Same job, different speed
Two students carry identical boxes up the same flight of stairs. One walks; the other runs. Both do the same amount of work, but the runner does it faster. The runner has more power.
Power is how fast energy is transferred or work is done.
The power formula
power = work ÷ time or power = energy ÷ time
P = W ÷ t
| Quantity | Unit |
|---|---|
| Power | Watt (W) |
| Work or energy | Joule (J) |
| Time | Second (s) |
1 watt = 1 joule per second.
The watt is named after James Watt, the Scottish engineer who greatly improved the steam engine in the 1700s.
Example 1
A student does 2400 J of work climbing stairs in 8 seconds.
P = 2400 ÷ 8 = 300 W
Example 2
A crane lifts a 500 kg load 20 m in 25 s.
- Work = force × distance = (500 × 9.8) × 20 = 98 000 J
- Power = 98 000 ÷ 25 = 3920 W (about 3.9 kW)
Bigger units
| Unit | Equal to | Example |
|---|---|---|
| Kilowatt (kW) | 1000 W | A microwave oven, about 1 kW |
| Megawatt (MW) | 1 000 000 W | A large wind turbine, 2–5 MW |
| Gigawatt (GW) | 1 000 000 000 W | A large power plant |
Ontario’s Bruce Nuclear Generating Station, one of the largest nuclear plants in the world, can produce over 6 GW. Quebec’s Robert-Bourassa hydroelectric station produces about 5.6 GW.
Horsepower
Horsepower (hp) is an older unit still used for engines. James Watt invented it to compare his steam engines with horses.
1 hp ≈ 746 W
| Machine | Power |
|---|---|
| A person working steadily | About 75–100 W (about 0.1 hp) |
| A horse working steadily | About 750 W (1 hp) |
| A lawn mower | About 3–4 kW |
| A family car | About 100–150 kW |
| An electric pickup truck | Several hundred kW |
Electrical power
For electrical devices:
P = V × I (power = voltage × current)
Example: A 120 V hair dryer draws 12.5 A. P = 120 × 12.5 = 1500 W
| Device | Typical power |
|---|---|
| Phone charger | 5–20 W |
| LED bulb | 8–10 W |
| Laptop | 50 W |
| TV | 100 W |
| Toaster | 900 W |
| Electric kettle | 1500 W |
| Clothes dryer | 3000 W |
Power and energy are different
- Power is a rate: how fast energy is used.
- Energy is an amount: how much is used in total.
energy = power × time
Electric companies measure energy in kilowatt-hours (kWh): 1 kWh is the energy used by a 1000 W device running for one hour (3.6 million joules).
A 10 W LED bulb left on for 100 hours uses 1 kWh. A 3000 W dryer uses 1 kWh in just 20 minutes.
Efficiency
No device turns all its input energy into useful output. Some is always "lost," usually as heat.
efficiency = useful power output ÷ total power input × 100%
Example: A motor takes in 500 W and produces 400 W of useful motion. Efficiency = 400 ÷ 500 × 100% = 80%.
| Device | Approximate efficiency |
|---|---|
| Incandescent bulb | 5% |
| LED bulb | 30–50% |
| Car engine (gasoline) | 20–35% |
| Electric motor | 85–95% |
| Human body | About 20–25% |
Human power
Your body is a power source too. A trained cyclist can sustain about 400 W for an hour, and sprint at over 1500 W for a few seconds. Your brain uses about 20 W, about the same as a dim light bulb!
Common mistakes
- Mixing up power and energy. A powerful device isn’t necessarily using a lot of energy if it’s only on briefly.
- Forgetting time is in seconds when calculating watts.
- Thinking kilowatt-hours measure power. They measure energy.
Try it yourself
- Time yourself walking and then running up a flight of stairs. Measure the height of the stairs. Calculate your power using P = (mass × 9.8 × height) ÷ time.
- Find the wattage of five appliances at home. Rank them from most to least powerful.
- A 60 W bulb runs for 5 hours. How many kWh does it use? What about a 9 W LED?
(Answers to 3: 0.3 kWh; 0.045 kWh)
Quick recap
- Power is the rate of doing work or transferring energy.
- P = W ÷ t; electrical power P = V × I.
- Power is measured in watts; 1 W = 1 J/s.
- Energy = power × time, often measured in kilowatt-hours.
- Efficiency compares useful output with total input.