The 4 Ohm conductor was pulled through the drawing machine so that the length

The 4 Ohm conductor was pulled through the drawing machine so that the length of the conductor increased by 4 times. How did the resistance become?

Given:

R = 4 Ohm – conductor resistance;

l1 = l – conductor length;

l2 = 4 * l – the length of the conductor after the drawing machine;

p1 = p2 = p is the resistivity of the conductor.

It is required to find the resistance of the conductor R1, after lengthening on the machine.

Since the condition of the problem is not specified, we consider that the conductor is made of an absolutely elastic material, that is, with an increase in its length by 4 times, the cross-sectional area also decreased by 4 times, or S1 = S, S2 = S / 4.

Conductor resistance before increasing the length on the machine:

R = p * l1 / S1 = p * l / S.

Conductor resistance after increasing the length on the machine:

R1 = p * l2 / S2 = p * 4 * l / (S / 4) = 16 * p * l / S.

Let’s divide one equation by another:

R / R1 = (p * l / S) / (16 * p * l / S) = p * l * S / 16 * p * l * S = 1/16, hence:

R1 = 16 * R = 16 * 4 = 64 Ohms.

Answer: the resistance of the conductor after increasing the length on the machine became 64 Ohms.