Question

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.

Answer 1

resistance R = 1.717 ×
`10^(-3)` Ω

diameter is 5.484 ×
`10^(-3)` m

Step-by-step explanation:

given data

length = 2.4 m

cross section = 6.2 mm

solution

we know resistance formula that is

resistance R =
`(\rho L)/(A)` ............1

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

so put her value

aluminum resistance R =
`(\rho L)/(A)`

resistance R =
`(2.75 * 10^(-8) * 2.4)/((6.2*10^(-3))^2)`

resistance R = 0.001717 = 1.717 ×
`10^(-3)` Ω

and

copper resistance R =
`(\rho L)/(A)`

resistance R =
`(1.69*10^(-8) * 2.4)/((\pi d^2)/(4) )`

1.717 ×
`10^(-3)` =
`(1.69*10^(-8) * 2.4)/((\pi d^2)/(4) )`

solve we get

d = 0.005484 = 5.484 ×
`10^(-3)` m

so diameter is 5.484 ×
`10^(-3)` m