Question

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

Answer 1

rB / rA = 3

Step-by-step explanation:

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

`R = (\rho*A)/(L)`

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:

`R = (\rho*\pi*r^(2))/(L)`

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

`(RB)/(RA) = ((rB)^(2))/((rA)^(2) ) = 9`

Taking square roots on both sides, we finally get:

`(rB)/(rA) = √(9) = 3`