Answer:
The conductivity of the wire is [tex]3.18\times10^{7}\ ohm-m[/tex].
Explanation:
Given that,
Diameter = 0.2 cm
Current = 20 A
Power = 4 W/m
We need to calculate the conductivity
We know that,
[tex]\sigma = \dfrac{1}{\rho}[/tex]
Using formula of resistance
[tex]R = \dfrac{\rho l}{A}[/tex]....(I)
Where,
[tex]\rho[/tex] = resistivity
A = area
l = length
Using formula of power
[tex]P = i^2 R[/tex]
[tex]R = \dfrac{P}{i^2}[/tex]
Put the value of R in equation (I)
[tex]\dfrac{P}{i^2}=\dfrac{\rho l}{\pi r^2}[/tex]
[tex]\rho=\dfrac{P\pi r^2}{l\timesi^2}[/tex]
[tex]\sigma=\dfrac{l\times i^2}{P\pi r^2}[/tex]
Put the all values into the formula
[tex]\sigma=\dfrac{1\times(20)^2}{4\times3.14\times(0.1\times10^{-2})^2}[/tex]
[tex]\sigma=3.18\times10^{7}\ ohm-m[/tex]
Hence, The conductivity of the wire is [tex]3.18\times10^{7}\ ohm-m[/tex].
