Question #190242

A wire 50 cm long and 1 mm in radius is connected to a battery 9.11 V with a current of 36 A. Taking the temperature at 20°C and using the table of resistivities for some materials above, determine the material of the wire.

Expert's answer

V= 9.11 V , I = 36A ,

L length = 50 cm or 0.5 m , radius = 1mm or 0.001 m

R= "\\frac{V}{I} = \\frac{9.11}{36}= 0. 2531 \\Omega"

R= "\\frac{pL}{A}"

"p= \\frac{AR}{L}" but area A = "\\pi r^2"

"A= \\pi\\times0.001^2= 3.142 \\times 10^{-6} m^2"

"p=\\frac{3.142\\times10^{-6}\\times 0.2531}{0.5}= 1. 5904 \\times 10^{-6}\\Omega m"

From the table above , there is likely hood that the material is a nichrome that has "1.0 \\times 10^{-6} \\Omega m" against calculated resistivity "1.5904\\times 10^{-6}\\Omega m"

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