Write a note on Power .

Explanation

The time rate of doing work is known as power .
Power is also defined as work done per unit time or the time rate at which work is done or energy is transformed .
If `DeltaW` is the work done in time interval `Deltat` , the average power in time interval `Delta t` is
` = (DeltaW)/(Deltat)`
` :. ` Instantaneous power at time t , is
`P = overset lim (Deltax to 0) (DeltaW)/(Deltat)`
` :. P = (dW)/(dt) " "...(1)`
If dW is the work done bu a force `vec(F)` during the displacement `vec(dr)`
` W = vec(F) . vec(dr)`
Substituting the value of W in equatio (1) .
Instataneous power `P = d/(dt) (vec(F).d vec(r ))`
` :. P = vec(F) . (dvec(r ))/(dt) " " [ :. vec(F) " constant " ] `
` :. P = vec(F) . vec(v ) " " [ :. (dvec(r ))/(dt) = vec(v )] `
Power is a scalar quantity , its dimensional formula is `M^(1)L^(2)T^(-3)` SI unit of power is `"Js"^(-1)` . This unit is named as watt in the honour of inventor of stream engine , James Watt .
`1 W = 1 "Js"^(-1)`
Large unit of power are like
` 1 kW = 10^(3) W , 1 MW = 10^(6) W`
To measure large power of vehicles and water pumps in practical , horse power is used which is the unit of British system .
` :. 1 ` horse power (hp) = 746 W
From `P = W/t , Pt = W`
(kWh) : The work done at the rate of 1 kilowatt in 1 hour is called 1 kilowatt hour .
1 kWh = `10^(3)` Watt `xx 3,600 ` second
` :. ` 1 kWh = `3.6 xx10^(6)` J work done
It is known as unit in electric consumption
` :. ` 1 kWh is not of power but it is a unit of energy (work) .