The resistance of a wire made of fechral with a cross section of 0.5 mm2 and a length of 2.5 m is equal to 5.47 Ohm

The resistance of a wire made of fechral with a cross section of 0.5 mm2 and a length of 2.5 m is equal to 5.47 Ohm. What is the specific resistance of a fechral? How many meters of such a conductor will be required to manufacture an electric heater operating from a network with a voltage of 220V at a current of 3A?

S = 0.5 mm2.

L = 2.5 m.

R = 5.47 ohms.

U = 220 V.

I = 3 A.

ρ -?

L1 -?

For a homogeneous cylindrical conductor, its resistance R is determined by the formula: R = ρ * L / S, where ρ is the resistivity of the conductor material, L is the length of the conductor, S is the cross-sectional area.

ρ = R * S / L.

ρ = 5.47 Ohm * 0.5 mm2 / 2.5 m = 1 Ohm * mm2 / m.

According to Ohm’s law for a section of the circuit: I = U / R1.

R1 = ρ * L1 / S.

I = U * S / ρ * L1.

We find the length of the wire L1 by the formula: L1 = U * S / ρ * I.

L1 = 220 V * 0.5 mm2 / 1 Ohm * mm2 / m * 3 A = 36.6 m.

Answer: the resistivity of the fechral is ρ = 1 Ohm * mm2 / m, the wire length is L1 = 36.6 m.