Question

Calculate the ratio of the resistance of 14.0 m of aluminum wire 1.5 mm in diameter, to 28.0 m of copper wire 2.9 mm in diameter. Assume electrical resistivity of aluminum is 2.65×10−8 Ω⋅m and electrical resistivity of copper is 1.68×10−8 Ω⋅m.

Answer 1

Length of aluminium wire = L =14 m

Diameter of aluminium wire = D = 1.5 mm = 1.5 x10^-3 m

Area of cross section of aluminium wire =A=

Electrical resistivity of aluminium = 2.65×10⁻⁸ Ω⋅m

Resistance of aluminium wire = R = Electrical resistivity of aluminium x (L/A) =  2.65×10⁻⁸ x (14/1.766 x 10^-6) = 0.21 ohms

Length of copper wire = L' =28 m

Diameter of copper wire = D' = 2.9 mm = 2.9 x10^-3 m

Area of cross section of copper wire =A'=

Electrical resistivity of copper =1.68×10⁻⁸ Ω⋅m

Resistance of copper wire = R' = Electrical resistivity of copper x (L'/A') =  1.68×10⁻⁸ x (28/6.6 x 10^-6) = 0.071 ohms

Ratio R/R' = 0.21/0.071 =2.95