Resistivity-Conductivity Formula

It is a measure of how strongly a specific material opposes the flow of electric current on resistors or conductors with a uniform cross-section, where current flows uniformly. As a reciprocal quantity, conductivity is a measure of how easy a material permits the flow of current. This are related by:

Resistivity = 1 / conductivity

The equation is:

ρ = 1 / σ

Where:

σ: Conductivity

ρ: Resistivity

Resistivity-conductivity Formula Questions:

1) What is the conductivity of a wire of cooper?

Answer:

From the resistivity-conductivity formula, we substitute the cooper resistivity which is 1.68*10^(-8) Ω*m:

σ = 1/1.68*10^(-8) Ω *m = 0.59 *10⁽⁸⁾ S/m (siemens per meter)

2) A wire with a resistance of 1.53 k Ω has a length of 1 m and A= 3 cm². What is its resistivity and conductivity?

Answer:

From the electric resistance formula, we find:

ρ = R A/L = 1.53 k Ω * 0.0003 m³ / 1 m = 4.6*10^(-1) Ω*m

the conductivity is, from the resistivity-conductivity relation:

σ = 1/ρ = 2.1 S/m