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. 1 : 2
• B. 2 : 1
• C. 4 : 1
• D. 1 : 4

Hint:

For $n$ identical capacitors, $C_p = nC$ and $C_s = C/n$. The ratio $C_s/C_p = 1/n^2$.

Answer 1

The Correct Option is D

Step 1: Let the capacity of each capacitor be $C$.
Step 2: In series: $C_s = \frac{C \cdot C}{C+C} = \frac{C}{2}$.
Step 3: In parallel: $C_p = C + C = 2C$.
Step 4: Ratio $C_s : C_p = \frac{C/2}{2C} = \frac{1}{4}$.