A heating coil was made from nichrome wire with a cross-sectional area of 0.25 mm2 to be connected to a 220V

A heating coil was made from nichrome wire with a cross-sectional area of 0.25 mm2 to be connected to a 220V electrical network. The power of the current flowing through the heating element is 600 W. How long does the wire need to be to make a spiral?

S = 0.25mm ^ 2.

U = 220 V.

N = 600 W.

ρ = 1.1 Ohm * mm ^ 2 / m.

l -?

The power of the electric current in the conductor N is determined by the formula: N = U ^ 2 / R, where U is the voltage at the ends of the conductor, R is the resistance of the conductor.

The resistance of a homogeneous cylindrical conductor R is determined by the formula: R = ρ * l / S, where ρ is the specific resistance of the substance from which the conductor is made, l is the length of the conductor, S is the cross-sectional area of the conductor.

N = S * U ^ 2 / ρ * l.

We find the length of the conductor by the formula: l = S * U ^ 2 / ρ * N.

l = 0.25 mm ^ 2 * (220 V) ^ 2 / 1.1 Ohm * mm ^ 2 / m * 600 W = 18.3 m.

Answer: the conductor has a length l = 18.3 m.