Electric Power
▶︎ Watch it animatedinteractive step-through · ~3 min · optional ⚙︎ Open the appletPower Lab · two bulbs, series or parallel, each bulb's power from its own current and voltage and once from a borrowed oneElectric power is the rate of energy conversion in a circuit element, $P = IV$, which for a resistor also reads $P = I^2R = V^2/R$. All three forms are equivalent, and all three require that the current, voltage and resistance in them belong to the same element. Because series elements share a current and parallel elements share a voltage, the larger resistance dissipates more in series while the smaller dissipates more in parallel. Energy follows from power by multiplying time, $E = Pt$, and the kilowatt-hour is that product, equal to $3.6$ million joules.
Three errors dominate. Feeding a power formula a value borrowed from elsewhere, classically $V_{\text{battery}}^2/R$ for one resistor in a series chain, which routinely returns more power than the whole battery delivers. Ranking bulb brightness by counting components, so a bulb added in parallel is expected to dim the others when with an ideal source it leaves them untouched and simply draws more from the battery. And interchanging power with energy, reporting watts where joules or kilowatt-hours belong, or dividing by the elapsed time instead of multiplying by it.
The work
3 ways in · any order
Lesson
Electric Power
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Derives the three power forms from P = IV, enforces that every symbol come from the element being asked about, and replaces bulb-counting with a recomputation of each bulb's own dissipated power.
Diagnostic
10-item topic check
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Ten items spanning the failure modes of this topic: feeding a power formula the battery's voltage instead of the element's own, ranking brightness by how many components are in the circuit, importing the series rule into a parallel network, and interchanging watts with joules and kilowatt-hours. Take it cold to find which one is yours, or after the lesson to confirm it is not.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears it for now and moves you to the next. Two in a row is a checkpoint, not proof: if the error resurfaces later, the misconception comes back.