How will the electric current change through a conductor connected to a current source if its length doubles?

Given:

l2 = 2 * l1 – the length of the conductor was doubled;

U1 = U2 = U – the voltage of the electrical network does not change;

s1 = s2 = s – the cross-sectional area of ​​the conductor does not change;

k1 = k2 = k – the resistivity of the conductor does not change.

It is required to determine I2 / I1 – how the strength of the current passing through the conductor will change with increasing its length.

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

R1 = k1 * l1 / s1 = k * l1 / s, and the current passing through the conductor: I1 = U / R1 = U * s / (k * l1).

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

R2 = k2 * l2 / s2 = k * l2 / s, and the current passing through the conductor: I2 = U / R2 = U * s / (k * l2).

Then:

I2 / I1 = (U * s / (k * l2)) / (U * s / (k * l1)) = l1 / l2 = l1 / (2 * l1) = 1/2, that is, the current will decrease 2 times.

Answer: with an increase in the length of the conductor, the current will decrease by 2 times.