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
AIIMS 2006, Medium
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In the first case, $3 \mathrm{C}$ and $2 \mathrm{C}$ are parallel. Equivalent capacitance is,
$\frac{c}{3}+\frac{c}{2}=\frac{5 c}{6}$
In the second case $1 \mathrm{C} \& 4 \mathrm{C}$ are parallel.
Equivalent capacitance $=\frac{C}{1}+\frac{C}{4}=\frac{5 C}{4}$
Ratio $=\frac{5 \mathrm{C}}{6} \times \frac{4}{5 \mathrm{C}}=2: 3$
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