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.