Power: P = W / t

The idea

Power is the rate at which energy is transferred or work is done. The equation P = W / t links power P in watts to work done W in joules and time t in seconds. One watt equals one joule per second, so a 60 W lamp transfers 60 J each second. To use the equation, identify the energy transferred (or work done) and the time taken, convert time to seconds and energy to joules, then divide.

For example: A motor doing 3000 J of work in 20 s has P = 3000 J ÷ 20 s = 150 W. Rearranged, W = P × t and t = W ÷ P. This relationship explains why the same work done faster requires greater power, and it applies to electrical devices, machines and muscles.

What earns the marks

• State that power is the rate of energy transfer or work done, measured in watts where 1 W = 1 J/s.
• Select and apply P = W / t, substituting work done in joules and time in seconds.
• Rearrange the equation correctly to W = P × t or t = W ÷ P when the question requires it.
• Convert units before substitution, for example minutes to seconds or kilojoules to joules, and give the answer with the correct unit.
• Interpret a numerical answer as the energy transferred each second, linking the value to the rate of transfer.

Common mistakes and how to put them right

• Dividing time by work instead of work by time.

  Put it right by checking that P = W / t and that a larger time gives a smaller power for the same work.

• Forgetting to convert minutes to seconds.

  Put it right by multiplying minutes by 60 before substituting into the equation.

• Mixing up joules and watts in the final answer.

  Put it right by remembering that power is measured in watts and work done or energy in joules.

Exam tips

• Write the equation, then substitute values with units before calculating so the examiner can follow your method.
• Check that time is in seconds and energy is in joules; convert first, then calculate.
• If the question asks for time or work done, rearrange the equation before substituting numbers to reduce errors.