Question

Calculate the resistivity of a wire whose length is 200 m and a cross section area of
15

Answer 1

The formula for electrical resistivity is:

$\rho = R\frac{A}{l},$

where:

• R is the electrical resistance of a uniform specimen of the material - material is not specified in the problem;
• A is the cross section area, given: $A = 15~\text{mm}^2$ (units not given in the problem, so assumed a standard unit for cross section - millimeters squared);
• l is the length, given: $l = 200~\text{m}.$

Substituting the numerical values into formula,

$\rho = R*\frac{15~\text{mm}^2}{200~\text{m}} = R*\frac{15*(10^{-3}~\text{m})^{2}}{200~\text{m}} = R*7.5*10^{-8}~\text{m}.$

The unit of R is ohm (Ω), thus the unit of the electrical resistivity is ohm-metre (Ωm).

For more information, see these Wikipedia pages:

https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance

https://en.wikipedia.org/wiki/Electrical_resistivities_of_the_elements_(data_page)