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Power in Physics: Definition, Formula, SI Unit, Examples & Numericals
Power in Physics is the rate of doing work or transferring energy. In simpler terms, power measures the speed at which work is being done by a person, machine, or body.
When two machines do the same amount of work but take different amounts of time, the machine that completes the work in lesser time has greater power. Power is therefore an important concept for understanding how quickly energy is used or work is completed.
This complete guide explains the definition of power, power formula, SI unit, different formulas, examples, numericals, power vs energy, horsepower, and important questions. It is useful for students preparing for JEE Main, CBSE, ICSE, AP Physics, IB Physics, and other international science examinations.
Power is defined as the amount of work done or energy transfer per unit time.
P = W/t
Where:
P = Power
W = Work done
t = Time taken
Power is also expressed as:
P = E/t
Where E = Energy transferred.
The expression for the power is derived by the ratio between the work done and time taken. Power can also be expressed using the energy and time formula: P=W/T and P=E/T.
| Formula | Meaning | When to Use It |
|---|---|---|
| P = W / t | Power = Work ÷ Time | Work is known and time is known |
| P = E / t | Power = Energy ÷ Time | Energy is known and time is known |
| P = F × d / t | Power using force and displacement | Force, displacement, and time are known |
| P = F × v | Power using force and velocity | Force and velocity are known |
| P = V × I | Electrical power | Voltage and current are known |
| P = I²R | Electrical power | Current and resistance are known |
| P = V² / R | Electrical power | Voltage and resistance are known |
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The speed at which work is done, or energy is converted, transmitted, or utilized, is referred to as power.
Power is mathematically calculated by:
Power = Work Done ÷ Time Taken
A machine that performs more work in lesser time possesses more power.
For instance:
Two students climb up the same stairs.
Student A does so in 10 seconds.
While Student B does it in 20 seconds.
If both perform an almost equal amount of work, then Student A has higher power than Student B.
Use this guide to plan JEE Main, JEE Advanced, DASA, mock tests, documents and engineering admission from the USA or another country.
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Power is defined as the rate at which work is done or energy is transferred. The SI unit of power is the watt (W).
1 Watt = 1 Joule of energy transferred per second
Therefore: 1 W = 1 J/s
This means that a device has a power of 1 watt when it performs 1 joule of work in 1 second.
The unit watt is named after James Watt, whose improvements to steam-engine technology played an important role in the development of modern engineering.
For larger values of power, commonly used units include:
1 kilowatt (kW) = 1,000 W
1 megawatt (MW) = 1,000,000 W
Other Common Units of Power:
| Unit | Equivalent |
|---|---|
| 1 Watt (W) | 1 Joule per second |
| 1 Kilowatt (kW) | 1,000 W |
| 1 Megawatt (MW) | 1,000,000 W |
| 1 Horsepower (hp) | Approximately 746 W |
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HP stands for horsepower, which is a unit for measuring power, particularly the power delivered by engines and motors. The unit also describes how fast engines and machines are at doing work.
The term horsepower was developed through history to give an analogy between the power delivered by steam engines and the amount of work that can be done by horses.
The most commonly used conversion is:
1 horsepower (hp) ≈ 746 Watts (W)
Since:
1 kilowatt (kW) = 1,000 Watts
Therefore:
1 hp ≈ 0.746 kW
The power output of a motor is 2 hp.
From: 1 hp = 746 W
Power = 2 × 746
Power = 1,492 W
Thus, a 2 hp motor has a power output of 1,492 W.
Horsepower (hp) is frequently used for automobiles, motorcycles, engines, pumps, and motors, whereas Watt (W) is the SI unit of power used in Physics.
The magnitude of power generated or consumed is based on a number of physical quantities. In different cases and formulas, the primary variables that determine power are work done, time taken, and force/velocity.
By using the equation:
P = W/t
For the same amount of time, doing more work requires more power.
Example: When one machine does 1,000 joules of work in 10 seconds and another machine does more work in the same amount of time, the machine doing more work requires greater power.
The relationship between power and time, when the amount of work remains the same, is inversely proportional.
P = W/t
This means that completing the same amount of work in less time requires more power.
Example: Two machines perform the same amount of work, but one machine takes less time than the other. The machine that completes the work in less time has greater power.
If power is determined from force and displacement, the equation is:
P = F × d/t
For the same displacement and time taken, the greater the force used, the greater the power produced.
With regard to force and velocity, the formula for determining power is:
P = F × v
For the same force, the greater the velocity, the greater the power produced.
Preparing for JEE Main Physics? Strengthen your understanding of important topics such as power, work, energy, electrical power, formulas, and numerical problems with expert guidance and focused JEE preparation resources from TestPrepKart.
The dimensional formula of power is [M L² T⁻³].
It can be found using:
Power = Work / Time
As:
Work = Force × Displacement
Therefore, the dimensional formula of work is [M L² T⁻²].
Dividing by time, we get:
[M L² T⁻³]
This topic is very helpful for JEE Main and Physics questions.
