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Resistance of a metal wire of length 1 \(m\) is 26 at \(20°C\). If the diameter of the wire is \(0.3\ mm\), what will be the resistivity of the metal at that temperature? Using table, predict the material of the wire.
Material's nature | Material | Resistivity of material (\(\Omega\ m\)) |
Conductors | Silver Copper Aluminium Tungsten Nickel Iron Chromium Mercury Manganese | \(1.60\times{10^{-8}}\) \(1.62\times{10^{-8}}\) \(2.63\times{10^{-8}}\) \(5.20\times{10^{-8}}\) \(6.84\times{10^{-8}}\) \(10.0\times{10^{-8}}\) \(12.9\times{10^{-8}}\) \(94.0\times{10^{-8}}\) \(1.84\times{10^{-6}}\) |
Alloys | Constantan Manganin Nichrome | \(49\times{10^{-6}}\) \(44\times{10^{-6}}\) \(100\times{10^{-6}}\) |
Insulators | Glass Hard rubber Ebonite Diamond Dry paper | \(10^{10}\) to \(10^{14}\) \(10^{13}\) to \(10^{16}\) \(10^{15}\) to \(10^{17}\) \(10^{12}\) to \(10^{13}\) \(10^{12}\) |
[Note: Enter the answer up to two decimal places by rounding off the third decimal value.]
\(L\) \(=\) 1 \(m\)
\(R\) \(=\) 26
\(d\) \(=\) \(0.3\ mm\)
On converting \(millimetre\) to \(metre\), we get \(\times{10^{-4}}\ m\).
The formula to calculate the resistivity of a material is
The formula to calculate the area of cross-section of the wire when diameter is given.
On substituting the known values in the formula, we get the value of resistivity,
\(\rho\) \(=\)
From the given table, it is seen that it is the resistivity of .
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