Problem 3: Calculate the resistance of wire 10 m long that has a diameter of 2 mm and resistivity 2.63 * 10^-2 Ω m.

Solution

Given                    Length of wire, L = 10 m                Diameter of cross-section = 2 mm = 2 * 10^-3 m

                              Resistivity, ρ = 2.63 * 10^-2 Ω m = 0.0263 Ω m

Required              Resistance of the wire, R =?

Strategy

Resistance is related to the length and cross-sectional area of the wire in the following equation.

Here A is the cross-sectional area of the wire. This can be calculated by the relation

Radius is half the dia. Therefore, radius of the wire = 1 * 10^-3 m

Put values in the formula (1)