(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.

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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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The $I-V$ graph for a conductor at two different temperatures $100^{\circ} C$ and $400^{\circ} C$ is as shown in the figure. The temperature coefficient of resistance of the conductor is about (in per degree Celsius).

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$A$ wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\,\Omega$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\,\Omega$?

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Two wires of equal diameters,of resistivities $\rho_1$ and $\rho_2$ and lengths $l_1$ and $l_2$,respectively,are joined in series. The equivalent resistivity of the combination is

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The resistance of a platinum resistance thermometer at $0\,^oC$ is $5\,\Omega$ and at $100\,^oC$ is $5.75\,\Omega$. When the resistance is $5.15\,\Omega$,the unknown temperature is ............ $^oC$.

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For which of the following does the resistance decrease upon increasing the temperature?

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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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The $I-V$ graph for a conductor at two different temperatures $100^{\circ} C$ and $400^{\circ} C$ is as shown in the figure. The temperature coefficient of resistance of the conductor is about (in per degree Celsius).

$A$ wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\,\Omega$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\,\Omega$?

Two wires of equal diameters,of resistivities $\rho_1$ and $\rho_2$ and lengths $l_1$ and $l_2$,respectively,are joined in series. The equivalent resistivity of the combination is

The resistance of a platinum resistance thermometer at $0\,^oC$ is $5\,\Omega$ and at $100\,^oC$ is $5.75\,\Omega$. When the resistance is $5.15\,\Omega$,the unknown temperature is ............ $^oC$.

For which of the following does the resistance decrease upon increasing the temperature?

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