How many meters of manganin wire with a diameter of 0.30 mm went to winding a rheostat with a resistance of 1000 ohms?

Data: d (diameter of the manganin wire) = 0.3 mm; R (required rheostat resistance) = 1000 ohms.
Reference data: ρ (resistivity of manganin) = 0.43 Ohm * mm2 / m.
The length of the manganin wire for winding the rheostat is determined from the formula: R = ρ * l / S = ρ * l / (0.25 * Π * d ^ 2), whence l = 0.25 * Π * d2 * R / ρ.
Calculation: l = 0.25 * 3.14 * 0.3 ^ 2 * 1000 / 0.43 = 164.3 m.
Dimensional check: m = mm2 * Ohm / (Ohm * mm2 / m) = m.
Answer: 164.3 m of manganin wire was used to wind the rheostat.



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