# Two equal capacitors

Question:

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

1. $4: 1$

2. $2: 1$

3. $1: 4$

4. $1: 2$

Correct Option: , 3

Solution:

For series combination

For parallel combination

$\mathrm{C}_{\mathrm{eq}_{2}}=\mathrm{C}+\mathrm{C} \Rightarrow \mathrm{C}_{\mathrm{eq}_{2}}=2 \mathrm{C}$

$\Rightarrow \frac{\mathrm{C}_{\mathrm{eq}_{1}}}{\mathrm{C}_{\mathrm{eq}_{2}}}=\frac{(\mathrm{C} / 2)}{2 \mathrm{C}}=\frac{1}{4}=1: 4$