Power

Power in physics

1. The time rate of doing work is called power. If W is the amount of work done in time t, then average power, Pav=W/t.

Power in physics

2. Because power is the ratio of two scalars, the average power is a scalar.

3. The power of an agent during a time interval may not be constant. The instantaneous power is defined as the limiting value of the average power of an agent in a small time interval, when the time interval approaches zero. Hence, if ΔW is the small amount of work done in a small time interval Δt, then instantaneous power is defined as:
P=dW/dt
Now, dW=F.ds
P=F.(ds/dt)

But ds/dt=v, the instantaneous velocity of the particle. Therefore,

P = F. v
Thus, instantaneous power of an agent is measured as the dot product of instantaneous velocity and force acting on it at the instant.
If θ is the angle between F and v, then
P =Fv cosθ
In case, θ =0 P =Fv

4. Dimension and unit of power
a) [P]=[W]/[t]=[ML²T^-2]/[T]=[ML²T^-3]
b) Its absolute unit is Watt in SI. In cgs system its absolute unit is ergs/sec

From the relation P = W/t,
1 Watt = 1 Jule/1 sec =1 Js^-1
The power of an agent is said to be 1 Watt, if 1 Jule of work is done in one second.

5. Bigger unit of power is Kilowatt(KW) i.e, 1KW=10³ W
In engineering, horse power is the practical unit of power.
1 h.p. = 746 W.