Question

A copper wire of length 2m and area of cross-section 1.7×10-6 m2 has a resistance of 2×10-2 ohms. Calculate the restivity of copper

Answer 1

R is resistance
A is area of cross section of wire
L is length of given wire
p is coefficient of resistivity

Answer 2

Answer:

The ‘resistivity of copper’ wire is $\bold{1.7 \times 10^{-8} \Omega \mathrm{m}.}$.

Solution:

The resistivity or the specific resistance of a material is the inherent property of each material but it varies depending upon the “length and cross-sectional area” of the material. The resistivity is said to be ‘directly proportional’ to the “cross-section area of the material” and ‘inversely proportional’ to the “length of the material”. The ‘resistance’ of the material acts as the proportionality constant.

Mathematically, the resistivity can be determined using the below equation,

$\bold{\rho=\frac{R A}{L}}$

Here, R is the resistance, A is cross-section area and L is the length of the material and ρ is the resistivity.

Thus for the given case, $\bold{\mathrm{R}=2 \times 10^{-2} \mathrm{ohms}, \mathrm{A}=1.7 \times 10^{-6} \mathrm{m}^{2} \text { and } \mathrm{L}=2 \mathrm{m}}$.

So the resistivity is  

$\rho=\frac{2 \times 10^{-2} \times 1.7 \times 10^{-6}}{2}=1.7 \times 10^{-2-6}$

$\bold{\rho=1.7 \times 10^{-8} \Omega m}$

Thus the ‘resistivity of copper’ wire is $1.7 \times 10^{-8} \Omega \mathrm{m}$.