# Power

**Power**

Power of a body is defined as the rate at which the body can do the work.

Average power

Instantaneous power [As ]

*i.e.* power is equal to the scalar product of force with velocity.

Important Points

(1) Dimension : [P]=[F][v]=[MLT^{-2}][LT^{-1}]

[P]=[ML^{2} T^{-3}]

(2) Units : *Watt* or *Joule*/*sec* [S.I.]

*Erg*/*sec* [C.G.S.]

Practical units : *Kilowatt* (*kW*), *Mega* *watt* (*MW*) and Horse power (*hp*)

Relations between different units : 1 watt= 1 Joule/sec = 10^{7} erg/sec

1hp=746 Watt

1MW=10^{6} Watt

1kW= 10^{3} Watt

(3) If work done by the two bodies is same then power is inversely proportional to time

*i.e.* the body which perform the given work in lesser time possess more power and vice-versa.

(4) As power = work/time, any unit of power multiplied by a unit of time gives unit of work (or energy) and not power, *i.e.* Kilowatt-hour or watt-day are units of work or energy.

1kWh=3.6 * 10^{6} Joule

(5) The slope of work time curve gives the instantaneous power. As *P* = *dW*/*dt* = tan*θ*

(6) Area under power time curve gives the work done as P=dW/dt

*W* = Area under *P*-*t* curve

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