Question

The dimensional formula for electric potential is:
(A). $\left[ M{{L}^{2}}{{T}^{-3}}{{A}^{-1}} \right]$
(B). $\left[ ML{{T}^{-3}}{{A}^{-1}} \right]$
(C). $\left[ M{{L}^{2}}{{T}^{-3}}{{K}^{-1}} \right]$
(D). None of these

Answer 1

Hint : The dimensional formula of electric potential can be found by using the dimensions of energy and charge, as electric potential is the work done per unit charge. Mathematically,
$V=\dfrac{W}{q}$ , where V is electric potential, W is the work done by the electric field on charge and q is charge.
So, to obtain a dimension of electric potential we will divide the dimension of work and charge.

Complete Step By Step Solution:
Electric potential of a point is the negative of work done by an electric field in moving unit positive test charge from reference point to given point. Reference point is the point where potential is assumed to be zero. Generally reference is at infinity.
Dimensional formula of a physical quantity is the expression of it in terms of symbols of fundamental units. It is enclosed in brackets. The fundamental units and their symbols are;
Mass [M] Length [L] Time [T] Current [A] Temperature [K] Amount of substance [mol] Luminous intensity [J]

Electric potential of electric field is the work done by field on unit coulomb charge. , mathematically we can write
$V=\dfrac{W}{q}$
The dimension of work is
$M{{L}^{2}}{{T}^{-2}}$
The dimension of charge is
${{M}^{0}}{{L}^{0}}{{T}^{1}}{{A}^{1}}$
So, dimension of pressure will be
$M{{L}^{2}}{{A}^{-1}}{{T}^{-3}}$
Hence the correct option is A.
So, S.I. unit of electric potential will be
$\dfrac{J}{C}$ i.e. joule per coulomb.

Note : Electric potential is a derived quantity, so its dimension is made from the dimension of base S.I. units. The S.I. base units are also known as fundamental units. Even if the power of dimension of length, time and mass in a physical quantity is zero, it is recommended to mention them.