Resolved Problems about Electrical Resistance

Problem 2.2 Source: Problem 17 - page 161 - HALLIDAY, RESNICK, WALKER, Jearl - Book: Fundamentos de Física - Vol 3 - Ed. LTC - 8ª edição - 2009.

An electric wire has 1.0 mm in diameter, 2.0 m in length and a resistance of 50 mΩ. What is the resistivity of the material?

Solution of the Problem 2.2

First, let's turn the given value of the wire resistance into mΩ for ohms, or:

R = 50 mΩ = 0.05 Ω

On the other hand, the wire diameter value (d = 1 mm = 10^-3 m) was given. The area, depending on the diameter, is given by:

A = ( π d² ) / 4 = [π (10^-3)²] / 4

Performing the calculation we find:

A = 7.85 x 10^-7 m²

Now that we have all the calculated values and isolating ρ in the eq. 02-01 that provides us with the value of the resistance, we come to:

ρ = ( R A ) / L

Replacing, in the above equation, the calculated values, we find the value of ρ:

ρ = 9.1875 x 10^-9 ohms. meter

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