Important Points
Category : JEE Main & Advanced
(1) Dimension : \[[P]=[F]\,[v]=[ML{{T}^{-2}}]\,[L{{T}^{-1}}]\]
\[\therefore \] \[[P]=[M{{L}^{2}}{{T}^{-3}}]\]
(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 :
\[1\,Watt=1\,Joule/\sec ={{10}^{7}}erg/\sec \]
\[1hp=746\,Watt\]
\[1\,MW={{10}^{6}}\,Watt\]
\[1\,KW={{10}^{3}}\,Watt\]
(3) If work done by the two bodies is same then power\[\propto \frac{1}{\text{time}}\]
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.
\[1\,KWh={{10}^{3}}\frac{J}{sec}\times (60\times 60sec)=3.6\times {{10}^{6}}\,Joule\]
(5) The slope of work time curve gives the instantaneous power. As P = dW/dt = tan \[\theta \]
(6) Area under power-time curve gives the work done as \[P=\frac{dW}{dt}\]
\[\therefore \] \[W=\int{P\,dt}\]
\[\therefore \] W = Area under P-t curve
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