What should be the diameter of the iron conductor in order to close an element

What should be the diameter of the iron conductor in order to close an element with an emf with it? 1.5 V and an internal resistance of 0.2 Ohm, get a current of 0.6 A? The conductor length is 5 m.

Given:

U = 1.5 Volts – electromotive force of the element;

r = 0.2 Ohm is the internal resistance of the element;

I = 0.6 Ampere – required current strength;

l = 5 meters – conductor length;

k = 0.098 Ohm * mm2 / m – iron resistivity.

It is required to determine d (millimeter) – what should be the diameter of the conductor.

Let’s find the resistance that the conductor should have:

U / (R + r) = I;

U / I = R + r;

R = U / I – r = 1.5 / 0.6 – 0.2 = 2.5 – 0.2 = 2.3 Ohm.

Then the cross-sectional area of ​​the conductor will be equal to:

s = k * l / R = 0.098 * 5 / 2.3 = 0.49 / 2.3 = 0.21 mm2.

Then the diameter of the conductor will be equal to:

d = s / n = 0.21 / 3.14 = 0.07 millimeters (n = 3.14 is a geometric constant).

Answer: the diameter of the conductor should be equal to 0.07 millimeters.