Physics

Physics

Problem

Four capacitors of capacitances 2 μF,  3 μF,  5 μF2\,\mu\text{F},\;3\,\mu\text{F},\;5\,\mu\text{F} and 10 μF10\,\mu\text{F} are connected in parallel to a 200 V200\,\text{V} direct-current source. (a) Calculate the equivalent capacitance of the combination. (b) Find the total charge supplied by the source to the four-capacitor system. (c) Determine the total electrical energy stored in the combination.
Intuitive explanation

When capacitors are connected in parallel, they all experience the same voltage across them, but each stores charge independently based on its own capacitance. The key insight is that parallel capacitances simply add together—think of it as combining storage tanks where each contributes fully to the total. Once you know the equivalent capacitance and the applied voltage, you can find total charge using Q=CVQ = CV, and energy using U=12CV2U = \frac{1}{2}CV^2.

Intuitive explanation

When capacitors are connected in parallel, they all experience the same voltage across them, but each stores charge independently based on its own capacitance. The key insight is that parallel capacitances simply add together—think of it as combining storage tanks where each contributes fully to the total. Once you know the equivalent capacitance and the applied voltage, you can find total charge using Q=CVQ = CV, and energy using U=12CV2U = \frac{1}{2}CV^2.

Browse the problem library