P = W/t
The above formula can be used when:
Work is known
Time is known
Example: A machine does work equal to 500 joules in 10 seconds.
P = W/t
P = 500/10
P = 50 W
Thus, the power of the machine is 50 W.
The formula for calculating power when energy is transferred or consumed is:
P = E/t
Example: An object uses 2,000 joules of energy in 20 seconds.
P = E/t
P = 2,000/20
P = 100 W
Therefore, the object has a power of 100 W.
Since Force × Displacement = Work, the power formula can be written as:
P = F × d / t
Where:
F = Force
d = Displacement
t = Time taken
Example:
An object travels 15 metres in 20 seconds with a force of 50 N.
P = F × d / t
P = 50 × 15 / 20
P = 750 / 20
P = 37.5 W
Therefore, the power is 37.5 W.
Another way to express power is:
P = F × v
Where:
F = Force
v = Velocity
When a force causes an object to move, this formula comes in handy.
Students should comprehend the direction of force and velocity for more complex scenarios.
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The rate at which electrical energy is converted or used is referred to as electric power.
The principal formula for electric power is:
P = V × I
Where:
P = Power in watts
V = Potential Difference in volts
I = Current in amperes
Using the relationships from Ohm’s Law, electric power can also be expressed as:
P = V²/R
P = I²R
Electricity power is derived using different formulae according to the electrical values known. The three widely applied formulae are:
1. P = V × I — Use this when voltage and current are known.
2. P = I²R — Use this when current and resistance are known.
3. P = V²/R — Use this when voltage and resistance are known.
An electrical circuit contains:
Voltage (V) = 10 V
Resistance (R) = 50 Ω
Next, by utilizing the formula:
P = V² / R
P = 10² / 50
P = 100 / 50
P = 2 W
Therefore, the electrical power of the circuit is 2 watts (W).
The above formulas are based on Ohm’s Law and are helpful to solve physics problems on electrical power.
There is often confusion between the terms “work,” “energy” and “power.” However, there are distinct differences.
| Feature | Work | Energy | Power |
|---|---|---|---|
| Meaning | Force causes displacement | Capacity to do work | Work done per unit time |
| Formula | W = F × d | Depends on type of energy | P = W / t |
| SI Unit | Joule (J) | Joule (J) | Watt (W) |
| Time Factor | Not directly required | Not directly required | Time is directly involved |
| Example | Lifting a box | Energy stored in a battery | The rate at which work is done |
Energy = Capacity to perform work
Work = Transfer of energy by means of force and distance
Power = Rate at which work is accomplished
Despite their similarities, power and energy are not the same thing.
Energy is the capacity to perform labor, whereas power is the rate at which energy is transferred or used.
When two appliances consume the same amount of energy, for example, the appliance that uses the same amount of energy in a shorter amount of time will have higher power.
| Feature | Energy | Power |
|---|---|---|
| Meaning | Capacity to do work | Rate of doing work or transferring energy |
| Formula | E = P × t | P = E / t |
| SI Unit | Joule (J) | Watt (W) |
| Time | Total energy can depend on how long a device operates | It tells about how fast energy is being consumed or transferred |
| Example | A battery stores electrical energy | Energy consumption rate of a 100 W bulb is 100 joules per second |
Assume that 1,000 Joules of energy are used by two machines.
In 10 seconds, Machine A uses up the energy.
In 20 seconds, Machine B uses up the energy.
Based on the formula:
P = E / t
For Machine A:
P = 1,000 ÷ 10 = 100 W
For Machine B:
P = 1,000 ÷ 20 = 50 W
Therefore, Machine A is more powerful because it transfers the same amount of energy in less time.
The total rate at which work is completed or energy is moved over a certain amount of time is described by average power. It is computed by dividing the total amount of energy transmitted or labor completed by the total amount of time required
Average Power = Total Work Completed / Total Time
Alternatively:
Average Power = Total Energy Transferred / Total Time
For instance, the average power of a machine that completes 2,000 J of work in 20 seconds is:
Average Power = 2,000 / 20 = 100 W
When a system’s or device’s power output fluctuates over time, average power is very helpful.
The power generated or used at a specific moment in time is known as instantaneous power. It tells us how quickly work is being done or energy is being transmitted at a particular moment, unlike average power, which describes the entire process.
For mechanical systems, instantaneous power can be written as:
P = F × v
Where F is the force and v is the velocity at that particular moment.
For electrical systems, instantaneous power can be written as:
P = V × I
Where V is the voltage and I is the current at that particular moment.
In sophisticated physics, electrical circuits, engines, motors, and engineering applications where power can fluctuate constantly over time, instantaneous power is particularly helpful.
A high power equipment is not necessarily the one that consumes the most amount of energy.
This is because:
An appliance rated at 1,500 W consumes energy at a rapid rate.
An appliance rated at 100 W consumes energy at a slower rate.
Power gives us the rate of energy consumption, but the total energy consumed depends on both power and time.
