# What cross-sectional area do you need to take an iron wire 10 m long so that its resistance

What cross-sectional area do you need to take an iron wire 10 m long so that its resistance is the same as that of a nickel wire with a cross-sectional area of 0.2 mm2 and a length of 1 m.

Lzh = 10 m.

ρzh = 0.1 Ohm * mm2 / m.

Sn = 0.2 mm2.

Ln = 1 m.

ρн = 0.4 Ohm * mm2 / m.

Rzh = Rn.

Szh -?

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

Rzh = ρzh * Lzh / Szh.

Rn = ρn * Ln / Sn.

ρl * Ll / Sl = ρn * Ln / Sn.

Sl = ρl * Ll * Sn / ρn * Ln.

Szh = 0.1 Ohm * mm2 / m * 10 m * 0.2 mm2 / 0.4 Ohm * mm2 / m * 1 m = 0.5 mm2.

Answer: the iron conductor must have a cross-sectional area Szh = 0.5 mm2.

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