How will the resistance of the wire change if you cut off half of it?

Given:

l2 = l1 / 2 – the length of some wire was halved (cut off half).

It is required to determine R2 / R1 – how the wire resistance will change.

The resistance of the wire in the first case will be equal to:

R1 = r * l1 / s, where r is the specific resistance of the material from which the wire is made, s is the specific cross-sectional area of ​​the wire.

The resistance of the wire in the second case will be equal to:

R2 = r * l2 / s = r * (l1 / 2) / s = r * l1 / (2 * s).

Then:

R2 / R1 = (r * l1 / (2 * s)) / (r * l1 / s) = 1/2, that is, it will decrease by half.

Answer: if you cut off half of the wire, its resistance will be halved.