Question

Two capacitors of same capacity are first joined in series and then in parallel. The ratio of resultant capacity in series to that in parallel combination will be

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

Hint:

Series combination reduces capacitance, while parallel combination increases it.

Answer 1

The Correct Option is B

Step 1: Capacitance in series.
For two identical capacitors each of capacitance $C$:
\[ \frac{1}{C_s}=\frac{1}{C}+\frac{1}{C}=\frac{2}{C} \Rightarrow C_s=\frac{C}{2} \]

Step 2: Capacitance in parallel.
\[ C_p = C + C = 2C \]

Step 3: Ratio of capacitances.
\[ \frac{C_s}{C_p}=\frac{C/2}{2C}=\frac{1}{4} \]

Step 4: Conclusion.
The required ratio is $1:4$.