# Determine the strength of the current passing through a steel wire 100m long and 0.5mm2 at a voltage of 40V.

1. We present all the data from given in SI systems:

Ssection = 0.5 mm² = 0.5 * 10-6 m²

2. According to Ohm’s law, the current value is directly proportional to the applied voltage and inversely proportional to its resistance:

I = U / R

3. To determine the resistance of the wire, we use the expression to determine the specific resistance of the wire:

ρsp = R * Ssech / l, where R is the resistance of the wire, l is the length of the wire, Ssech is the cross-sectional area.

Let us express R from here:

R = ρsp * l / Ssection

4. Substitute in Ohm’s law:

I = U / R = U * Ssection / (ρsp * l)

5. Substitute the numerical values and determine the current strength, taking into account that the specific resistance of steel ρsp = 0.125 * 10-6 Ohm m (according to the reference book):

I = U * Ssec / (ρsp * l) = (40 * 0.5 * 10 ^ -6) / (0.125 * 10-6 * 100) = 1.6 A.

Answer: the current strength is 1.6 A.