**Dimensional Formula of Power **

**with its Derivation**

In this article, we will find the Dimensional Formula of Power

Dimensional Formula for Power is given by

$[M^1 L^2 T^{-3}]$

Here**M** denotes Mass**L** denotes Length**T** denotes Time

### Derivation for expression

Power is defined as work done per sec

$Power = \frac {\text{work done}}{Time}$

or

$P = \frac {W}{t}$

Now

Dimension of Time= $[M^0 L^0 T^{1}]$

Dimension Formula of Work can be derived using work done formula

Work is defined as the cross product for Force and displacement

$W= F.d$

Where d -> displacement

F -> Force applied

W-> Work done by the Force

So,

Now the dimension of displacement= $[L^1]$

Dimension of force is given by=$[M^1L^1T^{-2}]$

Now we know both the displacement and Force dimension , we can calculate the dimension of Work easily as

$\text {dimension of Work} = \text {dimension of Force} \times \text {dimension of displacement}$

$= [M^1L^1T^{-2}] \times [L^1] = [M^1L^2T^{-2}]$

Now that we know the dimension of work done and time

Therefore

$\text{Dimension of Power} = \frac {[M^1 L^2 T^{-2}]}{[M^0 L^0 T^{1}]}= [M^1 L^2 T^{-3}]$

is denoted by $P$

Unit of Power is watt

Try the free Quiz given below to check your knowledge of Dimension Analysis:-

**Quiz on Dimensional Analysis**

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