Class 11 Physics Work Energy Power | Power |

**Power**

- Power is defined as the time rate at which work is done or energy is transferred.

- Average Power: Ratio of work done(W) in a total time interval of t.

P= W/t_{av } - Instantaneous Power: When the time interval ,t ,approaches zero the limiting value of average power becomes instantenous power.

P = dW/dt - We can write W = F.dr,

P = F . dr/dt

P = F.v , where v is instantaneous velocity. - Power is a scalar quanitity
- SI unit of power – Watt(W)
- 1 hp = 746 W

**Example**: A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m^{3} in 15 min. If the tank is 40 m above the ground, and the efficiency of the pump is 30%, how much electric power is consumed by the pump?

**Solution**: P = W/t = mgh/t

mass of water to be moved = ρV = 30000 kg

g = 9.8

h = 40 m

t = 15x60 = 900 s

P = 13066.67 W = 13.067 kW

Now η = P/P_{ACTUAL} => P_{ACTUAL }= 13.067/0.3 = 43.6 kW

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