Question

A negligibly small current is passed through a wire of length 15 m and uniform cross-section 6×10-7 m2 and its resistance is 50 Ω. Find out its resistivity. ​

Answer 1

Answer:

2×10^-6

Explanation:

from the equation of resistivity

Answer 2

Explanation:

$\Large{\green{\underline{\underline{\tt{\red{Solution:}}}}}}$

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$\hookrightarrow$ Length of the wire, $\sf l\:=\:15\,m$

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$\hookrightarrow$ Area of cross section of the wire, $\sf A\:=\:6.0\times 10^{-7}m^2$

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$\hookrightarrow$ Resistance of material of the wire, $\sf R\:=\:50\Omega$

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$\hookrightarrow$ Resistivity of material of the wire = $\rho$

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Resistance is related with resistivity as

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$\hookrightarrow$ $\boxed{\sf{\green{R\:=\: \rho \dfrac{l}{a}}}}$

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$\leadsto$ $\sf \rho\:=\: \dfrac{RA}{l}$

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$\leadsto$ $\sf \rho\:=\: \dfrac{5\times 6\times 10^{-7}}{15}$

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$\leadsto$ $\sf \rho\:=\:2\times 10^{-7}\Omega m$

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$\longrightarrow$ Hence the resistivity of the material is $\sf{\orange{2\times 10^{-7}\Omega m}}$