Question

An uncharged parallel plate capacitor filled with a dielectric of dielectric constant $K$ is connected to an air filled identical parallel capacitor charged to potential $V_1$. If the common potential is $V_2$, the value of $K$ is

• A. $\frac{V_{1}-V_{2}}{V_{1}}$
• B. $\frac{V_{1}}{V_{1}-V_{2}}$
• C. $\frac{V_{2}}{V_{1}-V_{2}}$
• D. $\frac{V_{1}-V_{2}}{V_{2}}$

Answer 1

Answer: (D)

$\frac{V_{1}-V_{2}}{V_{2}}$

Answer 2

Here,
$V_{2} =\frac{\left(C V_{1}+0\right)}{(C+K C)}$
$V_{2} =\frac{V_{1}}{1+K}$
$\frac{V_{2}}{V_{1}} =\frac{1}{1+K}$
$1+K =\frac{V_{1}}{V_{2}}$
$K =\frac{V_{1}}{V_{2}}-1$
$k =\frac{V_{1}-V_{2}}{V_{2}}$