The tungsten filament of the electric lamp has a length of 20 cm and a resistance of R = 20 ohms at a temperature

| July 28, 2021 | education

The tungsten filament of the electric lamp has a length of 20 cm and a resistance of R = 20 ohms at a temperature of t = 250 degrees Celsius. What is the thread diameter? Tungsten resistivity 5.6 * 10 ^ -8 Ohm * m, thermal resistance coefficient = 0.005 K ^ -1

Given: l (tungsten filament length) = 20 cm (0.2 m); R (resistance at t1) = 20 ohms; t1 (thread temperature) = 250 ºС.

Constants: ρ (specific resistance of tungsten) = 5.6 * 10 ^ -8 Ohm * m; α (thermal coefficient of resistance) = 0.005 K-1.

1) Thread resistance at 20 ºС: R0 = R / (1 + α * t1) = 20 / (1 + 0.005 * 250) = 8.89 Ohm.

2) Cross-sectional area of the thread: S = ρ * l / R0 = 5.6 * 10 ^ -8 * 0.2 / 8.89 = 1.25 * 10 ^ -9 m2.

3) Filament diameter: D = √ (4S / Π) = √ (4 * 1.25 * 10 ^ -9 / 3.14) = 3.99 * 10 ^ -5 m = 39.9 microns.



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