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Unit of Power

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Last updated date: 19th May 2024
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Introduction to Unit of Power

In Physics, work is done when a force acting on an object results in its displacement. Work done is not determined by the amount of time the force took to cause the displacement. Sometimes the work is done quickly, and other times it might be slow and take longer. If a bodybuilder and a sixth-grader carry a weight of 10 kgs up a flight of stairs, then the bodybuilder would most likely take less time than the sixth-grader to finish the same job. Here we can say that the bodybuilder has a higher power rating than the sixth-grader.

 

So we see it is the power that has to do with the rate at which work is done. We will look into a few concepts around power, work, and energy in this article and discuss the unit of power in si unit and provide you with units of power list in different measurement systems.

 

Formulas for Work and Power

The word “work” has a different meaning in the world of Physics. In Physics, work done is given by force applied on an object to move a distance (d), and its formula is:

 

W = F * d. 

 

Even after applying a lot of force, if an object does not move, then in the eyes of a physicist, no work is done.

 

The word “power” is also used differently by physicists. Power is the ratio of work and time, i.e. the time taken to complete a work gives the power of an entity. It is expressed mathematically as: 

 

Power = \[\frac{Work}{Time} \] or \[P = \frac{W}{t}\]

 

Power is the rate at which energy (heat and electrical) is transferred. While studying electricity, you would find the power is defined as:

Power = V * I, where V is the voltage within the circuit, and I is the current through the circuit.

 

We could derive another formula for power from the formula for work. Since Work = force * distance and power =worktime, then power = force * distancetime

 

Now we know that velocity = distance/time hence:

 

Power = Force * Velocity = F * V

 

What is the SI Unit of Power in Physics?

To define units of power let us look into how the SI system works. The SI or metric system has only 7 base units, and all the other units are derived from these base units. In the metric system, mass is measured in kilograms, length in metres, and time in seconds. Unit of force (which is mass times acceleration) is kg.m/s2. From this, we can get the unit of work as kg.m2/s2. But this unit gets cumbersome to write in every equation, so scientists have defined another unit Joule (J), which is named after the physicist James Prescott Joule. I Joule = 1 kg.m2/s2and it is the unit of energy in the SI system. 

 

The unit of power is the watt, which is abbreviated by W. It has an SI base unit and several derived units that are used to measure other physical quantities associated with energy or work. The International System (SI) states that one joule per second equals one watt. One kilowatt-hour represents 3600 joules, while a megawatt-hour stands for 1000000 watts/3600000 seconds - meaning it's equivalent to roughly 12 million horsepower! Here are some additional facts about the unit of power:


When measuring electrical voltage in volts, amperage in amps, or resistance in ohms you're using three different forms of this fundamental measurement


Power can be calculated knowing only two of the three aforementioned electrical values


Power is work divided by time; hence the SI unit of power is joules/second. Scientists have given a name for this unit, and the unit of power in the SI unit is Watt (named after James Watt, the Scottish inventor of steam engines that helped launch the Industrial revolution.).

 

1 Watt = 1 Joule /second = 1 kg m2 s-3

 

Submultiples and Multiples of Watt

The SI multiples and submultiples of Watt are listed in the table below:

 

Submultiples of Watt

Name

Symbol

Value

deciwatt

dW

10-1 W

centiwatt

cW

10-2 W

milliwatt

mW

10-3 W

microwatt

𝜇W

10-6 W

nanowatt

nW

10-9 W

picowatt

pW

10-12 W

femtowatt

fW

10-15 W

attowatt

aW

10-18 W

zeptowatt

zW

10-21 W

yoctowatt

yW

10-24 W

 

Multiples of Watt

Name

Symbol

Value

decawatt

daW

101 W

hectowatt

hW

102 W

kilowatt

kW

103 W

megawatt

MW

106 W

gigawatt

GW

109 W

terawatt

TW

1012 W

petawatt

PW

1015 W

exwatt

EW

1018 W

zettawatt

ZW

1021 W

yottawatt

YW

1024 W

 

Units of Power in Other Systems and their Equivalent in Watts

You can find below units of power list with formula on how to convert them into Watt

 

Unit

Equivalent in Watt

Horsepower (HP)

746 W

BTU (British Thermal Unit)

1 Watt = 9.47 * 10-4 BTU

Foot pounds

1 Watt = 0.737 foot-pounds

Calories per sec

1 Watt = 0.24 calories per second

 

How Can Varying Power Be Measured?

