Power Revision Notes

Power is defined as the rate at which work is done or energy is transferred. It tells us how quickly energy changes from one form to another or how fast work is performed by a force.

Power is a scalar quantity, meaning it has magnitude only and no direction.

In everyday terms, a more powerful machine can do the same amount of work in less time compared to a less powerful one.

• Power = work done per unit time
• Power = energy transferred per unit time
• Power is scalar

The mathematical expression for power is: P = W / t = ΔE / t, where:

P is power in watts (W) W is work done in joules (J) ΔE is the change in energy in joules (J) t is the time taken in seconds (s)

Since work done and energy transferred are measured in joules and time in seconds, the unit of power is joules per second, which is called a watt (W). One watt equals one joule per second (1 W = 1 J/s).

• P = W / t = ΔE / t
• Power unit: watt (W) = joule per second (J/s)
• Work and energy unit: joule (J)
• Time unit: second (s)

To calculate power, use the formula P = W / t or P = ΔE / t.

If the problem provides power and time, you can rearrange the formula to find work done or energy transferred: W = P × t or ΔE = P × t.

If power and work done are known, time can be found by t = W / P or t = ΔE / P. Always ensure units are consistent before substituting values into the formula to avoid errors.

• Calculate power: P = W / t
• Calculate work done: W = P × t
• Calculate time: t = W / P
• Check units before substitution
• Include units in final answers for clarity
• Example calculation:
• A motor does 500 J of work in 10 s. Calculate power:
• P = 500 J / 10 s = 50 W

Power depends on how quickly energy is transferred or work is done. For example, lifting a weight slowly requires less power than lifting it quickly, even though the work done is the same.

Power relates to the rate of energy conversion in machines, engines, and electrical devices.

Higher power means more energy is transferred per second, which often corresponds to greater performance or output.

• Power measures rate of energy transfer
• Same work done faster means higher power
• Power relates to machine performance

A frequent mistake is confusing work done with power or forgetting to include time in calculations.

Another common error is mixing units, such as using minutes instead of seconds without conversion.

Always write down the formula clearly, substitute values with units, and check that the final answer has the correct unit of watts (W).

• Do not omit time in power calculations
• Convert all time units to seconds
• Include units in all steps
• Use correct formula and rearrangements