1.7.4 Power

Learning objectives

1.7.4.1Power as work done per unit time or• Define power as work done per unit time or energy transferred per unit time; recall/use: P = W/t and P = ΔE/t

Power is the rate of doing work or the rate of transferring energy. It tells you how much work is done, or how much energy is transferred, per unit time.

$P=\frac{W}{t}$

$P=\frac{\Delta E}{t}$

Symbol	Meaning	SI unit
$P$	power	watt (W)
$W$	work done	joule (J)
$\Delta E$	energy transferred or change in an energy store	joule (J)
$t$	time interval	second (s)

One watt is one joule per second: $1\,\text{W}=1\,\text{J}/\text{s}$ . A kilowatt is $1000\,\text{W}$ , a megawatt is $10^6\,\text{W}$ and one minute is $60\,\text{s}$ .

Situation	Power comparison
same work done in less time	greater power
more energy transferred in the same time	greater power
same power for twice the time	twice the energy transferred
twice the work done in twice the time	unchanged power

Identify the work done or the relevant energy change, convert energy to joules and time to seconds, then divide by the time. Use $W=Pt$ or $\Delta E=Pt$ to find energy, and $t=W/P$ or $t=\Delta E/P$ to find time.

Example: a machine transfers $18\,\text{kJ}$ in $60\,\text{s}$ . Convert $18\,\text{kJ}=18{,}000\,\text{J}$ , so $P=18{,}000/60=300\,\text{W}$ .

Power is not the total energy transferred. A device can transfer a large amount of energy slowly and have low power. Force, speed or distance alone is also insufficient: the calculation needs work or energy and the associated time interval.

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