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

Answer 1

The correct option is A $\frac{V_0}{V}-1$

From given,
$V_{AB}=V$
$V=\frac{C{V}_0}{C^{\prime }+C}=\frac{C{V}_0}{KC+C}=\frac{C{V}_0}{C(K+1)}$
$V=\frac{V_0}{(K+1)}$
$K+1=\frac{V_0}{V}$

$K=\frac{V_0}{V}-1$