Units & Dimensions

JEE Main level, single correct, medium

140 of 149

Question 140 of 149

The electrical resistance RR of a conductor of length ll and area of cross section aa is given by R=ρlaR=\frac{\rho l}{a} where ' ρ\rho ' is the electrical resistivity. What is the dimensional formula for electrical conductivity ' σ\sigma ' which is reciprocal of resistivity?

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Answer: (A) [M−1L−3T3A2]\left[M^{-1} L^{-3} T^3 A^2\right]

Dimensional formula for electrical resistivity, ρ=[ML3 T−3 A−2]\rho=\left[\mathrm{ML}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right] Dimensional formula for electrical conductivity, σ=1ρ\sigma=\frac{1}{\rho} is [M−1 L−3 T3 A2]\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^3 \mathrm{~A}^2\right]

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