What Do We Understand by Power?
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.
(image will be uploaded soon)
On This Page, we will Learn About the Following :
What is power with example?
Definition of power
Power formula
Define average power
Define electric power
Power equation
Work energy and power
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.
(image will be uploaded soon)
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,
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.
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,
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,
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.
FAQs on Power
1. What is Power and Energy in Electric Terms?
In any given time interval, the energy consumed in a span of time is given by
PE = qV
Where E is the electric energy, V is the voltage, and q is the amount of charge moved via voltage V in a time interval t which is equal to the integral of power over time.
2. What is Power in Terms of Physics? Can Power be Negative?
Power is the measure of the rate at which the energy is transferred per unit time. Power is a scalar quantity. In electrical engineering, power represents the rate of electrical energy flowing into or out of a given component, negative power is just the power flowing in the opposite direction from positive power.
3. What are some of the differentiating points between power and energy?
The capacity of something to do work is defined as the energy while the rate at which the energy is transferred is known as the power. The most commonly used unit of energy is represented by Newton-meter or Watt-seconds while the most commonly used unit of power is Watt represented by Joules/second. Energy is a time component while power is an instantaneous quantity.
4. What is meant by electrical power?
Electrical power is measured as the rate of electrical energy which is transferred per unit time in an electrical circuit. It can also be defined as the rate at which, in an electrical circuit, the energy is transformed or the work is done. Its SI Unit is joule per second or watt and is denoted by P. The most common examples where electric power is supplied include electric generators and electric batteries. The formula for electric power is given by P=VI where power is represented by P’’, the potential difference in the circuit is represented by ‘V’, and the electric current across the circuit is represented by ‘I’.
5. What is meant by average power?
The amount of work done in a period of time that is equal to \[(\frac{\Delta W}{\Delta t})\] is referred to as the average power. It can also be described as the amount of energy that is transferred in \[(\frac{\Delta E}{\Delta t})\] period of time. In simple terms, the average power is the average amount of energy or average amount of work done which is converted per unit of time. It is sometimes referred to as ‘power’ as well.
6. What is meant by instantaneous power?
The power which is given at an instance is referred to as the instantaneous power. It can also be described as the amount of power that is required in a circuit at any instance of time. It is given by P = \[\frac{\Delta E}{\Delta t}\]. If the value of the average power is limited in such a way that the value of t is approached to 0, we get the instantaneous power. It is an important metric in electronics.
