Two conducting wires of the same material are to have the same resistance. One wire is 17.0 m long and 0.44 mm in diameter. If the other wire is 0.30 mm in diameter, how long should it be?

L = 7.90  m

Explanation:

The general expression for the resistance of a resistor is as follows:

       

When we are talking about a wire, of a given diameter, the above formula becomes as follows:

       

where ρ = resistivity of the material, L= length of the wire and d= diameter of the wire.If both wires are from the same material, and have the same resistance, we can say the following, simplifying common terms:

       

where L₁ = 17.0 m, d₁= 0.44 mm = 4.4*10⁻⁴ m, d₂= 3*10⁻⁴ m.Replacing these values, we can solve for L₂, as follows:

       

The wire should have 7.90 m length.

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