}$

Answer 1

The correct option is C $\frac{V_0-V}{V}$

Common potential , $V=\frac{Totalcharge}{Totalcapacitance}$
$V=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$
$=\frac{0+C{V}_0}{KC+C}$
$=\frac{C{V}_0}{C(1+K)}$
$V=\frac{V_0}{1+K}$
$\therefore$ $K+1=\frac{V_0}{V}$
$\Rightarrow$ $K=\frac{V_0}{V}-1$
$=\frac{V_0-V}{V}$