Two equal capacitances are connected first in series and then in parallel. The ratio of the effective series…

Analyze the question: Two capacitors of equal capacitance C are connected in series, then in parallel. We need the ratio C_series / C_parallel.

Concept:

• Series: 1/C_s = 1/C₁ + 1/C₂
• Parallel: C_p = C₁ + C₂

Solution:

Series: 1/C_s = 1/C + 1/C = 2/C C_s = C/2

Parallel: C_p = C + C = 2C

Ratio: C_s / C_p = (C/2) / (2C) = 1/4 = 0.25

Tip: For two equal capacitors, series gives C/2 and parallel gives 2C, so the ratio is always 1:4 (0.25). Remember that capacitors behave opposite to resistors: they add directly in parallel and by reciprocals in series. For n equal capacitors, the ratio is 1/n².