Question

Question 24:
(a) Define resistivity. Write an expression for the resistivity of a substance. Give the meaning of each symbol
which occurs in it.
(b) State the SI unit of resistivity.
(c) Distinguish between resistance and resistivity.
(d) Name two factors on which the resistivity of a substance depends and two factors on which it does not depend.
(e) The resistance of a metal wire of length 1 m is 26 Ω at 20°C. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature ?

Lakhmir Singh Physics Class 10

Answer 1

Resistivity is the measure of a material’s ability to oppose the flow of current . Resistivity of a conductor is a property of the material of the conductor.

Unit of resistivity is Ohm meter, Ω m .

Resistivity of the material of the conductor changes with temperature.

Following is the equation relating resistivity (ρ) and resistance (R) of a conductor of length (L) and area (A).

ρ = AR / LL

Difference:
The SI unit of the resistance is ohm, and the SI unit of resistivity is ohm-meter. The resistance of the material depends on the length, cross-section and area of conductor whereas the resistivity depends on the nature and temperature of the material

Answer 2

(a) Resistivity is a fundamental property of a material that quantifies how strongly it resists electric current.

$\rho =R{\frac {A}{\ell }}$ is the expression for the resistivity of a substance where R is the electrical resistance of a uniform specimen of the material, $\ell$ is the length of the specimen, A is the cross-sectional area of the specimen and  ρ is the resistivity of the substance.

(b) The SI unit of resistivity is ohm-meter (Ω⋅m)

(c) Resistance varies due to change in size or shape of the substance but resistivity is same for every substance of same material.

(d) Resistivity depends on nature of material and Temperature but doesn't depend on shape and size of the substance.

(e) Cross sectional area of the material is $\pi *(\frac{0.0003}{2})^2 = 7.0685*10^{-8}$ meter square.

So according to the formula the resistivity at that temperature is $26*\frac{1}{7.0685*10^{-8} } = 3.67*10^{8}$ ohm-meter.