Question

Suppose an electrical wire is replaced with one having every linear dimension doubled (i.e. the length and radius have twice theri original values). The wire now has ... a resistance which depends only on the material. the same resistance as before. less resistance than before. a resistance which can't be further predicted with the given information. more resistance than before.

Answer 1

Answer:

The wire now has less (the half resistance) than before.

Explanation:

The resistance in a wire is calculated as:

$R=\alpha \frac{l}{s}$

Were:

R is resistance

$\alpha$ is the resistance coefficient

l is the length of the material

s is the area of the transversal wire, in the case of wire will be circular area ($s=\pi r^{2}$).

So if the lenght and radius are doubled, the equation goes as follows:

$R=\alpha \frac{l}{\pi r^{2} } =\alpha \frac{2l}{\pi {(2r)}^{2} } =\alpha \frac{2l}{\pi 4 {r}^{2} }=\frac{1}{2} \alpha \frac{l}{\pi r^{2} }$

So finally because the circular area is a square function, the resulting equation is half of the one before.