In certain setups like houses, the power is used to varying degrees. For example, we use less electricity during the day than at night when all the lights are on. In these situations, power is expressed in three ways:

  • Instantaneous Power - This is the power measured at any given instant of time.

  • Average Power - When you measure power over long periods of time, you can get average power. This can be calculated by plotting a graph of power vs time and finding the area under the curve, which gives the total work done, and then dividing it by the total time.

  • Peak Power - The maximum value of instantaneous power in a specific system over a long period of time is peak power. In systems like car engines and stereo systems, peak powers occur much higher than the average power. But peak power is maintained only for a very short duration to avoid damages. 


The Unit of Power is used in Various Areas:

  1. Electrical Measurements

One watt is equal to 0.74549 horses or 550 foot-pounds per second

When measuring electrical voltage in volts, amperage in amps, or resistance in ohms you're using three different forms of this fundamental measurement

Power can be calculated knowing only two of the three aforementioned electrical values

Watts and horsepower are not interchangeable, as one watt is equal to 0.74549 horses or 550 foot-pounds per second.

  1. Voltage - Unit is power is used in measuring voltage

Voltage is the electrical potential difference between two points in a circuit.

It is measured in volts (symbolised by V).

One watt is equal to one volt applied across a resistance of one ohm.

  1. Ampere - Unit is power is used in measuring amperes

The rate at which electrical energy flows through a circuit or part of an electronic     system, defined as one coulomb per second.

One watt is equal to 0.001335 ampere

The watt is most commonly used when measuring electrical power, though it can be applied to other forms of power as well. In the United States, we use watts to measure our electricity usage on our monthly energy bills. We also rate motors in horsepower, which is a unit of power derived from the watt. Many appliances list their wattage or horsepower rating in order for you to know how much power they consume. For example, if you have a large air conditioner that consumes 5000 watts, your electric bill will likely be higher than if you had a small air conditioner that consumed only 1000 watts.

  1. Horsepower- Unit is power is used in measuring Horsepower

A unit of power derived from the watt, typically used to rate motors.

One horsepower is equivalent to approximately 0.74549 kilowatts or 550 foot pounds per second

As you can see, the watt is a very versatile and important unit of measurement! Hopefully this article has helped you become more familiar with it. If you have any additional questions, please feel free to ask in the comments section below.

FAQs on Unit of Power

1. What is Joule?

Joule is the SI unit of work (or energy) which is equal to the work done by a force of 1 Newton to move the point of application 1 metre in the direction in which the force is acting (J = N * m) . 1 Joule is equivalent to 3600th of watt-hour, and it is approximately the amount of energy which is required to lift an apple against Earth’s gravity by a distance of 1 metre. 

2. What is Horsepower?

A horsepower is a unit of power that originated in the 17th century. Horsepower is used to denote how much power a typical horse uses to turn a capstan. In an attempt to sell his steam engines, James Watt tried to quantify the amount of work it can do in a certain interval of time. A typical pony at that time could lift 220 pounds of coal to a height of 100 feet out of a mine in a minute which gave it the power of 22,000 ft-lb/min. Watt incorrectly assumed that a typical horse could perform 330 foot-pounds of work in a minute which is how the definition of horsepower came. In SI units 1 HP = 740 Watts. A Horsepower unit is generally reserved for defining the capacity of air conditioners and engines.

3. What are the benefits of the Unit of Power?

Unit of power is used in various areas to measure electrical voltage, amperage, resistance etc. It's most commonly used when measuring wattage on our monthly energy bills and it can be applied to other forms of power as well.

4. What are some common misconceptions about the Unit of Power?

Watt & horsepower are not interchangeable, watt = 0.74549 horses or 550 FT-LBS per second and one HP(horsepower) is equivalent to approximately 0.74549 kilowatts or 550 foot pounds per second! One unit of power equals a joule/second which equals a volt across the resistor with value Ω for one second. Lastly, watts and volts are not the same as power and voltage.

5. Is the unit of power only used with electricity?

No, it isn't! The Unit of Power can also be found in gas and water heating appliances which use electric elements as an additional heat source to help increase efficiency and reduce consumption costs.

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