Resistance of a metal wire of length 1, m is | vedclass

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(A) Given:Resistance $R = 26 \, \Omega$Length $L = 1 \, m$Diameter $D = 0.3 \, mm = 3 	imes 10^{-4} \, m$Radius $r = D/2 = 1.5 	imes 10^{-4} \, m$Th

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$1.84 	imes 10^{-6} \, \Omega \, m$

Vedclass · Answer

(A) Given:Resistance $R = 26 \, \Omega$Length $L = 1 \, m$Diameter $D = 0.3 \, mm = 3 	imes 10^{-4} \, m$Radius $r = D/2 = 1.5 	imes 10^{-4} \, m$The formula for resistance is $R = ho \frac{L}{A}$,where $A = \pi r^2 = \pi (D/2)^2 = \frac{\pi D^2}{4}$.Rearranging for resistivity $ho$:$ho = \frac{R A}{L} = \frac{R \pi D^2}{4 L}$Substituting the values:$ho = \frac{26 	imes 3.14 	imes (3 	imes 10^{-4})^2}{4 	imes 1}$$ho = \frac{26 	imes 3.14 	imes 9 	imes 10^{-8}}{4}$$ho = 1.8369 	imes 10^{-6} \, \Omega \, m \approx 1.84 	imes 10^{-6} \, \Omega \, m$.

Resistance of a metal wire of length $1\, m$ is $26\, \Omega$ at $20^{\circ} C$. If the diameter of the wire is $0.3\, mm$,what will be the resistivity of the metal at that temperature?

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