Resistivity class-10| cbse24.com

Mohit Rastogi •March 22, 2020

1

Resistivity:

Electrical resistivity (also called specific resistance or volume resistivity ) is a fundamental property of a material that quantifies how strongly it resists electric current. A low resistivity indicates a material that easily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-meter (Ω⋅m).

It has been found by experiments that

(i) The resistance of a given conductor is directly proportional to its length

R∝l-----------------(1)

(ii) The resistance of a given conductor is inversely proportional to its area of cross-section.

R∝1/A--------------(2)

By combining the relations (1)and (2), we get:

R∝l/A

R=ρl/A

Note= We learn this formula by trick R=Rhola

If the length of wire l=1m, Area of the cross-section of wire A=1 ㎡

than R=ρ

So the resistivity of a substance is numerically equal to the resistance of a rod of that substance which is 1 meter long and 1 ㎡ in cross-section.

Unit: ρ= R x A/l

ρ= ohm x ㎡/m

ρ=ohm x m (or Ω m)

SI unit of resistivity is ohm-meter (or Ω m)
The resistivity of a substance does not depend on its length or thickness. It depends on the nature of the substance and temperature.
A conductor has low resistivity so can flow better current and insulator has very high resistivity, so it not allows flowing current.

Resistivity of some common substances (at 20℃):

Resistance vs Resistivity :

A mixed question of S.Chand and NCERT of this topic:

Q1: What will be the resistance of a metal wire of length 2 meters and area of cross-section $1.55\times 10^{-6}$ ㎡ , if the resistivity of the metal be $2.8\times 10^{-8} ohm\times meter$ ?

Ans:

$R=\frac{\varrho \times l}{A}=\frac{2.8\times 10^{-8}\times 2}{1.55\times 10^{-6}}=\frac{5.6\times 10^{-8+6}}{1.55}=3.612\times 10^{-2}ohm$

Q2:(a) Give two examples of a substance that are good conductors of electricity. Why do you think they are good conductors of electricity?

(b) Calculate the resistance of a copper wire 1.0 km long and 0.50 mm diameter if the resistivity of copper is $1.7\times 10^{-8} ohm\times meter$ .

Ans:(a) Cu and Al are good conductors of electricity because both have more no of a free electron and their resistivity is low.

(b)

Q3:-Calculate the resistance of an aluminium cable of length 10 km and diameter 2.0 mm if the resistivity of aluminium is 2.7 x 10^(-8) ohm m.

Ans:-

Q4:-Calculate the area of cross-section of wire if its length is 1.0 mm, its resistance is 23 ohms and the resistivity of the material of the wire is 1.84×10−6ohm.m
Ans:-

Q5: -A piece of wire of resistance 20 ohms is drawn out so that its length increased to twice its original length. Calculate the resistance of the wire in the new situation.

Ans:-

Q6:-The resistance of a metal wire of length 1 m is 26 Ω at 20℃. If the diameter of the wire is 0.3 mm, what will be the resistivity of the metal at that temperature?