## 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 ㎡ , if the resistivity of the metal be ?

**Ans:**

**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 .

**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?

Very good

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