Question

A 4.0m long wire has diameter of 0.30 mm. If its resistance is 30 ohm, find its resistivity & conductivity

Answer 1

Electronics Tutorial about Electrical Resistivity and the Conductivity of a conductor which relies on the materials properties from which it  ...

Answer 2

Answer: The resistivity is $3.53\times10^{-6}\Omega-m$ and the conductivity is $2.83\times10^{5}\rho^{-1}m^{-1}$.

Explanation:

Given that,

Length of the wire l= 4.0 m

Diameter = 0.30 mm

Resistance R = 30 ohm

We know that,

The resistance  is the defined as:

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

$\rho= \dfrac{AR}{l}$.....(I)

Where,

$\rho$ = resistivity of the wire

$A$ = Area of cross section

$l$=length of the wire

Put the value in equation (I)

$\rho = \dfrac{30\times3.14\times0.15\times10^{-6}}{4.0}$

$\rho = 3.53\times10^{-6}\Omega-m$

The conductivity is the reciprocal of resistivity.

The conductivity is

$\sigma = \dfrac{1}{\rho}$

$\sigma = \dfrac{1}{3.53\times10^{-6}}$

$\sigma= 2.83\times10^{5}\Omega^{-1}m^{-1}$

Hence, The resistivity is $3.53\times10^{-6}\Omega-m$ and the conductivity is $2.83\times10^{5}\Omega^{-1}m^{-1}$.