(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 $

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(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
$M L^{-3} T^{-3} I^2$

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Class 12

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Current Electricity

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Resistance of wire, Resistivity and Conductivity

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JEE MAIN 2016 Paper All JEE MAIN years →

$A$ wire of a certain material is stretched slowly by $10\%$. Its new resistance and specific resistance become respectively:

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MediumJEE MAIN 2022

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The resistance of a resistor wire is $5 \, \Omega$ at $50^{\circ}C$ and $6 \, \Omega$ at $100^{\circ}C$. What is its resistance at $0^{\circ}C$ in $\Omega$?

Difficult

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The resistivity of alloys is $\rho_{\text{alloy}}$ and the resistivity of constituent metals is $\rho_{\text{metal}}$. Then,usually:

Easy

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$A$ wire of resistance $5 \Omega$ is stretched so that its new length is $3$ times its original length. What is the resistance of the new wire?

MediumWBJEE 2009

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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.

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$A$ wire of a certain material is stretched slowly by $10\%$. Its new resistance and specific resistance become respectively:

Resistance of the wire is measured as $2\,\Omega$ and $3\,\Omega$ at $10^{\circ}C$ and $30^{\circ}C$ respectively. The temperature coefficient of resistance of the material of the wire is............$^{\circ}C^{-1}$.

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