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 :

• A. $2:1$
• B. $1:4$
• C. $3:1$
• D. $3:2$

Answer 1

The correct option is B $1:4$

Given that the first connection is in series :

$\Rightarrow \frac{1}{C_{12}}=\frac{1}{C}+\frac{1}{C}\Rightarrow C_{12}=\frac{C}{2}$

The second connection is in parallel :
$\Rightarrow C_{34}=C+C=2C$

Now,
$\frac{C_{12}}{C_{34}}=\frac{\frac{C}{2}}{2C}$

$\Rightarrow \frac{C_{12}}{C_{34}}=\frac{1}{4}=1:4$