Question

Resistance of a metal wire of length 1m is 26 ohm at 20°C. if the diameter of the wire is 0.3mm, what will be the resistivity of the metal at that temperature.​

Answer 1

Given :

• Length of metal wire, l = 1 m.
• Resistance of the metal wire = 26 Ω
• Diameter of the metal wire = 0.3 mm.

To Find :

• Resistivity of the metal at the given temperature.

Solution :

We are given that, diameter = 0.3 mm = 0.3 × 10⁻³ m

Then, radius of wire = d/2 = 1.5 × 10⁻⁴ m

We know,

$\implies\rm{R={\rho}\dfrac{l}{A}}$

$\implies\rm{\rho=\dfrac{RA}{l}}$

$\implies\rm{\rho=\dfrac{R{\pi}r^2}{l}}$

where,

• ρ is the resistivity of the metal.
• R is the resistance of the wire.
• l is the length of the wire.
• A is the area of cross-section of the wire.

Putting these values, we get,

$\implies\rm{\rho=26\times{}\dfrac{22}{7}\times{}\dfrac{(1.5\times{}10^{-4})^2}{1}\:{\Omega}m}$

$\implies\rm{\rho=\dfrac{1287\times{}10^{-8}}{7}\:{\Omega}m}$

$\implies\rm{\rho=183.85\times{}10^{-8}\:{\Omega}m}$

$\implies\rm{\rho=}\:\bold{1.83\times{}10^{-6}\:{\Omega}m.}$