Question

Five capacitors, each of capacitance value $C$ are connected as shown in the figure. The ratio of capacitance between $P$ and $R$, and the capacitance between $P$ and $Q$, is :

• A. 3 : 1
• B. 5 : 2
• C. 2 : 3
• D. 1 : 1

Answer 1

Answer: (C)

The capacitors having same charge through them will be in series combination.
If a source is connected between points $P$ and $R$, same charge will flow through two capacitors in arms $PQ$ and $QR$. Similarly, same charge will flow through capacitors in arms PT, TS and SR.
So, equivalent capacitance of left side
$C^{\prime }=\frac{C\times C}{C+C}=\frac{C}{2}$
and equivalent capacitance of right side
$\frac{1}{C^{\prime \prime }}=\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{3}{C}$
$\therefore C^{\prime \prime }=\frac{C}{3}$
Now, $C^{\prime }$ and $C^{\prime \prime }$ will in parallel combination, hence,
$C_1=C^{\prime }+C^{\prime \prime }=\frac{C}{2}+\frac{C}{3}=\frac{5C}{6}$
Similarly, if a source is connected between points $P$ and $Q$, then equivalent capacitance
$C_2=C+\frac{C}{4}$
$=\frac{5C}{4}$
Hence, the required ratio is given by
$\frac{C_1}{C_2}=\frac{5C/6}{5C/4}=\frac{2}{3}$