The equivalent capacitance of 10 equal capacitors connected in series is 10 μF. When these are put in parallel and charged to 100 V, what will be the total energy stored?

Concept

Series connection of capacitors:

When 'n' capacitors are connected in series, the equivalent capacitance is given by:

\({1\over C_{eq}}={1\over C_{1}}+{1\over C_{2}}........{1\over C_{n}}\)

If all capacitors are equal, then:

\(C_{eq}={C\over n}\)

Parallel connection of capacitors:

When 'n' capacitors are connected in parallel, the equivalent capacitance is given by:

\(C_{eq}=C_1+C_2.......C_n\)

If all capacitors are equal, then:

\(C_{eq}=nC\)

Calculation

Given, n = 10

C_eq = 10 μF

\(10={C\over 10}\)

\(C=100\space \mu F\)

When capacitors are connected in parallel.

\(C_{eq}=10\times 100\times 10^{-6}\)

C_eq = 10^-3 F

The energy in the capacitor is given by:

\(E={1\over 2}CV^2\)

\(E={1\over 2}\times 10^{-3}\times (100)^2\)

E = 5 J