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  4. Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

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Q. Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be:

JEE MainJEE Main 2021Electrostatic Potential and Capacitance

Solution:

For series combination
image
$\frac{1}{C_{eq_1}} = \frac{1}{C} + \frac{1}{C} $
$\Rightarrow C_{eq_1} = \frac{C}{2}$
For parallel combination
image
$C_{eq_2} = C + C$
$\Rightarrow C_{eq_2} = 2C$
$\Rightarrow \frac{C_{eq_1}}{eq_2} =\frac{C/2}{2C}= \frac{1}{4} = 1 : 4$