Question

Two identical air core capacitors are connected in series to a voltage source of $15\, V$. 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

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