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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:

Or,

• 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.

or

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:

or

or

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

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,

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)

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,