(B) We know that resistivity is given by $\rho = \frac{R A}{\ell}$.Conductivity $\sigma = \frac{1}{\rho} = \frac{\ell}{R A}$.Since $V = I R$,we have $

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) We know that resistivity is given by $\rho = \frac{R A}{\ell}$.Conductivity $\sigma = \frac{1}{\rho} = \frac{\ell}{R A}$.Since $V = I R$,we have $R = \frac{V}{I}$. Substituting this,$\sigma = \frac{\ell I}{V A}$.The dimensions are:$[\ell] = [L]$$[I] = [I]$$[A] = [L^2]$$[V] = [M L^2 T^{-3} I^{-1}]$Substituting these into the formula:$\sigma = \frac{[L][I]}{[M L^2 T^{-3} I^{-1}] [L^2]} = \frac{[L][I]}{[M L^3 T^{-3} I^{-1}]}$$\sigma = [M^{-1} L^{-3} T^3 I^2]$.

Class 12 Physics Current Electricity Resistance of wire, Resistivity and Conductivity

Medium

In the following,$I$ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity.

JEE MAIN 2016 All JEE MAIN

A
$M^{-1} L^{-3} T^3 I$
B
$M^{-1} L^{-3} T^3 I^2$
C
$M^{-1} L^3 T^3 I$
D
$M L^{-3} T^{-3} I^2$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Current Electricity

Subtopic

Resistance of wire, Resistivity and Conductivity

Previous Year

JEE MAIN 2016 Paper All JEE MAIN years →

$A$ metal wire of specific resistance $64 \times 10^{-6} \, \Omega \cdot \text{cm}$ and length $198 \, \text{cm}$ has a resistance of $7 \, \Omega$. The radius of the wire will be ............. $\text{cm}$.

Easy

View Solution

$A$ cylindrical metallic wire is stretched to increase its length. If the resistance of the wire is increased by $4 \%$, then the percentage increase in its length is (in $\%$)

EasyTS EAMCET 2021

View Solution

The resistance of a wire is $20 \Omega$. It is stretched,so that the length becomes three times,then the new resistance of the wire will be (in $\Omega$)

EasyTS EAMCET 2020

View Solution

For which material does resistivity decrease with an increase in temperature?

Medium

View Solution

The resistance of a wire is $5\, \Omega$ at $50\, ^\circ C$ and $6\, \Omega$ at $100\, ^\circ C$. The resistance of the wire at $0\, ^\circ C$ will be .............. $\Omega$.

MediumAIEEE 2007

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

In the following,$I$ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity.

Similar Questions

$A$ metal wire of specific resistance $64 \times 10^{-6} \, \Omega \cdot \text{cm}$ and length $198 \, \text{cm}$ has a resistance of $7 \, \Omega$. The radius of the wire will be ............. $\text{cm}$.

$A$ cylindrical metallic wire is stretched to increase its length. If the resistance of the wire is increased by $4 \%$, then the percentage increase in its length is (in $\%$)

The resistance of a wire is $20 \Omega$. It is stretched,so that the length becomes three times,then the new resistance of the wire will be (in $\Omega$)

For which material does resistivity decrease with an increase in temperature?

The resistance of a wire is $5\, \Omega$ at $50\, ^\circ C$ and $6\, \Omega$ at $100\, ^\circ C$. The resistance of the wire at $0\, ^\circ C$ will be .............. $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module