Power

Power tells us how fast energy is transferred or how fast work is done. A powerful machine does the same job in less time, or more work in the same time.

Definition and equations

Power is the rate of energy transfer:

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

• P is power (watts, W)
• E or W is energy transferred/work done (joules, J)
• t is time (seconds, s)
• Unit fact: $1\,\text{W} = 1\,\text{J s}^{-1}$
• Bigger units: $1\,\text{kW} = 1000\,\text{W}$

Mechanical power

When a force makes something move at steady speed in the same direction as the force:

$$P = Fv$$

• Lifting at steady speed: $F = mg$, so $P = mgv$ or $P = \dfrac{mgh}{t}$
• Use $g \approx 9.8\,\text{N kg}^{-1}$ (or 10 for simple estimates)

Electrical power

In circuits, power tells how quickly electrical energy is transferred to devices:

$$P = IV$$

• I is current (amperes, A)
• V is potential difference (volts, V)

Power vs energy

• Power is “how fast.” Energy is “how much.”
• A 60 W bulb transfers 60 J every second. If it runs for 10 s, it transfers 600 J.
• High power does not always mean high efficiency; it just uses energy faster.