Question

Determine the overall resistance of a 100-meter length of 14 AWA (0.163 cm diameter) wire made of the following materials.
a. copper (resistivity = 1.67x10-8 O•m)
b. silver (resistivity = 1.59x10-8 O•m)
c. aluminum (resistivity = 2.65x10-8 O•m)
d. iron (resistivity = 9.71x10-8 O•m)

Answer 1

Area, A = 3.14 * (0.163/200)^2 = 2.08 * 10^-6 m^2
Length, L = 100 m
Resistance of the wire is given by,
R = (p * L)/A

(a)
Resistivity, ρ = 1.67 * 10^-8 Ωm
R = (p * L)/A
R = (1.67 * 10^-8  * 100)/(2.08 * 10^-6)
R = 0.80 Ω

(b)
Resistivity, ρ = 1.59 * 10^-8 Ωm
R = (p * L)/A
R = (1.59* 10^-8  * 100)/(2.08 * 10^-6)
R = 0.764 Ω

(c)
Resistivity, ρ = 2.65 * 10^-8 Ωm
R = (p * L)/A
R = (2.65* 10^-8  * 100)/(2.08 * 10^-6)
R = 1.27 Ω

(d)
Resistivity, ρ = 9.71 * 10^-8 Ωm
R = (p * L)/A
R = (9.71* 10^-8  * 100)/(2.08 * 10^-6)
R = 4.67 Ω

Answer 2

Find on Area,

A = 3.14 * (0.163/200)^2 = 2.08 * 10^-6 m^2
Length, L = 100 m
Resistance of the wire is given by,
R = (p * L)/A

(a)
Resistivity, ρ = 1.67 * 10^-8 Ωm
R = (p * L)/A
R = (1.67 * 10^-8 * 100)/(2.08 * 10^-6)
R = 0.80 ohm

(b)
Resistivity, ρ = 1.59 * 10^-8 Ωm
R = (p * L)/A
R = (1.59* 10^-8 * 100)/(2.08 * 10^-6)
R = 0.764 ohm

(c)
Resistivity, ρ = 2.65 * 10^-8 Ωm
R = (p * L)/A
R = (2.65* 10^-8 * 100)/(2.08 * 10^-6)
R = 1.27 ohm

(d)
Resistivity, ρ = 9.71 * 10^-8 Ωm
R = (p * L)/A
R = (9.71* 10^-8 * 100)/(2.08 * 10^-6)
R = 4.67 ohm