Power: To understand the concept of Power, we need to understand what is Work and Energy and their relation to Power. In Physics, work is defined as when the force acting on a body displaces the body in its direction. The capacity of doing any work is known as energy. And, work done in a given unit of time is called Power.

When we study throughout the day, it is not considered work done according to Physics. But when we lift a bucket of water to some height, it is considered work done by us according to Physics. Let’s get into the article to learn about the concept of power, its formula, units, practice problems and solved examples in detail. Read on to find out more.

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What is Power in Physics?

In Physics, power is the rate of doing work. For example, let’s consider three men participating in a race, running the same distance but completing the race in different time intervals. The time taken by man \(A,\) man \(B\) and man \(C\) are \(6\,{\rm{s, 8}}\,{\rm{s}}\) and \(10\;{\rm{s}}\) respectively. Here, the man who is taking less time is more powerful than the man who is taking more time to complete the race. In this case, man \(A,\) is the most powerful among the three men.

For doing some work, we need energy which is the capacity or the ability to do some work. So, power can also be said to be the rate of consumption of energy. For example, if an electric motor consumes the same amount of energy in a lesser time in comparison to another motor, then the power of the first motor is said to be higher than the second motor.

Definition of Power

Power is defined as the rate of doing work. It can also be written as the rate of consumption of energy.

Power Formula

If a device does a work \(\left( W \right)\) in time \(\left( t \right),\) then its power \(\left( P \right)\) is given by the formula,
\(P = \frac{W}{t}\)
We can calculate work \(\left( W \right)\) using the formula \(W = F \times s\)
where,
\(F\) is the force applied
\(s\) is the displacement caused by the force along its direction
Thus, the formula of power can also be written as
\(P = \frac{W}{t} = \frac{{F \times s}}{t}\)
Power is also the rate of consumption of energy. So, the formula of power can be written as
\(P = \frac{E}{t}\)
where,
\(E\) is the energy consumed
Power can also be expressed in terms of force \(\left( F \right)\) and velocity \(\left( v \right)\) as,
\(P = F \times v\)

Unit of Power

The SI unit of work is joule \(\left( {\rm{J}} \right)\) and the SI unit of time is second \(\left( {\rm{s}} \right).\) Thus, the SI unit of power is \({\rm{J}}\;{{\rm{s}}^{ – 1}}.\) This unit of power is watt \(\left( {\rm{W}} \right)\) and is named in honor of James Watt.
The power of a device is said to be one watt if it can work at the rate of one joule in one second.
Another common unit used to measure power is horsepower \(\left( {{\rm{hp}}} \right)\) where \({\rm{1}}\,{\rm{hp = 746}}\,{\rm{W}}.\)

Applications of Power

Power is an essential concept in terms of knowing how to get our work done at a particular rate. Few applications in our day-to-day life are given below:

1. While traveling in an elevator, we see the instructions regarding how many people the elevator can accommodate at a time. Such decisions are taken based on the power of the engine used to operate the elevator.
2. We have different types of cars available in the market. Some may have a high pick up while some can carry a higher number of people. Such demarcation is based on the power of the engine used in the car.
3. Motors are used to pump water and take it to a certain height. The decision of choice and installation of the motor is done based on the work required to be done and the power of the motor to be used.
4. The concept of power can be utilized to estimate the time required to complete a certain task if we know at what rate the work is being delivered. Alternatively, we can estimate the rate at which work is to be delivered if we are clear with the time to be invested and the amount of work is to be completed.
5. Power helps to decide the number of devices to be employed to get a task done. That is, what would be the amount of power of the devices to be utilized is known to us along with their limitations.  

Solved Examples

Q.1. A device does \(50\) joules of work in \(5 \) seconds. What is its power?
Ans: Given that,
The work done by the device is \(W = 50\;\,{\rm{J}}{\rm{.}}\)
The time taken by the device is \(t = 5\,{\rm{s}}{\rm{.}}\)
The power of the device is \(P = \frac{W}{t} = \frac{{50}}{5} = 10\,{\rm{W}}{\rm{.}}\)

Q.2. An engine has a power of \(30\,{\rm{W}}.\) How much work does the engine do in \(15\,{\rm{s}}\)?
Ans: Given that,
The power of the engine is \(P = 30\;\,{\rm{W}}{\rm{.}}\)
The time taken by the engine is \(t = 15\,{\rm{s}}.\)
The work done by the engine is \(W = P \times t = 30 \times 15 = 450\,{\rm{J}}\)

Q.3. A water tank placed on five storeyed building is at a height of \(25\,{\rm{m}}\) from the ground level. The volume of the tank is \(5\,{{\rm{m}}^3}.\) Find the power rating of the pump required to fill the tank in \(10\,{\rm{min}}{\rm{.}}\)
Ans: Given that,
The volume of the tank \(V = 5\,{{\rm{m}}^3}\)
Mass of water needs to be shifted from ground
\(m = V \times \rho  = 5 \times 1000 = 5000\,{\rm{kg}}\)
Height through which water needs to be taken \(h = 25\,{\rm{m}}\)
Time in which tank needs to be filled \(t = 10\,{\rm{min}} = 600\,{\rm{s}}\)
Work done in moving water from ground to top of 5^th floor \(W = m \times g \times h\)
\(\Rightarrow W = 5000 \times 10 \times 25 = 1250000\,{\rm{J}}\)
Power of the pump required \(P = \frac{W}{t} = \frac{{1250000}}{{600}} = 2083.3\,{\rm{W}}\)
Therefore the power of the pump required is \(2083.3\,{\rm{W}}\)

Related Topics to Power

1. Work 2. Energy and Law of Conservation 3. Alternative Sources of Energy 4. Potential Energy

Study Materials On Embibe

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Frequently Asked Questions on Power

The frequently asked questions on Power are given below: