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. $4:1$
• D. $1:2$

Answer 1

The correct option is B

$1:4$

Step 1: Given;

$C_1=C_2=C$(say)

Step 2: Formula used;

$$\begin{gathered} \frac{1}{C_{series}}=\frac{1}{C_1}+\frac{1}{C_2} \\ {C}_{parallel}=C_1+C_2 \end{gathered}$$

Step 3: Find equivalent capacities;

Case 1: When connected in series.

$$\begin{gathered} \frac{1}{C_{series}}=\frac{1}{C}+\frac{1}{C} \\ \Rightarrow C_{series}=\frac{C}{2} \end{gathered}$$

Case 2: When connected in parallel.

$$\begin{gathered} C_{parallel}=C+C \\ \Rightarrow C_{parallel}=2C \end{gathered}$$

Step 4: Find the ratio of the equivalent capacities in the two cases;

$$\begin{gathered} \frac{C_{series}}{C_{parallel}}=\frac{{\displaystyle \raisebox{1ex}{$C$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{2C} \\ \Rightarrow \frac{C_{series}}{C_{parallel}}=\frac{1}{4}=1:4 \end{gathered}$$

Thus, option B is the correct answer.