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. $\frac{V_{1}-V_{2}}{V_{2}}$
• E. $\frac{V_{1}-V_{2}}{V_{1}+V_{2}}$

Answer 1

Answer: (D)

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