In the experiment of Ohm's law, a potential difference of 5 . 0 V is applied across the end of a conductor of length 10 . 0 cm and diameter of 5 . 00 mm . The measured current in the conductor is 2 . 00 A . The maximum permissible percentage error in the resistivity of the conductor is :-

Step-by-step solution

R = ρ ℓ A = V I ρ = A V I ℓ = π d 2   V 4 I ℓ    A = π d 2 4 ∴    Δ ρ ρ = 2 Δ d d + Δ V V + Δ I I + Δ ℓ ℓ Δ ρ ρ = 2 0 . 01 5 . 00 + 0 . 1 5 . 0 + 0 . 01 2 . 00 + 0 . 1 10 . 0 Δ ρ ρ = 0 . 004 + 0 . 02 + 0 . 005 + 0 . 01 Δ ρ ρ = 0 . 039 % error = Δ ρ ρ × 100 = 0 . 039 × 100 = 3 . 90 % .