An aluminum rod with a square cross section is 2.4 m long and 6.2 mm on edge. (a) What is the resistance between its ends? (b) What must be the diameter of a cylindrical copper rod of length 2.4 m if its resistance is to be the same as that of the aluminum rod? The resistivity of aluminum is 2.75 × 10-8 Ω·m and the resistivity of copper is 1.69 × 10-8 Ω·m.

Question

contestada

Respuesta :

DeniceSandidge DeniceSandidge · Answer 1 · 2019-11-05T10:10:50+01:00

Answer:

resistance R = 1.717 × [tex]10^{-3}[/tex] Ω

diameter is 5.484 × [tex]10^{-3}[/tex] m

Explanation:

given data

length = 2.4 m

cross section = 6.2 mm

solution

we know resistance formula that is

resistance R = [tex]\frac{\rho L}{A}[/tex] ............1

here ρ is resistivity and A is cross section and L is length

so put her value

aluminum resistance R = [tex]\frac{\rho L}{A}[/tex]

resistance R = [tex]\frac{2.75 * 10^{-8} * 2.4}{(6.2*10^{-3})^2}[/tex]

resistance R = 0.001717 = 1.717 × [tex]10^{-3}[/tex] Ω

and

copper resistance R = [tex]\frac{\rho L}{A}[/tex]

resistance R = [tex]\frac{1.69*10^{-8} * 2.4}{\frac{\pi d^2}{4} }[/tex]

1.717 × [tex]10^{-3}[/tex] = [tex]\frac{1.69*10^{-8} * 2.4}{\frac{\pi d^2}{4} }[/tex]

solve we get

d = 0.005484 = 5.484 × [tex]10^{-3}[/tex] m

so diameter is 5.484 × [tex]10^{-3}[/tex] m