Define power as work done per unit time and also as energy transferred per unit time; recall and use the equations (a) P = W / t (b) P = ΔE / t

Published by Patrick Mutisya · 8 days ago

Cambridge IGCSE Physics 0625 – Power (1.7.4)

1.7.4 Power

Learning Objective

Define power as the rate at which work is done or energy is transferred, and use the equations

  • \$P = \dfrac{W}{t}\$

  • \$P = \dfrac{\Delta E}{t}\$

Definition

Power is the amount of work done (or energy transferred) per unit time. It tells us how quickly energy is being used or produced.

Mathematically,

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

where

  • \$P\$ = power (watts, W)

  • \$W\$ = work done (joules, J)

  • \$\Delta E\$ = change in energy (joules, J)

  • \$t\$ = time taken (seconds, s)

Units

QuantitySymbolSI UnitDerived Unit
Power\$P\$wattW = J·s⁻¹ = N·m·s⁻¹
Work / Energy\$W\$, \$\Delta E\$jouleJ = N·m
Time\$t\$seconds

Relationship to Work and Energy

Since work is the product of force and displacement (\$W = Fd\$) and energy is the capacity to do work, power links these concepts to the time factor. A larger power value means the same amount of work or energy is completed in a shorter time.

Worked Example

  1. A motor lifts a 50 kg mass vertically through a height of 10 m in 5 s. Calculate the average power output of the motor.

  2. First find the work done (which equals the increase in gravitational potential energy):

    \$W = mgh = (50\ \text{kg})(9.8\ \text{m s}^{-2})(10\ \text{m}) = 4\,900\ \text{J}\$

  3. Then use the power formula:

    \$P = \frac{W}{t} = \frac{4\,900\ \text{J}}{5\ \text{s}} = 980\ \text{W}\$

  4. Therefore the motor’s average power is 980 W (approximately 1 kW).

Common Mistakes to Avoid

  • Confusing average power with instantaneous power. The formula \$P = \frac{W}{t}\$ gives the average over the time interval.

  • Using inconsistent units (e.g., minutes instead of seconds) which leads to incorrect power values.

  • Forgetting that \$1\ \text{W} = 1\ \text{J s}^{-1}\$; do not treat watts as a separate unit unrelated to joules.

Summary Table

ConceptFormulaUnits
Power (average)\$P = \dfrac{W}{t}\$W (J s⁻¹)
Power (using energy change)\$P = \dfrac{\Delta E}{t}\$W (J s⁻¹)
Work / Energy\$W = Fd = mgh\$J (N·m)

Suggested diagram: A graph of power (vertical axis) versus time (horizontal axis) showing a rectangular area whose size equals the work done.

Key Take‑aways

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

  • Use \$P = W/t\$ or \$P = \Delta E/t\$ depending on whether you know work or an energy change.

  • Always keep time in seconds to obtain power in watts.