Table of Contents

## Resistance and Resistivity:

### What is Resistance?

Resistance of the conductor is defined as the obstruction posed by the conductor to the flow of electric current.

From Ohm’s Law, R = V / I |

Hence Resistance of the conductor may also be defined as the ratio of potential difference (V) between ends of the conductor to the current (I) flowing through it.

### Cause of Resistance:

Resistance of the conductor is due to the collisions of free electrons with the atoms/ions of the conductor while drifting towards the positive end of a conductor. We know-

R = V/I = ml / nAe^{2}τR = m/ne ^{2}τ X l/A |

Put m / ne^{2}τ = ρ = Specific resistance or resistivity of the material of the conductor.

R = ρ X l/A |

Hence the resistance of the conductor depends upon the dimensions of the conductor and also on the nature of the material of the conductor.

### Units of Resistance:

(1) The S.I. unit of resistance is Ohm.

We know, R = V / I 1 Ohm = 1 Volt / 1 Ampere |

Hence the resistance of the conductor is said to be one ohm if a current of one ampere flows through the conductor against a potential difference of 1 volt applied across its ends.

(2) The C.G.S. or electrostatic unit of resistance is stat-ohm.

We know, R = V / I 1 Stat-ohm = 1 Stat-volt / 1 Stat-ampere |

Hence the resistance of a conductor is said to be 1 stat-ohm if a current of 1 stat-ampere flows through the conductor when a potential difference of 1 stat-volt is applied across its ends.

(3) International Ohm.

It is defined as the resistance of a **106.3 cm** long mercury column of **1 cm ^{2}** cross-sectional area and mass

**14.45 gram**at

**0°C**.

### What is Resistivity?

We know, the resistance of the conductor is directly proportional to the length of the conductor i.e.

R ∝ l …………(1) |

Also, the resistance of the conductor is inversely proportional to the area of cross-section of the conductor i.e.

R ∝ 1 / A …………(2) |

Combining (1) and (2)-

R ∝ l / AR = ρ X l/A …………(3) |

Where ρ is the constant of proportionality and is called resistivity or specific resistance of the material of the conductor. Its value depends upon the nature of the material of the conductor.

If *l *= 1 and A = 1, then from (3)

R = ρ |

Hence specific resistance or resistivity of the material of the conductor is defined as the resistance of the conductor having unit dimensions. The S.I. unit of resistivity if **ohm-metre**.

**Note:** The resistivity of silver is 1.47 X 10^{-8} ohm-metre, the resistivity of copper is 1.72 X 10^{-8} ohm-metre, the resistivity of germanium (semi-conductor) is 0.60 ohm-metre and the resistivity of glass (insulator) is 10^{10} – 10^{14} ohm-metre.