Work and Energy

04 Power

POWER

  • Power can be defined as the rate of doing work.
  • It is the work done in unit time.
  • It decides how quickly work could be done.
  • It can be given by the formula:
Power = Work DoneTime taken

Or,

p = Wt
  • The work, power and energy are all scalar quantities.
  • When work is done, an equal amount of energy is consumed. Power as the rate at which energy consumed can be given by.
Power = Energy consumedTime taken

 

or

 

p = Et

UNIT OF POWER

The SI unit of power is watt.

 

Watt

The power of an agent is one watt if it does work at the rate of 1 joule per second or if it consumes energy at the rate of 1 joule per second.

It can be expressed as:

1 Watt = 1 Joule1 Second

or

1 W = 1 J s1

 

1 kilowatt = 1000 watt  

or

1 kW = 1000 W

1 megawatt = 1000,000 watts      or     1 MW =1000,000 W      or

1MW = 106 W

 

Power of motor vehicles and other machines are given in terms of Horsepower (hp).

 

1 Horse power = 746 watts  or 1 H.P. = 746 W

INSTANTANEOUS POWER

The power at any given instant of time is called instantaneous power.

AVERAGE POWER

Average-power is defined as the total energy consumed divided by the total time taken.

Power is always dependent on work done.

If a person does work at different rates his power also differs at different times. In such cases the concept of average-power is used.

EXAMPLE:

Consider Bulb A of 60 watt bulb is switched ON 24 hours a day and there is another Bulb B of 60 watt turned ON for only 12 hours. Given the context, calculate the energy consumed by both the bulbs in one day.

For the first 12 hours both bulb A and B are turned ON therefore,

Power = 60 + 60 = 120 watts

 

Energy = Power x Time

 

= 120 × 12 = 1.44 kWh (kilo watt hour)

Now for the next 12 hours only bulb A would remain ON:

power = 60 watt

energy = power x time

= 120 x 12 = 1.44 kWh (kilo watt hour)

Now for the next 12 hours only bulb A would remain ON:    

 

power = 60 watts

 

energy = 60 × 12 = 0.72 kWh

The power consumed during the whole day varies because one bulb is turned ON for only 12 hours so we need to calculate average power,

Average power = Total energy consumedTotal time taken
= (1.44 + 0.7224)2

 

= 0.092 kW

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