Question

The physical quantity having the dimensions [ M^-1 L^-3 T³ A² ] \(\left[ {{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}} \right]\)is
1. resistance
2. resistivity
3. electrical conductivity
4. electromotive force

Answer 1

Correct Answer - Option 3 : electrical conductivity

CONCEPT:

• Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a Dimension is a mathematical tool used for studying the nature of physical quantities. 
• The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
• And the dimensional formula is defined as the expression of the physical quantity in terms of mass, length, and time.

CALCULATION

• The resistance may be written as

\(⇒ R =\frac{V}{I} =\frac{W}{It^{2}}\)

Where W is the work done and I is the current and t is the time

• The dimension of R will be given by

\(⇒ \frac{W}{It^{2}}= \frac{ML^{2}T^{-2}}{A^{2}T} = ML^{2}T^{-3}A^{-2}\)

• The resistivity is given by

\(⇒ \rho = \frac{RA}{l}\)

Where A =Area and l = length

• The dimension of resistivity is 

\(⇒ \rho = \frac{RA}{l} = \frac{ML^{2}T^{-3}A^{2}\times L^{2}}{L} = ML^{3}T^{-3}A^{-2} \)

• As we know, the conductivity is the inverse of resistivity taking the inverse of the dimension of resistivity, then the dimension of electrical conductivity is 

⇒ σ = M^-1L^-3T³A²

• Hence, option  3 is the answer