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  4. Three capacitors connected in series have an effective capacitance of 4 μ F. If one of the capacitance is removed, the net capacitance of the capacitor increases to 6μ F.. The removed capacitor has a capacitance of

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Q. Three capacitors connected in series have an effective capacitance of 4 $\mu F.$ If one of the capacitance is removed, the net capacitance of the capacitor increases to 6$\mu F.$. The removed capacitor has a capacitance of

KEAMKEAM 2013Electrostatic Potential and Capacitance

Solution:

We knows when three capacitors connected in series
$\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}$
Here, $\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}=\frac{1}{4}$
Now, on remóving one capacitơ the resultant is
$\frac{1}{C_{1}}+\frac{1}{C_{2}}=\frac{1}{6}$
So, $\frac{1}{6}+\frac{1}{C_{3}} =\frac{1}{4} $
$\frac{1}{C_{3}}=\frac{1}{4}-\frac{1}{6} =\frac{6-4}{24}=\frac{2}{24}=\frac{1}{12}$
$C_{3} =12 \,\mu F$