You might’ve observed that wrestlers pick up the heavy mass in very little time because they have the power to perform such an activity.
So, what is power?
Power is the rate of doing an activity or work in the minimum possible time. It is the amount of energy transferred or converted per unit time where large power means a large amount of work or energy.
For example, when a powerful car accelerates speedily, it does a large amount of work which means it exhausts large amounts of fuel in a short time.
On This Page, we will Learn About the Following :
What is power with example?
Example1: Suppose, person A and B are assigned the task of picking up an equal number of boxes to the top floor of the building.
Let’s say there are 10 boxes of 10 kg each to be picked up by both A and B. Each time they walk a distance of 5 m. Since the work done by both is in the form of potential energy mgh is given by,
W = mgh = 10 x 10 x 5 = 500 J is the work done by you both.
Suppose, A finishes his task in 50 s and B in 100 s.
As you can see the relationship of Work done per unit time is nothing but the Power.
The rate at which work is done is referred to as power. It is always dependent on the work done. It is defined as the amount of energy that is converted per unit of time. Its International System of Unit is Watt which is equal to one joule per second. It is a scalar quantity.
For instance, a large amount of work is done and a large amount of fuel is consumed in a short period of time when a powerful car is accelerated rapidly.
Definition of Power
The power is the time taken by you to complete any task or activity.
The power doesn’t remain constant, but how?
Let’s consider Example.1,
Suppose the boy A walks at a pace (high power), he slows down (less power), continues with this speed, takes rest in between (P= 0 as W = 0), then walks with the pace.
Here, when he makes variations in the speed, the work done varies too, at an instant, the power delivered is different at the different instant.
We can conclude that at different instants, the power (Example.1) doesn’t remain the same.
So the power delivered in a certain period of time is called instantaneous power.
If the Δt approaches to zero then power will be instantaneous and given by,
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Pav=[lim_{Delta trightarrow 0}frac{Delta W}{Delta t}] |
ΔW is the work done in a short interval of time Δt (instant time).
Power, the least possible time required by a person or an object to do the work.
Power Formula
The power is a time-based quantity that is related to the pace at which work is done. The power of an object can be given by-
[textrm{Power}=frac{textrm{work done}}{Time}]
[textrm{Power}=frac{W}{t}]
SI Unit of Power
The standard metric unit of work is represented in the terms of Joule and the unit for standard metric time is represented in seconds. Thus, the unit for standard metric power is given as-
[textrm{Power}=frac{textrm{Joule}}{textrm{second}}=Js^{-1}=Watt]
The multiples of power: KW, MW, GW…
Watt: When a body does work of one joule in one second it is called one-watt power.
Another unit of power (In British engineering) is Horsepower (hp).
Where 1hp = 746 W
Dimensional Formula of P: [[M^1][L^2][T^{-3}]]
When a body does work of 550 foot-pounds per second (746 W) is called its one horsepower.
Average Power
The ratio of the total amount of work done in the total amount of time is called the average power.
There are certain instruments used to compute average power. If we talk about Fibre optic power instruments, they measure the average power of a continuous light beam that is used to test signal power in fiber-optic networks.
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Pav = [frac{Delta W}{Delta t}] |
Note: If the work is done at a uniform rate, then the average and instantaneous power becomes equal, and the common equation comes out to be,
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P = [frac{Delta W}{Delta t}] |
Electric Power
Electric power is defined as the rate, per unit time at which energy is transformed from the electrical energy of the moving charges to some other form, e.g. heat, mechanical energy, usually created by electric generators.
Electric generators convert mechanical energy obtained from an external source (the power of motion) into electrical energy.
Electric Power Formula is Stated as,
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P = V I Where P is the power V is the potential difference in the circuit and I is the electric current. Other formulas of power are: P = [I^2R=frac{V^2}{R}] (This expression is obtained by Ohms’ law V = IR) R = Resistance |
P = [frac{W}{t}]
states that higher the electrical current (I) the higher the heat generated, and so the higher the power/ energy loss since electrical energy is transformed into heat.
Work, Energy, and Power
Suppose, you want to displace a body (do some work W) to some distance S by applying your energy (Force F).
The mathematical relationship to describe the above scenario is given by,
W = F S …(1)
P = [frac{W}{t}]…..(2)
Using the above two equations,
P = [frac{Fs}{t}]
We know that V = [frac{s}{t}]
So
This is the relation between power and force.
Consumption of Energy and Power
The power consumption rate is higher as the appliance is used for a long time which results in a greater cost of that appliance. Therefore the power consumption rate for an appliance is given by-
P = [frac{W}{t}] = [frac{E}{t}]
Where the energy supplied is represented by E
Therefore, the energy which is consumed in time t will be given by-
E
= Pt
Power – Solved Examples
Problem1: Riya has a mass of 60 kg and runs up to 13 m high in 50 seconds. Compute her power. (Take g = 10m/s²)
Solution: Given h = 13 m, m = 60 kg and t = 50 s
P = W/t = mgh /t
= 60 x 10 x 13/ 50
On solving we get,
P = 156 W
Problem2: If the current and voltage of an electric circuit are 3 A and 15 V respectively. Calculate the electrical power.
Solution: Given I = 3 a and V = 15 V
Since P =VI
= 3 x 15
We get, P = 45 W
Problem3- If the mass of a person climbing a tree which is 5 meters high is 60 kg and he climbs up the tree in 10 seconds. What is the power required for him to climb up the tree? g=10 m/s²
Solution- Given
Mass of the person m = 60 kg
Height of the tree h = 5 meters
Acceleration due to gravity g = 10 m/s²
Time interval t = 10 seconds
Therefore work done will be,
Work = m.g.h
Work = 60 × 10 × 5 = 3000 Joules
Thus the power will be work done per unit time,
Power = [(frac{Watt}{t})] = [(frac{3000}{10})] = 300 Joule/second
Hence the power required to climb up the tree will be 300 J/s.
Conclusion:
Electricity is a type of power which is produced by electric means and it has wide applications in everyday life. It has become an essential part of modern life and is used by people for cooling, heating, and refrigeration, and for operating appliances such as machinery, electronics, public transportation systems, and so on.