Question

A wire must be replaced in a circuit by a new wire of the same material but nine times longer. If the new wire's resistance is the same as the original wire's, what is the diameter of the new wire?

O the same as the original diameter
O one half the original diameter
O one third the original diameter
O three times the original diameter
O nine times the original diameter

Answer 1

Answer:

three times the original diameter

Explanation:

From the wire's resistance formula, we can calculate the relation between the diameter of the wire and its length:

$R=\rho\frac{l}{\pi \frac{d^2}{4}}\\d=\sqrt{\rho \frac{4 l}{\pi R}}$

Here, d is the wire's diameter, $\rho$ is the electrical resistivity of the material and R is the resistance of the wire. We have $l'=9l$

$d'=\sqrt{\rho \frac{4 l'}{\pi R}}\\d'=\sqrt{\rho \frac{4 (9l)}{\pi R}}\\d'=3\sqrt{\rho \frac{4 l}{\pi R}}\\d'=3d$