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Chapter 4: Q18E (page 842)

What diameter must a copper wire have if its resistance is to be the same as that of an equal length of aluminium wire with diameter 2.14mm?

Short Answer

Expert verified

The diameter of the copper wire must be 1.69mm.

Step by step solution

01

Determine the formula to find the diameter of a wire

We know,

A=π4d2

Substituting in the equation

R=ρLA=4ρLπd2

Now, according to the given question, we know the resistivities of both copper and aluminium wires which thus, will make it easy to find the diameter of a copper wire.

02

Calculation to find the diameter of the copper wire

We are given that,

Rcu=RAI,Lcu=LAIanddAI=1.72×10-3mm

Also, the resistivities of aluminium and copper wire is

pAl=2.75×10-8Ωm andpcu=1.72×10-8Ωm

So,

Therefore, the diameter of the copper wire must be 1.69 mm so as the resistance to be the same as that of an equal length of aluminium wire with diameter 2.14 mm

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