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FACTORS ON WHICH THE RESISTANCE OF A CONDUCTOR DEPENDS - (Concept)

The resistance of a Conductor-

 The property of a conductor due to which it opposes the flow of current through it is called resistance. 

From Ohm's law, we can say that

The resistance of a conductor is numerically equal to the ratio of potential difference across its ends to the current flowing through it. 

 Resistance = Potential difference  Current  or R=VI


The SI unit of resistance is ohm which is denoted by the symbol omega, (Ω)
Now, if the potential difference V is 1 volt and the current I is 1 ampere, then resistance R in the above equation becomes 1 ohm.

That is,

1ohm=1 volt 1 ampere 
 

Resistance of the conductor depends on 

  • the length of the conductor. I.e A long wire (or conductor) has more resistance and a short wire has less resistance. 

  • The thickness of the conductor.  I.e a thick wire has less resistance whereas a thin wire has more resistance.

  • nature of the material of the conductor. 

  • the temperature of the conductor. I.e Rise in temperature of a wire (or conductor) increases its resistance.

 

From this dependency, we can say that 

 The resistance of a uniform metallic conductor is directly proportional to its length (L) and inversely proportional to the area of cross-section (A)

I.e

R∝ land R∝1A we get R∝lA or. R=ρlA

where ρ (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor.

The SI unit of resistivity is Ωm. It is a characteristic property of the material.
Both the resistance and resistivity of a material vary with temperature.
Fact-
The metals and alloys have very low resistivity in the range of 10−8Ω m to 10−6Ω m . They are good conductors of electricity. Insulators like rubber and glass have a resistivity of the order of 1012Ω m to 1017Ω m.
- Formula-

For a conductor of resistivity ρ having a length of a conductor= I
and Area of a crosssection of conductor= A
Then the resistance of a conductor is given as

R=ρlA

Where ρ→ Resistivity

Exam Chapter
JEE FOUNDATION Electricity
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