Question

Write the relation between resistance R and electrical resistivity (ρ) of the material of a conductor in the shape of cylinder of length I and area of cross-section (a). Hence, derive the SI unit of electrical resistivity.

Answer 1

Relation between Resistance (R) and Electrical Resistivity (ρ): The resistance (R) of a conductor is directly proportional to its length (L) and inversely proportional to the cross-sectional area (A). The relationship is given by:

R = `(ρL)/A`
Where:

• R is the resistance,
• ρ is the electrical resistivity,
• L is the length of the conductor and
• A is the cross-sectional area of the conductor.

Derivation of the SI Unit of Electrical Resistivity: The SI unit of resistance (R) is the ohm (Ω), the unit of length (L) is the meter (m) and the unit of cross-sectional area (A) is square meters (m²).

1 Ω = `Ω  . m/m^2`

So, the SI unit of electrical resistivity (p) is the ohm meter (Ω.m).