Power: definition, equations and examples
Principles of energy • Energy stores and changes
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Key concepts
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Precise definition and units
Power equals the rate at which energy is transferred. Power also equals the rate at which work is done. The SI unit of power is the watt (W). One watt equals one joule of energy transferred per second (1 W = 1 J/s). The definition emphasises time: doubling the energy transferred in the same time doubles the power, while doubling the time for the same energy halves the power.
Key equations and rearrangements
Two commonly used equations express power in terms of energy or work: P = E/t and P = W/t, where P is power, E is energy transferred in joules (J), W is work done in joules (J), and t is time in seconds (s). Rearrangement allows solving for energy or time: E = P × t, W = P × t, and t = E / P or t = W / P. Correct use of units ensures consistent answers: J for energy or work, s for time, and W for power.
Examples in everyday devices
A kettle with a power rating of 2.0 kW transfers energy to water faster than a 1.0 kW kettle; the higher-power kettle boils the same mass of water in about half the time because the energy per second is larger. Power ratings on appliances state the maximum rate of energy transfer under normal operation. Practical examples in textbooks use kettles and cookers to show how P = E/t predicts heating times.
Comparing machines that do the same job
Two motors that lift the same mass through the same height transfer the same amount of gravitational potential energy for each lift. The motor that completes the lift in less time has the greater power. Cause → effect: faster lifting (smaller t) causes larger P for the same energy change (E), since P = E/t. Textbook examples contrast cranes and motors to show that power measures how quickly a task is done even when the work per task is identical. fileciteturn0file12turn0file14
Key notes
Important points to keep in mind