Electrical Power and Energy flashcards

$P=VI$: power in watts equals volts times amperes. Rearranged, $I=\frac{P}{V}$ and $V=\frac{P}{I}$. A 1,200 W microwave on 120 V draws 10 A.

$P=I^{2}R$ (use with current and resistance) and $P=\frac{V^2}{R}$ (use with voltage and resistance). 3 A through 4 $\Omega$ gives 36 W; 6 V across 3 $\Omega$ gives 12 W.

$E=P\times t$. Watts x seconds = joules; watts x hours = watt-hours; kilowatts x hours = kilowatt-hours. A 1.5 kW heater for 2 hours uses 3 kWh. 1 Wh = 3,600 J.

Watts measure a rate (power, joules per second). Watt-hours measure an amount (energy). If time is involved and the question asks how much was used, the answer is in Wh, kWh or J.

Convert to kWh (watts / 1,000 x hours), then multiply by the price per kWh. An 1,800 W hair dryer used 20 minutes a day for 30 days uses 18 kWh, costing $2.70 at 15 cents per kWh.

$\eta =\frac{P_{out}}{P_{in}}\times 100\%$. Lost power = input minus useful output. A charger drawing 50 W and delivering 40 W is 80 percent efficient and loses 10 W as heat. Never above 100 percent.

Energy (Wh) = voltage x capacity (Ah). Runtime (h) = Wh / load watts. A 12 V, 10 Ah battery holds 120 Wh, running a 30 W load about 4 hours. Ah alone is charge, not energy.

It becomes 4 times larger, because $P=I^{2}R$. But at fixed voltage, doubling current only doubles power ($P=VI$). Only current or voltage is ever squared, never resistance.