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 :
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
$\frac{ C _{1}}{ C _{2}}=\frac{5 C / 6}{5 C / 4}=\frac{2}{3}$
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Top Questions on electrostatic potential and capacitance
The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.
Some major things that we should know about electric potential:
They are denoted by V and are a scalar quantity.
It is measured in volts.
Capacitance
The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is “farads”.
The capacitor is in Series and in Parallel as defined below;
In Series
Both the Capacitors C1 and C2 can easily get connected in series. When the capacitors are connected in series then the total capacitance that is Ctotal is less than any one of the capacitor’s capacitance.
In Parallel
Both Capacitor C1 and C2 are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is Ctotal is any one of the capacitor’s capacitance.
