Question

The dimensions of electromotive force in terms of current $A$ are:
A) $\left[ {M{L^{ - 2}}{A^{ - 2}}} \right]$
B) $\left[ {M{L^2}{T^{ - 2}}{A^2}} \right]$
C) $\left[ {M{L^2}{T^{ - 2}}{A^{ - 2}}} \right]$
D) $\left[ {M{L^2}{T^{ - 3}}{A^{ - 1}}} \right]$

Answer 1

Hint: To solve this question we should know about the base quantities which are used to form the dimensional formulae of any quantity. Also we should know how electromotive force is calculated i.e., the quantities involved in its calculation and their dimensional formulae.

Formulae used:
$V = \dfrac{W}{q}$
Here $V$ is the potential difference across the cell or the electromotive force of the cell, $W$ is the work done by the charge and $q$ is the charge.

Complete answer:
To solve this question we should know what electromotive force is. Electromotive force or the EMF, for short, of a cell is defined as the electric potential produced either by an electrochemical cell or by changing the magnetic field.
We know that,
$V = \dfrac{W}{q}$
Here $V$ is the potential difference across the cell or the electromotive force of the cell, $W$ is the work done by the charge and $q$ is the charge.
Let this be equation 1.
The potential difference gives us the value of the electromotive force or EMF of a cell. So,
$ \Rightarrow V = \dfrac{W}{q}$
Let this be equation 1.
This will give the value of electromotive force or EMF of a cell.
We know that the dimensional formulae of
$\left[ q \right] = \left[ {AT} \right]$
$\left[ W \right] = \left[ {M{L^2}{T^{ - 2}}} \right]$
Substituting the values of the above quantities in the equation 1 we get,
$ \Rightarrow \left[ V \right] = \dfrac{{\left[ {M{L^2}{T^{ - 2}}} \right]}}{{\left[ {AT} \right]}}$
$ \Rightarrow \left[ V \right] = \left[ {M{L^2}{T^{ - 3}}{A^{ - 1}}} \right]$
So the answer will be option (D).

Note: To solve questions related to dimensional analysis of any quantity, break the quantity into its smaller known units. Use the dimensional formulae of the smaller known units to find the dimensional formulae of the given quantity. Electromotive force is the energy per unit electric charge. It is the force driving all electrons. Flow of electrons is due to this force.