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  4. Three capacitors 3 μ F , 6 μ F and 6 μ F are connected in series to a source of 120 V. The potential difference, in volt, across the 3 μ F capacitor will be

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Q. Three capacitors $3\, \mu F , 6 \, \mu F$ and $6\, \mu F$ are connected in series to a source of $120 \, V$. The potential difference, in volt, across the $3 \, \mu F$ capacitor will be

WBJEEWBJEE 2014Electrostatic Potential and Capacitance

Solution:

The combination of three charges in series
$\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} $
$\frac{1}{C}=\frac{1}{3}+\frac{1}{6}+\frac{1}{6} $
$\Rightarrow C=\frac{6}{4}=1.5\, \mu F$
The charge of this circuit
$q=C V=1.5 \times 120$
$q=180\, \mu C$
The potential difference across the $3\, \mu F$
$q=C \,V$
$V=\frac{q}{C}=\frac{180}{3}=60\, V$