Question

Two wires are identical, except that one is aluminum and one is copper. The aluminum wire has a resistance of 0.874?. What is the resistance of the copper wire? Take the resistivity of copper to be 1.72 x 10-8 ?

Answer 1

Resistance is given by

$R=\rho \frac{l}{A}$

since the two wires are identical, there length(l) and cross sectional area (A) are same

therefore for aluminium wire

$R_{Al}=\rho_{Al} \frac{l}{A}............................................(1)$

therefore for copper wire

$R_{Cu}=\rho_{Cu} \frac{l}{A}............................................(2)$

Dividing Equation 2 by 1 we get:

$\Rightarrow \frac{R_{Cu}}{R_{Al}}= \frac{\rho_{Cu}}{\rho_{Al}}$

$\Rightarrow \frac{R_{Cu}}{0.874}= \frac{1.72*10^{-8}}{2.82*10^{-8}}$

$\Rightarrow R_{Cu}=0.533 ohm$

Answer 2

resistivity of Cu is 1.72 x 10^-8
resistivity of Al is 2.82 x 10^-8

(1.72 x 10^-8)/ (2.82 x 10^-8) = 0.609929078014184
0.609929078014184 x .874 x 100 =
R = .53.31 ohm

Answer 3

The equation for reisstance is

R = rho L/A

both wires have same length and area then the resistance of aluminum wire

R1= rho (aluminum)

R2= rho ( copper)

R2/R1= rho ( copper)/ rho (aluminum)

R2 = R1 (rho ( copper)/ rho (aluminum))

   =(0.874?.)(1.72 x 10-8 ?

Answer 4

If wires are identical then, resistance R is directly proportional to the resistivity $\rho$

$Ra/Rc = \rho a/\rho c$

$Rc =Ra (\rho c/\rho a)$

$Rc = 0.874 (1.72 *10^{-8}/2.82 * 10^{-8}) = 0.533\Omega$