Question

A wire of length 1 metre and radius 0.02 cm has a resistance of 50 ohm. Calculate the resistivity of the material of the wire.

Answer 1

Please make my answer the brainliest answer

Answer 2

Given:

length of wire l = 1 m

radius r = 0.02 cm

resistance R = 50 ohm

To find:

resistivity of the material ρ =?

Step-to-step-explanation:

• The electrical resistivity is a fundamental property of a material that measures how strongly it resists electric current.
• A low value of resistivity indicates a material that readily allows electric current.  
• Resistivity is useful in comparing various materials on the basis of their ability to conduct electric currents.
• A high value of resistivity designates poor conductors. Its SI unit is ohm meter.
• Mathematically, resistivity of the material of the wire is expressed as:

$\displaystyle \rho=\frac{Ra}{l}$                       ...(1)

where

ρ = resistivity of a material

R = resistance of a material

a = cross-sectional area of a material

l = length of a material

• But the cross-sectional area of a material is circular.

a = π$r^2$

• Put this value in equation (1)

$\displaystyle \rho=\frac{R\pi r^2}{l}$

  = $\displaystyle\frac{50 \times 3.14 \times0.02 \times10^{-2}\times0.02 \times 10^{-2}}{1}$

ρ = 6.28 μΩm

• The resistivity of the material of the wire is 6.28 μΩm.