Question

For a metal that has an electrical conductivity of 5.1 × 10⁷ (Ω-m)^–1:

1. Calculate the resistance of a wire 3.5 mm in diameter and 7.5 m long.                

1. Calculate the current if the potential drop across the ends of the wire is 0.05 V.                

1. Calculate the current density.                                                

1. Compute the magnitude of the electric field across the ends of the wire.               

Answer 1

Calculate the resistance of a wire 3.5 mm in diameter and 7.5 m long.

d=3.5 mm

l=7.5 m

$a = \frac{\pi}{4}d^2 = \frac{\pi}{4} \times 0.0035^2 = 9.62 \times 10^{-6} \;m^2$

Resistance $r = \frac{l}{ca} = \frac{7.5}{5.1 \times 10^7 \times 9.62 \times 10^{-6}}$

r = 0.0153 ohm

Calculate the current if the potential drop across the ends of the wire is 0.05 V.

Current $i = \frac{V}{R}$

Potential drop = 0.05 V

$i = \frac{0.05}{0.0153} = 3.268 \;amphere$

Calculate the current density.

Current density $J = \frac{i}{a} = \frac{3.268}{9.62 \times 10^{-6}} = 3.397 \times 10^5$

Compute the magnitude of the electric field across the ends of the wire.

$E = \frac{J}{c} = \frac{3.397 \times 10^5}{5.1 \times 10^7} = 6.66 \times 10^{-3}$