Power

What is Power?

Power measures how quickly energy is transferred or work is done.

P = \frac{E}{t}

A powerful machine does the same job as a less powerful one but in less time.

Units of Power

Unit	Meaning
Watt (W)	1 J per second
Kilowatt (kW)	1 000 W
Megawatt (MW)	1 000 000 W

Everyday Power Values

Device	Approximate power
Phone charger	10–20 W
Light bulb (LED)	8–15 W
Hair dryer	1 500–2 000 W
Electric kettle	2 000–3 000 W
Family car engine	50–150 kW

Comparing two lifters: Mia lifts 500 J in 5 s; Tom lifts 500 J in 10 s.

Mia's power: $P = 500 \div 5 = 100 \text{ W}$

Tom's power: $P = 500 \div 10 = 50 \text{ W}$

Mia is twice as powerful as Tom (same work, half the time).

A 200 W motor runs for 3 minutes. How much energy does it use?

$t = 3 \times 60 = 180 \text{ s}$

$E = P \times t = 200 \times 180 = 36\,000 \text{ J} = 36 \text{ kJ}$

Note

The light bulb myth: an old 60 W incandescent bulb uses 4× more power than a 15 W LED for the same brightness.

Real world: electricity bill and kilowatt-hours

A household uses a 2 kW electric kettle for 10 minutes each day. Daily energy: $E = 2000 \times (10 \times 60) = 1\,200\,000\text{ J} = 1.2\text{ kWh} \div 1000 = 0.333\text{ kWh}$ . At €0.30/kWh, monthly cost $= 0.333 \times 30 \times 0.30 \approx 3\text{ EUR}$ . Power and energy calculations help households manage electricity costs.

Real world: comparing athlete performance

In weightlifting, two athletes both lift 100 kg by 2 m ( $W = 100 \times 9.8 \times 2 = 1960\text{ J}$ ), but Athlete A does it in 1 s and Athlete B in 2 s. Power A $= 1960\text{ W}$ ; Power B $= 980\text{ W}$ . Power measures athletic explosiveness — not just how much work is done but how fast.

Real world: solar panel output

A rooftop solar panel is rated at 400 W. In 5 hours of peak sunshine: $E = 400 \times (5 \times 3600) = 7\,200\,000\text{ J} = 7.2\text{ MJ} = 2\text{ kWh}$ . Homeowners use power ratings and sunshine hours to calculate how much energy their panels generate and how much they save on electricity bills.

Tip Power is energy per second:

P = E/t

. To find energy used, rearrange:

E = P \times t

. Always convert time to seconds before calculating energy in joules.

Practice Problems

A student climbs stairs, lifting their 50 kg body 3 m in 6 s (g = 10 N/kg). Calculate the power output.

Show answer

W = F × d = 500 × 3 = 1500 J. P = 1500 ÷ 6 = 250 W.

A 1.5 kW kettle runs for 4 minutes. How much energy (in kJ) does it use?

Show answer

E = 1500 × 240 = 360,000 J = 360 kJ.