Question

State and define the S.I. units of power.

Answer 1

There are certain systems for the measurement of physical quantities. This includes S.I. (Standard international) units, FPS (Foot pound second system), CGS (Centimeter gram second system), etc. These are named as per the base units taken for measurements. For example in FPS units the base unit for length is foot, that for mass is pound and that for time is second.

Complete step by step answer:
Power is defined as the rate at which work is done. It is a scalar quantity as it is the ratio of work done to the total time taken i.e. $P = \dfrac{Work}{time}$.
Work is defined as the quantity of energy spent on a system to make it. It is also the measure of the body displaced by a certain force. It is also a scalar quantity.
Now, work is defined as the dot product of force and displacement. Since dot product results in a scalar quantity, so it’s a scalar quantity. So, $W = \int F.ds$.
S.I. units of work will be: $N (Newton) \times m (meter) = Nm$, which is also known as Joule (J).
Hence, $P = \dfrac{Work}{time}$, S.I. units of power $= \dfrac{J}{sec}\ or\ J/s$
This is also known as Watt.

Now, 1 Watt is defined when 1 Joule of work is done for 1 sec.

Additional Information: The commercial unit of energy is kilowatt-hour. One might get confused that as watt is mentioned in the unit, so it must be the unit of power. But this is not true. Observe the presence of the hour either. This suggests that it is the product of power and time, which is work.

Note: In all physical phenomenon topics, power plays an important role. There are many ways (formulae) from which the S.I. units of power could be predicted. One of these is $P = \vec F.\vec v$. One must be careful in case of optics where power means the ability of an optical system to converge or diverge the light rays.