How long should you take a nickeline conductor of round cross-section with a diameter of 0.5 mm

How long should you take a nickeline conductor of round cross-section with a diameter of 0.5 mm to make an electric fireplace operating at a voltage of 220 V and a current strength of 2 A in it? The specific electrical resistance of nickelin is considered equal to 0.4 μOhm⋅hm.

d = 0.5 mm = 0.5 * 10 ^ -3 m.

U = 220 V.

I = 2 A.

ρ = 0.4 μOhm * m = 0.4 * 10 ^ -6 Ohm * m.

L -?

Let us express the resistance of the nickel wire R from Ohm’s law for a section of the circuit, the ratio of the voltage at the ends of the conductor U to the current I in it: R = U / I.

Since a nickelin conductor has a homogeneous structure and a cylindrical shape, its resistance is expressed by the formula: R = ρ * L / S, where ρ is the resistivity of the material from which the conductor is made, L is the length of the conductor, S is the cross-sectional area of ​​the conductor.

S = P * d ^ 2/4.

R = 4 * ρ * L / P * d ^ 2.

U / I = 4 * ρ * L / P * d ^ 2.

The length of the wire L will be determined by the formula: L = U * P * d ^ 2 / I * 4 * ρ.

L = 220 V * 3.14 * (0.5 * 10 ^ -3 m) ^ 2/2 A * 4 * 0.4 * 10 ^ -6 Ohm * m = 54 m.

Answer: the nickel wire has a length L = 54 m.