Question

Two identical air core capacitors are connected in series to a voltage source of $15V$. If one of the capacitors is filled with a medium of dielectric constant $4$, the new potential across this capacitor is

• A. 5 V
• B. 8 V
• C. 10 V
• D. 12 V

Answer 1

Answer: (C)

Let capacitance of each capacitor is $C$. Then equivalent capacitance in series is

$\frac{1}{C^{\prime }}=\frac{1}{C}+\frac{1}{C}=\frac{2}{C}$
$\Rightarrow C^{\prime }=\frac{C}{2}$
Charge $Q=C^{\prime }V=\frac{C}{2}\times 15$..(i)
When filled with dielectric
$C_1=4C,C_2=C$
$\frac{1}{C^{\prime }}=\frac{1}{4C}+\frac{1}{C}=\frac{5}{4C}$
$\Rightarrow C^{\prime \prime }=\frac{4C}{5}$
Since, charge is conserved
$Q=C^{\prime }{V}^{\prime }=\frac{4C}{5}{V}^{\prime }\dots \text{ (ii) }$
From Eqs. (i) and (ii), we get
$\frac{C}{2}\times 15=\frac{4C}{5}{V}^{\prime }$
$\Rightarrow V^{\prime }=\frac{15\times 5}{4\times 2}=9.4V=10V$