Question

(a) What do you understand by the "resistivity" of a substance?
(b) A wire is 1.0 m long, 0.2 mm in diameter and has a resistance of 10 Ω. Calculate the resistivity of its material?

Answer 1

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(a) We know that resistance, $R=\frac{\mathrm{\rho }l}{A}$

So resistivity, $\mathrm{\rho }=\frac{RA}{l}$

When the area of cross-section, A is 1 m² and the length of the wire, l is 1 m, resistance is equal to resistivity.

Resistivity may be defined as the resistance offered by a conductor of length 1 m and area of cross-section 1 m².

(b) Given length of the wire, l = 1 m

Diameter of the wire, d = 0.2 mm

So the radius of the wire, r = 0.1 mm = 0.0001 m

Area of cross-section of the wire = $A=\mathrm{\pi }{r}^2=3.14\times {\left(0.0001\right)}^2=3.14\times {10}^{-8}{\mathrm{m}}^2$

Resistance of the wire, R = 10 Ω

So resistivity = $\mathrm{\rho }=\frac{RA}{l}$

$\mathrm{\rho }=3.14\times {10}^{-7}\mathrm{\Omega }\mathrm{m}$

Thus, the resistivity of the material, $\mathrm{\rho }=3.14\times {10}^{-7}\mathrm{\Omega }\mathrm{m}$​.