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. 3:01
• B. 5:02
• C. 2:03
• D. 1:01

Answer 1

Answer: (C)

2:03

Answer 2

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 $P Q$ and $Q R$. Similarly, same charge will flow through capacitors in arms PT, TS and SR. So, equivalent capacitance of left side $C '=\frac{ C \times C }{ C + C }=\frac{ C }{2}$ and equivalent capacitance of right side $\frac{1}{C''} =\frac{1}{C}+\frac{1}{C}+\frac{1}{C}=\frac{3}{C}$ $\therefore C''=\frac{C}{3}$ Now, $C'$ and C' ' will in parallel combination, hence, $C _{1}= C'+ C''=\frac{ C }{2}+\frac{ C }{3}=\frac{5 C }{6}$ Similarly, if a source is connected between points $P$ and $Q$, then equivalent capacitance $C_{2} =C+\frac{C}{4}$ $=\frac{5 C}{4}$ Hence, the required ratio is given by $\frac{ C _{1}}{ C _{2}}=\frac{5 C / 6}{5 C / 4}=\frac{2}{3}$