Concept of Power

Power is a measure of how quickly work is done. It tells us whether work is being completed at a fast or slow rate. In simple terms, power is the rate at which work is done. If a certain amount of work $W$ is done in time $t$, the power $P$ can be calculated as:

Power =`"Work"/"Time"` 

P=`"W"/"t"`

An introduction to scientists:

Units of Power:

1. SI Unit

The standard unit of work is the joule (J), and time is measured in seconds (s). Therefore, the SI unit of power is:

Power (P) =`"Joule (J)" / "Second(s)"` = Watt (W)

1 watt (W) means that 1 joule of work is done in 1 second.

2. Horsepower (hp)

In industries, power is also measured in horsepower (hp). 1 horsepower = 746 watts.

The unit used to measure large amounts of energy consumption, like electricity in homes, is the kilowatt-hour (kWh). 1 kilowatt-hour is the energy consumed when 1000 watts (1 kilowatt) of power is used for 1 hour. Conversion of 1 kWh to Joules:

1 kW = 1000 W, and 1 hour = 3600 seconds.

The energy used in 1 kWh is:

1 kWh = 1000 W × 3600 s = 3,600,000 J.

So, 1 kWh = 3.6 × 10⁶J

In electricity bills, 1 kWh = 1 unit.

If a 1000 W (1 kW) heater is used for 2 hours, the energy consumption can be as follows:

Energy = 1 kW × 2 hours = 2 kWh. 

This means 2 units of electricity were used.

The rate of doing work is called power.

Power P = \[\frac{\text{Work done }W}{\text{Time taken }t}\]

or

P = \[\frac {W}{t}\]

• S.I. unit: If 1 joule of work is done in 1 second, the power spent is said to be 1 watt.
• C.G.S. unit: The C.G.S. unit of power is erg per second (erg s^-1).
• Relationship between S.I. and C.G.S. units:
   1 W = 1 J s^-1 = 10⁷ erg s^-1
• 1 horse power (H.P.) = 746 W = 0.746 kW