Capacitors together and the energy they hold. Series and parallel combinations, energy stored in a charged capacitor, and what happens to charge and energy when capacitors are joined or a battery stays connected.
3 lessons, about 1 h 55 min3 simulations11 problems8 practice questionsPython in every lesson
Created by StemPy LabCapacitors in parallel share one voltage, and their charges add, so . Capacitors in series carry one charge, and their voltages add, so . In series the smaller capacitor takes the larger voltage. A network is solved by replacing pairs, one step at a time.
Charging a capacitor means doing work against its own voltage. The energy stored is . A battery does twice this work, , and the other half is lost as heat. The energy lives in the field, with a density , and it explains the pull between the plates.
Joining two capacitors shares their charge until the voltages match: . The energy lost is , and it is zero only if the voltages were equal. If a change makes the capacitance times as big, then with the battery on and , and with the battery off and .
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