The electrical resistance R of a conductor of length I and area of cross section a is given by R = (ρ l/a) where âρâ is the electrical resistivity. What is the dimensional formula for electrical conductivity âσâ which is reciprocal of resistivity?

Question

The electrical resistance R of a conductor of length I and area of cross section a is given by R = (ρ l/a) where âρâ is the electrical resistivity. What is the dimensional formula for electrical conductivity âσâ which is reciprocal of resistivity? (A) [M-1L-3T3A2] (B) [ML-3T3A2] (C) [ML3T-3A-2] (D) [M-2L3T2A-1]

Tardigrade Admin · Accepted Answer

Dimensional formula for electrical resistivity, ρ = [ML3T-3A-2] Dimensional formula for electrical conductivity, σ = (1/ρ) is [M-1L-3T3A2]

Q. The electrical resistance R of a conductor of length $I$ and area of cross section a is given by $R = \frac{ρl}{a}$ where $‘ ρ ’$ is the electrical resistivity. What is the dimensional formula for electrical conductivity ‘\sigma’ which is reciprocal of resistivity?

$[M^{- 1} L^{- 3} T^{3} A^{2}]$

$[M L^{- 3} T^{3} A^{2}]$

$[M L^{3} T^{- 3} A^{- 2}]$

$[M^{- 2} L^{3} T^{2} A^{- 1}]$

Dimensional formula for electrical resistivity, $ρ = [M L^{3} T^{- 3} A^{- 2}]$
Dimensional formula for electrical conductivity, $σ = \frac{1}{ρ}$ is $[M^{- 1} L^{- 3} T^{3} A^{2}]$

Q. The electrical resistance R of a conductor of length I and area of cross section a is given by R=aρl​ where ‘ρ’ is the electrical resistivity. What is the dimensional formula for electrical conductivity ‘\sigma’ which is reciprocal of resistivity?

[M−1L−3T3A2]

[ML−3T3A2]

[ML3T−3A−2]

[M−2L3T2A−1]