Problem

Consider two capacitors with different capacitance and . The formula for calculating the stored charge across a capacitor is .

Part 1: Determine the equivalent capacitance when the two capacitors are connected in series.

Part 2: Determine the equivalent capacitance when the two capacitors are connected in parallel.


Capacitor circuit-0.png

Solution

Part 1: Capacitors connected in series (same charge, different voltage)

When two capacitors are connected in series, the stored charge across each capacitor is the same, and the voltage of each capacitor is inversely-proportional to their respective capacitance.

Since ,

.

Therefore,

.

In general, given capacitors added in series

Part 2: Capacitors connected in parallel (same voltage, different charge)

When two capacitors are connected in parallel, the voltage across each capacitor is the same, and the stored charge of each capacitor is proportional to their respective capacitance.

Since ,

.

Therefore,

.

In general, given capacitors added in parallel

.
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