Determine the length of the nickel wire if, with a voltage at its ends of 45V, the current is equal to 2.25A

Determine the length of the nickel wire if, with a voltage at its ends of 45V, the current is equal to 2.25A. The cross-sectional area of the wire is exactly 1mm squared.

U = 45 V.

I = 2.25 A.

S = 1 mm2.

ρ = 0.4 Ohm * mm2 / m.

L -?

The resistance R of a uniform cylindrical conductor with a length L and a cross-sectional area S is determined by the formula: R = ρ * L / S, where ρ is the resistivity of the substance from which the conductor is made.

We express the resistance of the same conductor R according to Ohm’s law for a section of the circuit, the ratio of the voltage U to the current in it: R = U / I.

ρ * L / S = U / I.

The formula for determining the length of the nickel wire will be: L = S * U / I * ρ.

L = 1 mm2 * 45 V / 2.25 A * 0.4 Ohm * mm2 / m = 50 m.

Answer: nickel wire has a length of L = 50 m.