Ohm’s Law and Resistance

According to ohm’s law the current (I) flowing through a conductor is directly proportional to the potential difference (V) across the ends of the conductor, provided temperature of the conductor is kept constant, i.e.

                 I        V

       or      V         I

       or      V    =    R    X    I

     Where R is constant and is called resistance.

Resistance of a Conductor

The resistance of a conductor is the property of a conductor to oppose the flow of current passing through it. The resistance of a conductor may be defined as the ratio of potential difference (V) across the ends of the conductor to the current (I) flowing through it, i.e.

               Resistance    =    

                   or       R    =    

The S.I. unit of a resistance is ohm. It is represented by the symbol omega (Ω)

1 ohm (Ω)
1 ohm is the resistance of a conductor through which a current of 1 ampere flows when a potential difference of 1 volt is applied across its ends ; e.g.

               1 Ohm    =    

Factors Affecting the Resistance of a Conductor

The various factors that affect the resistance of a conductor are:

1. Length of the Conductor
The resistance of a conductor is directly proportional to the length of the conductor, i.e.

                 R        l

Therefore the resistance of the conductor becomes double it the length of a conductor is doubled, and the resistance of the conductor becomes half if the length of a conductor is halved.

2. Area of Cross Section of the Conductor
The resistance of a conductor is inversely proportional to area of cross-section of the conductor, i.e.

                 R        

Therefore the resistance of the conductor becomes half when the area of cross-section of a wire is doubled, and the resistance of the conductor becomes double when the area of cross-section of wire is halved. This means that a thick wire has less resistance than a thin wire.

3. Nature of Material of the Conductor
The resistance of a conductor depends on the nature of the material of which it is made.

4. Effect of Temperature
The value resistance of a conductor increases on raising the temperature and decreases on lowering the temperature.

Specific Resistance or Resistivity

       We know that                 R        I     (1)

       and                                R             (2)

       By combining both equation we get

                                            R        

       or                                  R    =    ρ    X         (3)

Where ρ (rho) is a constant and is know as specific resistance or resistivity.

              By re-arranging equation (3) we get

                                            ρ    =    R    X         (4)

       if A = 1m² and l = 1m then from equation (4), we get

                                            ρ    =    R

Thus the specific resistance or resistivity of a conductor is resistance of a conductor which is 1 meter long and 1 square meter in cross section. S.I. Unit of specific resistance or resistivity is ohm-m or Ω-m.

Test Your Understanding and Answer These Questions:

1. What is ohm’s law?
2. What is definition of resistance?
3. What is specific resistance?
4. What is S.I. unit of specific resistance?
5. What is S.I. unit of resistance of a conductor?
6. What are the factors effecting resistance of a conductor?
7. Why electrician wear rubber hand gloves while working with electricity?