with its Derivation<\/strong><\/span><\/p>\n\n\n\n In this article, we will find the Dimensional Formula of Power<\/p>\n\n\n\n Dimensional Formula for Power is given by<\/p>\n\n\n\n $[M^1 L^2 T^{-3}]$<\/p>\n\n\n\n Here Power is defined as work done per sec Dimension of Time= $[M^0 L^0 T^{1}]$<\/p>\n\n\n\n Dimension Formula of Work can be derived using work done formula So, Now we know both the displacement and Force dimension , we can calculate the dimension of Work easily as<\/p>\n\n\n\n $\\text {dimension of Work} = \\text {dimension of Force} \\times \\text {dimension of displacement}$<\/p>\n\n\n\n $= [M^1L^1T^{-2}] \\times [L^1] = [M^1L^2T^{-2}]$<\/p>\n\n\n\n Now that we know the dimension of work done and time<\/p>\n\n\n\n Therefore<\/p>\n\n\n\n $\\text{Dimension of Power} = \\frac {[M^1 L^2 T^{-2}]}{[M^0 L^0 T^{1}]}= [M^1 L^2 T^{-3}]$ Unit of Power is watt<\/p>\n\n\n\n Try the free Quiz given below to check your knowledge of Dimension Analysis:-<\/p>\n\n\n\n
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M<\/strong> denotes Mass
L<\/strong> denotes Length
T<\/strong> denotes Time<\/p>\n\n\n\nDerivation for expression<\/h3>\n\n\n\n
$Power = \\frac {\\text{work done}}{Time}$
or
$P = \\frac {W}{t}$
Now<\/p>\n\n\n\n
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<\/p>\n\n\n\n
Now the dimension of displacement= $[L^1]$
Dimension of force is given by=$[M^1L^1T^{-2}]$
<\/p>\n\n\n\n
is denoted by $P$<\/p>\n\n\n\n
\nQuiz on Dimensional Analysis<\/strong><\/span><\/h4>\n
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