Question

An uncharged parallel plate capacitor having a dielectric of dielectric constant $K$ is connected to a similar air cored parallel plate capacitor charged to a potential $V_0$. The two share the charge, and the common potential becomes $V$. The dielectric constant $K$ is :

• A. $\frac{V}{V_0}+1$
• B. $\frac{V_0}{V}+1$
• C. $\frac{V}{V_0}-1$
• D. $\frac{V_0}{V}-1$

Answer 1

Answer: (D)

$C_1=C,V_1=V_0,C_2=KC,V_2=0$ and $V_{common}=V$

We know that $V_{common}=\frac{C_1{V}_1+C_2{V}_2}{C_1+C_2}$

$\therefore V=\frac{C{V}_0+KC\times 0}{C+KC}$
$K=\frac{V_0}{V}-1$