Question

Calculate the ratio of the resistance of 15.0 m of aluminum wire 2.3 mm in diameter, to 26.0 m of copper wire 1.9 mm in diameter. The resistivity of copper is 1.68×10−8Ω⋅m and the resistivity of aluminum is 2.65×10−8Ω⋅m. Express your answer using two significant figures.

Answer 1

Resistance is given by,

R = rho*L/A

R = rho*L/(pi*d^2/4)

then, (Resistance of aluminium(R1))/(Resisatnce of copper(R2)) = (rho1/rho2)*(L1/L2)*(d2/d1)^2

given, rho1 = resistivity of aluminum = 2.65*10^-8 Ω*m

rho2 = resistivity of copper = 1.68*10^-8 Ω*m

L1 = length of aluminium wire = 15.0 m

L2 = length of copper wire = 26.0 m

d1 = diameter of aluminium wire = 2.3 mm

d2 = diameter of copper wire = 1.9 mm

then, R1/R2 = (2.65/1.68)*(15.0/26.0)*(1.9/2.3)^2

R1/R2 = 0.621

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