Answer :
Answer:
rB / rA = 3
Explanation:
The resistance of any conductor, can be expressed by the following equation:
[tex]R = \frac{\rho*A}{L}[/tex]
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:
[tex]R = \frac{\rho*\pi*r^{2}}{L}[/tex]
If we know that wire B is to have nine times the resistance of wire B, we can establish the following proportion between them:
[tex]\frac{RB}{RA} = \frac{(rB)^{2}}{(rA)^{2} } = 9[/tex]
Taking square roots on both sides, we finally get:
[tex]\frac{rB}{rA} = \sqrt{9} = 3[/tex]