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What voltage is required to charge a parallel combination of a 7.90-μF and a 4.00-μF capacitor to the same total energy as when connected in series across a 24.0-V battery?
a) 16 V
b) 24 V
c) 12 V
d) 6 V

Answer :

Final answer:

The correct option is B. To store the same energy in a parallel combination of capacitors as in a series combination charged by a 24.0-V battery, the required voltage is also 24 V.

Explanation:

The energy stored in a capacitor is given by the formula E=1/2(C*V^2), where E is the energy, C is the capacitance, and V is the voltage across the capacitor.

When capacitors are connected in series, the total capacitance is less than any individual capacitor's capacitance. The charge on capacitors in series is the same, and the voltage divides. Thus, the total voltage across the series combination is the sum of individual voltages.

When capacitors are connected in parallel, the total capacitance is simply the sum of individual capacitances. In a parallel connection, each capacitor has the same voltage across it. To charge the parallel combination to the same energy as the series combination with a 24.0-V battery, the required voltage can be found by setting the total energy in both configurations equal and solving for the unknown voltage. Using these relationships, we find that the required voltage is 24 V (option b).

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