If 20 capacitors, each 100 μF, were connected in parallel across a 12-V battery, what would be the total energy stored in these capacitors?

Question

Quizplus · Accepted Answer

The total capacitance when capacitors are connected in parallel is given by:

Ctotal = C1 + C2 + C3 + ... + Cn

where C1, C2, C3, ..., Cn are the capacitances of individual capacitors.

Therefore, in this case:

Ctotal = 20 × 100 μF = 2000 μF = 2 mF

The energy stored in a capacitor is given by the formula:

E = 0.5 × C × V^2

where C is the capacitance and V is the voltage across the capacitor.

Therefore, the energy stored in one capacitor is:

E1 = 0.5 × 100 μF × (12 V)^2 = 7.2 × 10^-3 J

The total energy stored in 20 capacitors connected in parallel is:

Etotal = 20 × E1 = 20 × 7.2 × 10^-3 J = 1.44 × 10^-1 J = 1.4 × 10^-1 J (rounded to one significant digit)

Hence, the answer is D.

If 20 Capacitors, Each 100 μF, Were Connected in Parallel