Question

A particular wire has a diameter of 1.7 mm and length of 1.3 m. If the resistivity of the metal from which the wire is made is 2.0 × 10-8 Ωm, and 45 μV is the observed potential drop measured across the wire, what current is flowing in the wire?

Answer 1

Resistance R of a wire of length L and cross-sectional area A made of material of resistivity ρ is given by:

R = ρL / A

Cross sectional area of a wire of diameter d is given by:
A = πd²/4 { This just comes from area of a circle = πr² }

A = π * (1.7 * 10^-3)² / 4
A = 2.27 * 10^-6 m²

Plugging in the values:

R = (2.0 * 10^-8) * 1.3 / (2.27 * 10^-6)
R = 1.145 * 10^-2 ohms

Using Ohm's Law
i = v / r
i = (45 * 10^-6) / (1.15 * 10 ^-2)
i = 3.9 * 10^-3 A

i = 3.9 mA