Resistance & Conductance of Conductor

Current Electricity

Resistance of Conductor-

 

We know-

  • When a potential difference is applied across the two ends of a conductor, an electric field is established inside it.
  • The electric field exerts an electric force on the free electrons and they start drifting in the direction opposite to electric field.

 

 

The property of a conductor by virtue of which it opposes the flow of charges through it is called as its resistance.

 

Any material that has a property of offering resistance is called as a resistor.

 

Cause of Resistance-

 

  • When electrons drift inside the conductor, they frequently collide with the positive metal ions.
  • The collisions of free electrons with the positive metal ions is the main cause of resistance of the conductor.

 

Calculation of Resistance-

 

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

 

 

SI Unit of Resistance-

 

  • The SI unit of resistance is ohm (Ω).
  • The resistance of a conductor is said to be one ohm if a current of 1 A flows through it when a potential difference of 1 V is applied across its ends.

 

Factors Affecting The Resistance-

 

The resistance of a conductor depends upon the following factors-

 

1. Length of Conductor-

 

  • The resistance of a conductor increases with the increase in its length.
  • Thus, resistance of a conductor is directly proportional to its length i.e.

R ∝ L

 

2. Cross-sectional area of Conductor-

 

  • The resistance of a conductor decreases with the increase in its cross-sectional area.
  • Thus, resistance of a conductor is inversely proportional to its cross-sectional area i.e.

R ∝ 1/A

 

3. Nature of material of Conductor-

 

  • The resistance of a conductor also depends upon nature of material of the conductor.
  • For example- the resistance of nichrome wire is 60 times that of a copper wire of same length and same area of cross-section.

 

4. Temperature of Conductor-

 

  • The resistance of a conductor increases with the increase in its temperature.
  • With the rise in temperature, the drift velocity of electrons increases and hence they collide more frequently with each other.
  • Due to increased collisions, the resistance of conductor also increases.

 

At a constant temperature, on combining the above factors, we get-

 

OR

 

Here, ρ is a constant of proportionality called as resistivity or specific resistance of the material of the conductor.

 

Conductance of Conductor-

 

The conductance of a conductor is the ease with which electric charges flow through it.

 

  • More is the resistance of a conductor, lesser is its conductance and vice-versa.
  • So, conductance of a conductor is defined as reciprocal of resistance of the conductor.
  • It is denoted by G.

 

Mathematically,

 

OR

 

The SI unit of conductance is ohm-1 or mho or siemens (S).

 

Read the next article on-

Resistivity & Conductivity of Conductor

 

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