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# State and define the S.I. unit of power.

Last updated date: 17th Sep 2024
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Hint: First, understand what power is. Define power and write the formula for it. In simple words power is nothing but work done per unit time. Convert the mathematical formula of power into basic units in the MKS system. Now, define 1 unit of power in the S.I. system. Power can also be defined as energy per unit time.

The International System of Units (SI) is the modern form of the metric system. It is the only system of measurement with official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units.
The work done per unit time is referred to as power. Sometimes Power is also defined as the energy consumed per unit time or rate of consumption of energy.
Therefore,
$\text{Power =}\dfrac{\text{Workdone}}{\text{Time}}\text{=}\dfrac{\text{Energy consumed }}{\text{Time}}$
If $W$is the work done in time t then power is given as
$P=\dfrac{W}{t}$
In order to get S.I. unit of power, the units of work done and time must be in S.I. system
Thus, if work done is in joules and time is in seconds then S.I. unit of power is given as
S.I. unit of power $\text{= }\dfrac{\text{Joule}}{\text{Second}}=Watt$
Thus, S.I. the unit of power is Joule per second or Watt.
Definition of 1 Watt:
If 1 Joule of work is done in 1 second then we say that 1 Watt of power is consumed.

Units used to measure different quantities vary from place to place. So to have a uniformity in units a system called ‘The International System of Units’ (abbreviated as SI) is used.
There are seven basic units defined in the SI system:
Length – meter $\left( m \right)$
Time – second $\left( s \right)$
Amount of substance – mole $\left( mole \right)$
Electric current – ampere $\left( A \right)$
Temperature – kelvin $\left( K \right)$
Luminous intensity – candela $\left( cd \right)$
Mass – kilogram $\left( kg \right)$
Power is also expressed in other units like kWh (kilowatt hour), hp (horsepower), ergs per second, milliwatt, etc.
$1\text{ horsepower }=\text{ }745.7\text{ }Watts$

Note:
It is not necessary to memorize units. Only understand the concept of power from that you can deduce the formula and units. Do not get confused with the S.I. unit of power since usually it is expressed in many units.
Power can also be written as $\text{P = Vx I = Volt x Amp}$
Unit of power can also be deduced by the following method.
\begin{align} & P=V\times I \\ & 1volt\times 1Amp=\dfrac{1J}{1C}\times \dfrac{1C}{1s} \\ & \dfrac{1J}{1s}=W(watt) \\ \end{align}
The S.I. unit of power is $W$.