Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :

Solution

Physics sir · 3 steps

Series halves one capacitor, parallel doubles it, so the ratio is a half to two.

1. Series. In series the reciprocals add: 1/Cₛ = 1/C + 1/C = 2/C. So Cₛ = C/2.
2. Parallel. In parallel the capacitances add directly: Cₚ = C + C = 2C.

   Cₛ/Cₚ = (C/2)/2C = 1/4

3. So. The ratio of series to parallel capacitance is 1 : 4, which is option (d).

The idea to keep. For n equal capacitors, series gives C/n and parallel gives nC, so the series-to-parallel ratio is always 1 : n². Capacitors combine the opposite way to resistors.

Answer from the NTA final answer key. Solution by PrepWiser.