The radius r , length l and resistance R of a metal wire was measured in the laboratory as r = 0 .35 ± 0 .05 cm , R = 100 ± 10 ohm , l = 15 ± 0 .2 cm The percentage error in resistivity of the material of the wire is :

Step-by-step solution

The resistance of the wire is given as, R = ρ l A Therefore, ρ = R A l ρ = R π r 2 l For percentage error, we can write Δ ρ ρ = Δ R R + 2 Δ r r + Δ l l Δ ρ ρ × 100 = Δ R R × 100 + 2 Δ r r × 100 + Δ l l × 100 = 10 100 + 2 × 0 .05 0 .35 + 0 .2 15 × 100 = 1 10 + 2 7 + 1 75 × 100 Hence, Δ ρ ρ = 39 .9 %