if you double the radius of the metal wire...?

Question

what happens to its cross-sectional area? if you double its diameter? does the resistance of the wire increase or decrease?

Answer 1

A = πr²
if r' = 2r
then
A' = πr' ² = π(2r)² = 4πr² = 4A
it's cross sectional area is 4 times larger than the original

pretty much the same argument as above
A = πd² /4
if d' = 2d
then
A' = π(d')² /4 = π(2d)² /4 = 4(π(d)² /4) = 4A
it's cross sectional area is 4 times larger than the original

R=resistance, L=length, A=area, p=resistivity
then
R = pL/A
if A' = 4A
then
R' = pL/A' = pL/4A = (1/4)pL/A = (1/4)R
so the resistance decreases, it will be 1/4 of the original

the end
.

Answer 2

In scaling up ANYTHING:
If you scale the linear dimension by factor F,

* You increase cross sectional area,
(strength, conductivity, etc. by 'F` squared.

* You increase volume, (weight, capacity, etc),
by 'F` cubed.

It's called the "square cube law".
It's important in many ways.
Learn it.

Answer 3

resistance decreases