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it is the property by virtue of which a conductor oppose the low of charges through it.
SI unit of resistance is Ohm. 1 ohm is the resistance offered by a conductor if a current of 1 ampere flows through it on applying a potential difference of 1 volt across its ends.
Factor affecting the resistance :-
- Length – the resistance R of a conductor is directly proportional to its length. i.e. R α I
2. Area of cross – section : the resistance R of a conductor is inversely proportional to its area of cross section:
Combining the above factors, we get
Where ρ is constant of proportionality called resistivity or specific resistance of the material of the conductor.
Specific resistance:- in the equation
Then R= ρ thus, the specific resistance of a material may be defined as the resistance of a conductor of that material having unit length and unit area of cross- section.
It is the resistance offered by the unit cube of the material of a conductor.
SI unit of resistivity is ohm-m.
Current density:- the amount of charge flowing per second per unit area normal to the flow of charge. It is a vector quantity having the same direction as that of motion of positive charge.
For normal flow of charge
SI unit is mho or Siemens or ohm-1.
Conductivity :- the reciprocal of the resistivity of a material is called conductivity and is denoted by σ.
SI unit is mho m-1 or Siemens m-1 or ohm-1 m-1.
Vector form of ohm’s law:- if E is the magnitude of electric field in a conductor of length I, then the Potential difference across its ends is
V = EI
Also, from ohm’s law, we can write,
As the direction of current density j is same as that of electric field E, we can write the above eqn as
The above equation is the vector form of ohm’s law. It is equivalent to scalar from, V = RI.