Power: time, t, in seconds, s

The idea

Time, t, is the duration over which energy is transferred, measured in seconds, s. In power calculations, t is the denominator: P = E ÷ t, so 1200 J transferred in 40 s gives 30 W. Time must be in seconds before substitution, so convert minutes by multiplying by 60 and hours by multiplying by 3600. For example, a 2 kW kettle boiling for 3 minutes transfers E = 2000 W × 180 s = 360 000 J. Rearranging gives t = E ÷ P, useful when finding how long a device must run. Record t in s, not minutes or hours, and check the answer is sensible: a low-power device takes longer to transfer the same energy.

What earns the marks

• State that t is time in seconds, s, and that it measures the duration of an energy transfer.
• Convert minutes to seconds by multiplying by 60, and hours to seconds by multiplying by 3600, before substitution.
• Use t = E ÷ P to find the time taken when energy transferred and power are known.
• Substitute time in seconds into P = E ÷ t, keeping E in joules and P in watts.
• Give the unit s with the numerical answer and reject answers left in minutes or hours.
• Interpret a longer time as a smaller power for the same energy transferred.

Common mistakes and how to put them right

• Substituting minutes directly into P = E ÷ t.

  Put it right by converting to seconds, for example 5 min = 300 s.

• Writing the unit as min or h.

  Put it right by converting the final answer to seconds, or by stating the unit clearly as s.

• Confusing t with the number of repetitions or cycles.

  Put it right by using the total duration of the energy transfer in seconds.

Exam tips

• Convert all times to seconds before substituting into any power equation.
• Show the conversion step, such as 4 min × 60 = 240 s, so the examiner can award method credit.
• Check the answer is sensible: a 100 W lamp transferring 5000 J takes 50 s, not 50 min.