# Resistance & Conductance of Conductor

## 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.

#### 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.

#### 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).