Energy = Power × Time
So:
Power tells us how quickly energy is consumed or transferred.
Energy tells us the total amount consumed or transferred.
Time determines how much total energy is used for a given power level.
For electric appliances:
Energy = Power x Time In measuring the use of electricity at home, one standard unit that is used is the kilowatt-hour (kWh).
1 kWh = 1,000 W × 1 hour
This is referred to as one unit of electricity.
ExampleA machine of 500 W runs for 10 hours.
Convert power into kilowatts:
500 W = 0.5 kW
Calculate energy:
Energy = Power × Time
= 0.5 × 10
= 5 kWh
Therefore, the machine consumes 5 kWh of electrical energy.
The concept of power enables us to quantify how fast work can be done.
An engine with more power will do mechanical work faster than an engine with less power.
The power rating of an electric motor is used to measure its speed of doing work.
A 100 W bulb consumes electrical energy faster than a 10 W bulb.
A man running up the stairs faster might be generating more power than a person going up slowly, despite their end point being at the same height.
The pump with high power is able to deliver the energy faster than the other one.
Power is a crucial topic that is included in Physics for the JEE Mains and other academic exams. Questions can be based on mechanical work done, electrical circuitry, energy consumed, or the speed with which the work is done. Knowing how the different variables interact is more valuable than just learning formulas.
| Concept | Formula |
|---|---|
| Power | P = W / t |
| Power using Energy | P = E / t |
| Work | W = F × d |
| Mechanical Power | P = F × v |
| Electrical Power | P = V × I |
| Electrical Power | P = I²R |
| Electrical Power | P = V² / R |
| Electrical Energy | E = P × t |
The students who are going to take JEE Main must understand the use of formula, but not just memorize formulas.
The power numerals can be easily and effectively solved by employing an easy-to-use algorithm. The key element in solving power numerals is to identify the known values and the right formula.
Step one is to clearly read the question and state the values given.
For instance,
Work done = 500 J
Time taken = 10 s
In this case, it will be easy to determine the formula to use.
The appropriate formula should be selected from the options provided based on the values stated in the question.
Some commonly used power formulas are:
P = W/t -> If work done and time are provided
P = E/t -> If energy and time are provided
P = F × d/t -> If force, distance, and time are provided
P = F × v -> If force and velocity are provided
P = V × I -> If voltage and current are provided
P = I²R -> If current and resistance are provided
P = V²/R -> If voltage and resistance are provided
Before applying the formula, make sure your units are compatible.
Units of example:
1,000 W = 1 kW
3,600 seconds in an hour
1 horsepower ≈ 746 W
This will assist you in preventing computation errors.
Plug the given values in the selected equation, and solve the problem accordingly.
Example
600 J of work is done by the machine in 15 seconds.
Given:
W = 600 J
t = 15 seconds
Using:
P = 40 W
P = 600/15
P = W/t
Power of the machine is thus 40 W.
Lastly, confirm that the unit in your response is right.
The SI unit of power is:
(W) Watts
Convert the final response if the query requests power in kilowatts (kW) or another unit.
TestPrepKart helps students strengthen their JEE Physics preparation with focused study material, formula practice, numerical questions, and expert guidance. Improve your understanding of important topics such as Power, Work, Energy, Electricity, and Mechanics and prepare more effectively for JEE Main.
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Indian students studying abroad can have an education based on American curriculum, IB, British, CBSE, and others. Even if their school curriculum is not the same, the topic of power is crucial in Physics.
As for students preparing for Indian engineering entrance tests like JEE, the main thing that matters is numerical practice.
| School Learning | JEE-Focused Preparation |
|---|---|
| Understand the concept | Use the concept for challenging questions |
| Learn formulas | Know when to apply which formula |
| Solve basic numericals | Multi-stage problem solving |
| School tests | Timed competition practice |
| Chapter exercises | Last year’s questions & mocks |
Students studying in the USA, UAE, Saudi Arabia, Qatar, Kuwait, Bahrain, and Oman can improve their preparation by integrating their classroom education along with JEE numeric questions.
TestPrepKart helps students prepare for JEE Main Physics with structured learning resources, numerical practice, formula revision, and expert guidance. Build a stronger understanding of topics such as Power, Work, Energy, Mechanics, and Electrical Power while improving your problem-solving skills.
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Power is the rate at which energy is transferred or work is completed in a given amount of time.
The basic formula for power is P = W / t, where P represents power, W represents work done, and t represents the time taken.
The SI unit of power is the watt (W).
One watt means that one joule of energy is transferred or one joule of work is done per second.
1 W = 1 J/s
Work refers to the energy transferred when a force causes displacement, while power measures how quickly that work is done or energy is transferred.
The basic electrical power formula is:
P = V × I
Other commonly used electrical power formulas are:
P = I²R
P = V² / R
Mechanical power can be calculated using:
P = F × v
Here, F represents force and v represents velocity.
Power is a scalar quantity because it has magnitude but no direction.
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