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. 4:01
• B. 2:01
• C. 1:04
• D. 1:02

Answer 1

The Correct Option is C

Let's determine the ratio of the equivalent capacities when two equal capacitors are connected in series and in parallel.

1. Consider the capacitance of each capacitor as \(C\).
2. Capacitors in Series:
   When capacitors are connected in series, the reciprocal of the total capacitance (\(C_{\text{series}}\)) is the sum of the reciprocals of the individual capacitances: \(\frac{1}{C_{\text{series}}} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C}\)
   Simplifying gives: \(C_{\text{series}} = \frac{C}{2}\)
3. Capacitors in Parallel:
   When capacitors are connected in parallel, the total capacitance (\(C_{\text{parallel}}\)) is the sum of the individual capacitances: \(C_{\text{parallel}} = C + C = 2C\)
4. Finding the Ratio:
   The ratio of the equivalent capacities in the two cases is given by: \(\frac{C_{\text{series}}}{C_{\text{parallel}}} = \frac{\frac{C}{2}}{2C} = \frac{1}{4}\)

The ratio of equivalent capacitances when connected in series to that when connected in parallel is 1:4.

Thus, the correct answer is: 1:04.