Resistance of alloy sheet along length and thickness

Use R = ρ l/A, where l is the length of the current path and A the cross-section at right angles to the current.

Data

ρ = 50 × 10⁻⁸ Ω·m, length = 15 cm = 0.15 m, width = 6 cm = 0.06 m, thickness = 0.014 cm = 1.4 × 10⁻⁴ m

(a) Along the length

Path length l = 0.15 m Area A = width × thickness = 0.06 × 1.4 × 10⁻⁴ = 8.4 × 10⁻⁶ m²

R = 50 × 10⁻⁸ × 0.15/(8.4 × 10⁻⁶) = 8.93 × 10⁻³ Ω

(b) Along the thickness

Path length l = 1.4 × 10⁻⁴ m Area A = length × width = 0.15 × 0.06 = 9 × 10⁻³ m²

R = 50 × 10⁻⁸ × 1.4 × 10⁻⁴/(9 × 10⁻³) = 7.78 × 10⁻⁹ Ω

Answer: (a) ≈ 8.93 mΩ; (b) ≈ 7.78 nΩ