2. When a potential difference of 12 V is applied to a wire 6.9 m long and 0.33 mm in diameter

the result is an electric current of 2.1 A. What is the resistivity of the wire?

Apply Ohm's law:

V = IR

V = potential difference, I = current, R = resistance

Resistance of a wire:

R = ρL/A

ρ = resistivity, L = length, A = cross-sectional area

Area of wire's cross-sectional area:

A = π (d/2) ²

A = area, d = diameter

Substitute R:

V = IρL/A

Substitute A:

V = IρL / (π (d/2) ²)

Given values:

V = 12V, I = 2.1A, L = 6.9m, d = 0.33*10⁻³m

Plug in these values and solve for ρ:

12 = 2.1ρ (6.9) / (π (0.33*10⁻³/2) ²)

ρ = 7.1*10⁻⁸Ω·m