Power Calculations

Power is the rate of energy transfer, or the rate of doing work. A more powerful device transfers the same amount of energy in less time.

The equations

$P = \frac{E}{t} \quad \text{or} \quad P = \frac{W}{t}$

Symbol	Quantity	Unit
$P$	Power	W (watts)
$E$ or $W$	Energy transferred or work done	J
$t$	Time	s

1 watt = 1 joule per second.

Worked example

An electric motor transfers 5400 J of energy in 30 s. Calculate its power.

$P = \frac{5400}{30} = 180\text{ W}$

Worked example: finding time

A 60 W light bulb is on for 5.0 minutes. Calculate the energy transferred.

Convert time: $5.0 \times 60 = 300$ s

$E = P \times t = 60 \times 300 = 18\,000\text{ J} = 18\text{ kJ}$

Common errors and how to correct them

Forgetting to convert minutes to seconds. Power is in watts (J/s), so time must be in seconds.

Confusing power and energy. Power is the rate; energy is the total amount transferred. A 100 W bulb running for 10 s transfers 1000 J. The power is constant at 100 W; the energy grows with time.

How to apply this in an exam

State the equation, convert time to seconds, substitute, calculate, and give the unit (W). For multi-step problems (e.g. power of a student climbing stairs), calculate the energy transferred first (using GPE or work done), then divide by time.