If wire B is to have nine times the resistance of wire A, what must be the ratio of their radii, rB/rArB/rA?

rB / rA = 3

Explanation:

The resistance of any conductor, can be expressed by the following equation:

where:

ρ = resistivity of the material

A = area through which the current is flowing

L = length of the object

If we are talking about wires, usually we approximate them as cylindrical objects, where A is the circular cross-section of the wire.

So, we can write the value of the resistance, as follows:

If we know that wire B is to have nine times the resistance of wire B, we can establish the following proportion between them:

Taking square roots on both sides, we finally get:

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Explanation: