Physics – 4.2.4 Resistance | e-Consult

Solution:

1. Calculate the resistivity at 80°C: The resistivity at 80°C is given as ρ = 1.6 x 10^-8 Ωm.
2. Apply the resistance formula: R = ρL/A. We know the resistance at 20°C (R₂₀ = 5.0 Ω), the resistivity at 20°C (ρ₂₀ = 1.0 x 10^-8 Ωm), and the resistivity at 80°C (ρ₈₀ = 1.6 x 10^-8 Ωm). We can assume the length and cross-sectional area remain constant. Therefore, we can write: R₈₀ = ρ₈₀L/A. We also know R₂₀ = ρ₂₀L/A. Dividing the two equations: R₈₀ / R₂₀ = (ρ₈₀L/A) / (ρ₂₀L/A) = ρ₈₀ / ρ₂₀.
3. Calculate R₈₀: R₈₀ = R₂₀ * (ρ₈₀ / ρ₂₀) = 5.0 Ω * (1.6 x 10^-8 Ωm / 1.0 x 10^-8 Ωm) = 8.0 Ω.

Answer: The new resistance of the conductor is 8.0 Ω.