The homogeneous metal bar became twice as long after rolling. How many times has its electrical resistance changed?

The volume of one bar does not change during rolling. Equality of volumes before and after rolling:

l1S1 = l2S2,

where l1 and S1 are the length and cross-section of the bar before rolling, l2 and S2 are the length and cross-section of the bar after rolling.

Section of the bar after rolling at l2 = 2l1:

S2 = l1S1 / l2;

S2 = l1S1 / 2l1 = S1 / 2.

Bar resistance before and after rolling:

R1 = ρl1 / S1;

R2 = ρl2 / S2 = (ρ * 2l1) / (S1 / 2) = 4 ρl1 / S1.

Comparison of resistances:

R2 / R1 = (4 ρl1 / S1) / (ρl1 / S1) = 4;

R2 = 4R1.

Answer: after rolling, the resistance of the bar increased by 4 times.