Ten capacitors, each of capacitance 20 μF, are first connected in series and then in parallel. The ratio of the equivalent capacitance in series to the equivalent capacitance in parallel is:

Concept of Equivalent Capacitance:

For capacitors connected in series, the equivalent capacitance (C_series) is given by:

1 / C_series = 1 / C₁ + 1 / C₂ + ... + 1 / C_n

For n identical capacitors each of capacitance C, the formula simplifies to:

C_series = C / n

For capacitors connected in parallel, the equivalent capacitance (C_parallel) is given by:

C_parallel = C₁ + C₂ + ... + C_n

For n identical capacitors each of capacitance C, the formula simplifies to:

C_parallel = nC

Given Data:

• Each capacitor has capacitance (C) = 20 μF
• Number of capacitors (n) = 10

Calculation:

First, calculate the equivalent capacitance for the series connection:

C_series = C / n

C_series = 20 μF / 10

C_series = 2 μF

Next, calculate the equivalent capacitance for the parallel connection:

C_parallel = nC

C_parallel = 10 × 20 μF

C_parallel = 200 μF

Finally, calculate the ratio of the equivalent capacitance in series to the equivalent capacitance in parallel:

Ratio = C_series / C_parallel

Ratio = 2 μF / 200 μF

Ratio = 1 / 100

Conclusion:

Hence, the ratio of the equivalent capacitance in series to the equivalent capacitance in parallel is 1:100.