Question

The unit of power is:
A) Watt per second
B) Joule
C) Kilojoule
D) Watt

Answer 1

Hint: Power is a ratio of work done to the time taken. It is defined as the time rate at which work is done or energy is transferred.

Complete step by step solution:
We know that Power is defined as the time rate at which work is done or energy is transferred.
If $W$ is the amount of work done in a time t then the average power $P$ is given by the ratio of the work done W to the total time t.
 Therefore, power is given by the formula
$P = \dfrac{W}{t}$
Where $P$ is the power, $W$ is the work done and $t$ is the time.
We are interested to find out the SI unit of power.
The work is given as,
Thus, the SI unit of work done is the Joule, and the SI unit of time is second.
Therefore, the unit of power will be,
$P = \dfrac{{Joule}}{{\sec }}$
Which can be also written as Joule per second or $J{s^{ - 1}}$
But $J{s^{ - 1}}$ is known as the Watt (W).
Thus, if we look at the options given, the option (A),(B) and (C) does not represent the unit of power.

$\therefore $The unit of power is Watt(W). Hence, the Correct option is (D).

Additional information:
If $dw$ is the work done in an extremely small time interval $dt$, the instantaneous power is,
$P = \dfrac{{dW}}{{dt}}$
Since $dW = \overrightarrow F .\overrightarrow {ds} $ ,
Then $P = \dfrac{{\overrightarrow F .\overrightarrow {ds} }}{{dt}}$
We know that,$\dfrac{{\overrightarrow {ds} }}{{dt}} = \overrightarrow v $ is the velocity of a body.
Thus, we have,$P = \overrightarrow F .\overrightarrow v $
Therefore, power can also be defined as the dot product of force and velocity.
Where $\overrightarrow v $ is the instantaneous velocity when the force applied is $\overrightarrow F $.
We know that The SI unit of power is the watt (W).
If one joule of work is done per second, the power is one watt.
\[1{\text{ }}watt{\text{ }}\left( W \right){\text{ }} = {\text{ }}1joule/\sec ond\]
\[1{\text{ }}kilowatt{\text{ }}\left( {kW} \right){\text{ }} = {\text{ }}1000watt\]
\[1{\text{ }}megawatt{\text{ }}\left( {MW} \right){\text{ }} = {\text{ }}{10^6}watt\]
\[1{\text{ }}horse{\text{ }}power{\text{ }}\left( {HP} \right){\text{ }} = {\text{ }}746watts\]
Kilowatt-hour (kWh) is a large practical unit of work and energy. It is used particularly in calculating the consumption of electrical energy. The electricity bill carries the energy consumption in units of kWh. A kilowatt-hour is equal to the total quantity of energy consumed or work done in one hour at a rate of thousand joules per second.
\[1{\text{ }}kWh{\text{ }} = {\text{ }}1{\text{ }}kilowatt \times 1hour\]
\[= {\text{ }}1000{\text{ }}joule/\sec ond \times 3600{\text{ }}\sec onds\]
\[1kwh{\text{ }} = {\text{ }}36 \times {10^5}joules\]

Note:
(i) Power can also be defined as the dot product of force and velocity.
(ii) Power is a scalar quantity.