Question

Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. $V$. If one of the capacitor is completely filled with dielectric material of constant $K$, then potential difference of the other capacitor will become

• A. $\frac{K}{V\left(K+1\right)}$
• B. $\frac{KV}{K+1}$
• C. $\frac{K-1}{KV}$
• D. $\frac{V}{K\left(K+1\right)}$

Answer 1

Answer: (B)

$\frac{KV}{K+1}$

Answer 2

Let the capacitance of capacitor $C _{2}$ be $C$.
Thus capacitance of capacitor $C _{1}$ is $KC$.
Potential across the capacitor $C _{2}, V _{2}=\frac{ C _{2}}{ C _{1}+ C _{2}} V$
$\therefore V _{2}=\frac{ KC }{ C _{1}+ KC } V$
$\Rightarrow V _{2}=\frac{ KV }{ K +1}$