resistance in physics?

R=ρ l /S
R - resistance
ρ- specific resistance of the given wire
l - length of wire
S - cross-section surface area

I gather that both wires are made from the same material so they have the same ρ. So your solution goes as followed:

the surface area of a circle is: S=2π r^2

mm=10^-3 m

x is the value you are looking for

A: R=ρ 4m / 2 π (2 10^-3)^2 m
B: R=ρ x /2 π (8 10^-3)^2 m

ρ 4m / 2 π (2 10^-3)^2 m = ρ x /2 π (8 10^-3)^2 m

and after some calculations, if I'm correct:

x=64 m
 
Electric current flows on the outside surface of a wire, because the free electrons repel each other and are forced as far apart as possible. So if there's more surface, the electrons flow more easily - less resistance! The resistance of a wire is inversely and linearly proportional to its surface area,

R = p/A

where p is a constant which depends on the material, called the resistivity.

The wire is a very long cylinder, and a cylinder's surface area is equal to its circumference times its length.

A = C*L

The circumference is related to the diameter by C = pi*D, so

A = pi*D*L

So,

R = p/(pi) * 1/(D*L)

Since p is a constant (assuming the wires are the same material), if D goes up by a factor of 2, then L must go down by a factor of 2 to have the same resistance. So the length of wire B is 4 m/2 = 2 m.
 
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