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

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

Step-by-step explanation:

The resistance in a wire is calculated as:

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

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