(a) List the factors on which the resistance of a uniform cylindrical conductor of a given material depends.…
(a) List the factors on which the resistance of a uniform cylindrical conductor of a given material depends.
(b) The resistance of a wire of 0.01 cm radius is 10 Ω. If the resistivity of the wire is 50 × 10−8 Ω m, find the length of this wire.
Solution
(a) (i) Length of the conductor (l)
(ii) Area of cross-section of the conductor (A)
(b) Radius of wire, r = 0.01 cm = 0.01 × 10−2 m
Resistance, R = 10 Ω
Resistivity, ρ = 50 × 10−8 Ωm
R = ρ l/A = ρ l/(π r2) ⇒ l = R π r2 / ρ
l = [10Ω × 22 × (0.01 × 10−2)2 m] / [7 × 50 × 10−8 Ωm]
= 22/35 m = 0.629 m / 0.628 m / 0.62 m