Two pieces of iron wire have the same mass. The length of one of them is 10 times the length of the other.

Two pieces of iron wire have the same mass. The length of one of them is 10 times the length of the other. Which piece of wire has more resistance; how many times?

Given:

m1 = m2 = m – the mass of pieces of iron wire is the same;

l1 = 10 * l2 – the length of the first piece of wire is 10 times longer than the length of the second piece;

ro is the density of iron;

k is the resistivity of iron.

It is required to determine which of the pieces of wire has the greatest resistance and by how many times.

Since the pieces of wire are cylindrical, we find the ratio of their cross-sectional areas:

m1 = m2;

ro * V1 = ro * V2, where V1 and V2 are the volumes of the pieces of wire;

V1 = V2;

S1 * l1 = S2 * l2, where S1 and S2 are cross-sectional areas;

S1 * 10 * l2 = S2 * l2;

10 * S1 = S2;

S1 = S2 / 10.

Then:

R1 / R2 = (k * l1 / S1) / (k * l2 / S2) = k * l1 * S2 / (S1 * l2 * k) =

= l1 * S2 / (S1 * l2) = 10 * l2 * S2 / (S2 * l2 / 10) = 10 * 10 = 100 times.

Answer: the resistance of the first piece of wire is 100 times greater.