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Power: Learn its Definition, Formula, Units with Solved Examples
IMPORTANT LINKS
Work Energy and Power
To grasp the concept of power, we must first comprehend what work and energy are and how they relate to power. Work is described in physics as the displacement of a body caused by a force acting on it. The capacity to carry out any work is defined as energy. Work done in a specified unit of time is referred to as Power.
Power
It is measured as the rate at which work is performed. Since time is not a vector quantity, neither is energy or work because work is not directional. As a result, the it is defined as the ratio of two scalar quantities. Thus, it is a scalar quantity.
Formula
It is expressed mathematically as
where W is the amount of work done in Joules and t is the amount of time taken in seconds.
According to the above equation, more power is used or conveyed when a large amount of work is completed in a short period of time.
Dimensional Formula of Power
It’s dimensional formula is given by
To derive that
Now
Dimension of time =
Dimension of Work = dimension of Force x dimension of displacement
=
Dimension of Power =
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Unit of PowerS.I. Unit of Power
Watt is the S.I. unit of power (W). One watt is one joule of power transmitted per second.
1 Watt=1 J /s
Horsepower was used as a unit of power prior to Watt becoming the S.I. unit of power. However, because horsepower is a very large unit, Watt was introduced to find a smaller unit of power.
1 Horsepower = 746 Watts.
Average Power
The ratio of total work done by the body to the total time taken by the body is defined as average power.
The average power unit is the kilowatt hour (kWh).
Electric Power
It is the rate at which work is done in an electrical circuit. In other words, it is defined as the rate at which energy is transferred.
It is classified into two types: alternating current (AC) power and direct current (DC power). The nature of the current determines the classification of electric power.
Instantaneous Power
The word instantaneously implies ‘right away.’ The electric power anywhere at a point in time, measured in watts, is referred to as instantaneous power.
where dW is the amount of work done in time dt.
Since dW=F. dx
We know that
Where
Consumption of Energy and Power
Energy consumption is determined by dividing the number of power units consumed by the length of time consumed. Thus, the energy consumption formula is given as below
E = P*(t/1000)
where, E is the amount of energy measured in Joules or Kilowatt-hours (kWh), P is the amount of power measured in watts, and t is the amount of time over which the power or energy was consumed.
The amount of input energy needed for an electrical device to function is referred to as power consumption. This really is opposed to power output which is a measure of the level of performance of a heat pump, for example.
Difference Between Power and Energy Parameters Power Energy Meaning It is defined as the rate at which a specific amount of work is completed or energy is transmitted. The capacity to do work is defined as energy. It is the power that accumulates over time. Component It is an instantaneous quantity. Energy is either a time quantity or a component. S.I. unit Watts or Joules per second. Joules or Watt-seconds. Denoted by P W Conversion It can not convert from one form to another. Energy undergoes transformation from one form to another. Storage It cannot be stored. It can be stored.
| Parameters | Power | Energy |
| Meaning | It is defined as the rate at which a specific amount of work is completed or energy is transmitted. | The capacity to do work is defined as energy. It is the power that accumulates over time. |
| Component | It is an instantaneous quantity. | Energy is either a time quantity or a component. |
| S.I. unit | Watts or Joules per second. | Joules or Watt-seconds. |
| Denoted by | P | W |
| Conversion | It can not convert from one form to another. | Energy undergoes transformation from one form to another. |
| Storage | It cannot be stored. | It can be stored. |
Solved Examples
Example 1. A pump is needed to lift 500 kg of water per minute from an 8m deep well and eject it at a speed of 25 m/s. Determine the pump’s power.
Solution 1. Given,
The mass of water, m = 500 kg
h = 8 m height covered
Water ejection velocity, v = 25 m/s
Delivery time, t = 1 minute = 60 seconds
Total energy is converted into work,
P=W / t
Hence, power delivered by pump is 3271 W.
Example 2. A force of 5 N is required to move a body at a constant velocity of 5 m/s on a frictional floor. Determine the force’s generated power.
Solution 2. Given:
Velocity, v = 5 m/s
F = 5 N is the force required to maintain velocity.
P = 5 x 5
= 25W
As a result, the force generates 25 W of power.
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Power FAQs
How is power calculated?
The amount of work done or energy transformed in a given amount of time is defined as power. It is expressed mathematically as
What are the 3 equations for power?
P = V x I
Is watt a power?
Watt is the S.I. unit.
Can power be negative?
Yes, because it is the rate at which work is completed. So, if work done is negative, time taken is positive, then power is negative.
How is force related to power?
Force and power appear to have similar meanings and are frequently confused for one another. However, they are not interchangeable in physics.
What is meant by Instantaneous Power?
The power at a given instant is referred to as instantaneous power.