The electrical resistance R of a conductor of length l and area of cross section a is given by R=( l)/(a) where ' ' is the electrical resistivity. What is the dimensional formula for electrical conductivity ' σ ' which

Correct answer: A. [M^ -1 L^ -3 T^3 A^2] Dimensional formula for electrical resistivity, =[ML^3 ~T^ -3 ~A^ -2 ] Dimensional formula for electrical conductivity, σ=(1)/( ) is [M^ -1 ~L^ -3 ~T^3 ~A^2]

JEE Main 201226 MayOnline

Exam: JEE Main
Year: 2012
Date: 26 May
Mode: Online
Subject: Physics
Chapter: Units and Dimensions

JEE Main 2012 · 26 May · Online · Physics · Units and Dimensions

The electrical resistance R of a conductor of length l and area of...

The electrical resistance

R

of a conductor of length

l

and area of cross section

a

is given by

R=\frac{\rho l}{a}

where '

\rho

' is the electrical resistivity. What is the dimensional formula for electrical conductivity '

\sigma

' which is reciprocal of resistivity?

Options

A $\left[M^{-1} L^{-3} T^3 A^2\right]$
B $\left[M L^{-3} T^{-3} A^2\right]$
C $\left[M L^3 T^{-3} A^{-2}\right]$
D $\left[M^{-2} L^3 T^2 A^{-1}\right]$

Correct answer

A. $\left[M^{-1} L^{-3} T^3 A^2\right]$

Step-by-step solution

Dimensional formula for electrical resistivity,

\rho=\left[\mathrm{ML}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]

Dimensional formula for electrical conductivity,

\sigma=\frac{1}{\rho}

is \left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^3 \mathrm{~A}^2\right]

Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s… JEE Advanced 2026 A new unit (α) of length is chosen such that it is equal to the speed of light in vacuum.… JEE Main 2026 Consider the equation H = (x^p ε^q E^r)/(t^s) , where H= magnetic field; E= electric… JEE Main 2026 The percentage error in the calculated volume of a sphere, if there is 2\% error in its… JEE Main 2026 Match List - I with List - II. List - I List - II A. Boltzmann constant I. [M^ -1 L^3T^… JEE Main 2026 The potential energy of a particle changes with distance x from a fixed origin as V = A x… JEE Main 2026 Match List-I with List-II. List-I List-II A. Meter (L) I. (hc)/(G) B. Second (S) II.… JEE Main 2026 L , C and R represents physical quantities inductance, capacitance and resistance… JEE Main 2026 Full Units and Dimensions list All JEE Main PYQs