Question

Resistance of a metal wire of length 1m is $26\Omega$at ${20}^0$C. If the diameter of the wire is 0.3 mm, the resistivity of the metal is $=1.83\times {10}^{-x}ohm-meter$ that temperature. find x.

Answer 1

Step 1, Given data

Resistance = 26 ohm

Length = 1 meter

Diameter = 0.3 mm = $0.3\times {10}^{-3}m$

Step 2, Finding the resistivity of the metal

We know resistance is given as

$R=P\frac{l}{A}$

Or,

$P=\frac{RA}{l}=\frac{26\times ({0.3)}^2\frac{\pi }{4}\times {10}^{-6}}{1}$

$=1.83\times {10}^{-6}ohm-meter$

From the above we can say that the value of x is 6.