Question

For a metal that has an electrical conductivity of 6.1 × 107 (Ω∙m)–1, what is the resistance of a wire that is 4.3 mm in diameter and 8.1 m long? (A) 3.93 × 10–5 Ω (B) 2.29 × 10–3 Ω (C) 9.14 × 10–3 Ω (D) 1.46 × 1011 Ω

Answer 1

Answer: (C) 9.14 . 10⁻³ Ω

Explanation:

The resistance of a resistor, is proportional to his length and inversely proportional to his area, being the proportionality constant a property of the material, called resistivity.

The resistivity  is defined as the inverse of  the electrical conductivity, which depends on the number of charge carriers  and the mobility of these carriers, which is different for each material.

So, we can calculate the resistance as follows:

R = 1/σ . L / A, where:

σ = electrical conductivity, l= length of the wire , A = wire cross-section (assumed circular).

Replacing by the values, we can calculate R as follows:

R = 1/6.1. 10⁷ (Ω.m) . 8.1 m. / π (0.0043)² m / 4 = 9.14 . 10⁻³ Ω