What is the length of the wire of the spiral of a 420 W heating element made of manganin, if its cross-sectional

What is the length of the wire of the spiral of a 420 W heating element made of manganin, if its cross-sectional area is 0.14 mm2, and the voltage in the network is 210 V?

Task data: P (heating element power) = 420 W; S (cross-sectional area of the manganin wire) = 0.14 mm2; U (mains voltage) = 210 V.

Reference values: ρ (electrical resistivity of manganin at 20 ºС) = 0.43 Ohm * mm2 / m.

The length of the manganin wire can be expressed from the following equality: U ^ 2 / P = R = ρ * l / S, whence l = U2 * S / (P * ρ).

Let’s perform the calculation: l = 210 ^ 2 * 0.14 / (420 * 0.43) ≈ 34.2 m.

Answer: The manganin wire should be 34.2 m long.