Question

The dimension of electromotive in terms of Current A are
A. \[\text{ }\!\![\!\!\text{ M}{{\text{T}}^{\text{-2}}}{{\text{A}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
B. \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}{{\text{A}}^{\text{2}}}\text{ }\!\!]\!\!\text{ }\]
C. \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}{{\text{A}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
D. \[\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-3}}}{{\text{A}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]

Answer 1

Hint: The formula of electromotive force is work done on the charge per unit charge that is
\[\text{EMF=}\dfrac{\text{work}}{\text{charge}}\]
Using the formula dimensions can be measured.

Complete step-by-step answer:
Given to find the dimension of electromotive force
The formula to find Electromotive force is
\[\text{EMF=}\dfrac{\text{work}}{\text{charge}}\] ….. 1
Where
EMF = Electromotive force
Work done on the charge
The formula for work is
Work = force displacement
Work = mass acceleration displacement
Dimension of mass = \[\text{ }\!\![\!\!\text{ M }\!\!]\!\!\text{ }\]
Acceleration = \[\text{ }\!\![\!\!\text{ L}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
Since acceleration = \[\text{m/}{{\text{s}}^{\text{2}}}\]
Displacement = \[\text{ }\!\![\!\!\text{ L }\!\!]\!\!\text{ }\]
Therefore dimension of work
Work = \[\text{ }\!\![\!\!\text{ M }\!\!]\!\!\text{ }\!\![\!\!\text{ L}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\!\![\!\!\text{ L }\!\!]\!\!\text{ = }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }\]
Formula for charge = Current $\times$ Time
Dimension of
Current = \[\text{ }\!\![\!\!\text{ A }\!\!]\!\!\text{ }\]
Time = \[\text{ }\!\![\!\!\text{ T }\!\!]\!\!\text{ }\]
Therefore dimension of charge=\[\text{ }\!\![\!\!\text{ AT }\!\!]\!\!\text{ }\]
From 1
Dimensions of \[\text{EMF=}\dfrac{\text{ }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}\text{ }\!\!]\!\!\text{ }}{\text{ }\!\![\!\!\text{ AT }\!\!]\!\!\text{ }}\text{= }\!\![\!\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-3}}}{{\text{A}}^{\text{-1}}}\text{ }\!\!]\!\!\text{ }\]
Therefore required dimensions of electromotive force is \[[M{{L}^{2}}{{T}^{-3}}{{A}^{-1}}]\]
Therefore option D is correct.

Note: In general force is defined as
$F=ma$
That’s why we write the dimension of force as $\left[ ML{{T}^{-2}} \right]$.
As we wrote dimensional formulas in terms of exponents that’s why we can only do division and multiplication with this.