What will be the maximum electric field in this filament?
A cylindrical tungsten filament, 14.0 cm in length and 1.30 mm in diameter, is to be used in a machine where the temperature will vary from room temperature (20°C) to 120°C. The filament will carry a constant current of 11.5 A across this temperature range. The resistivity of tungsten at 20°C is 5.25×10⁻⁸ Ω·m, and its temperature coefficient of resistivity at 20°C is 0.0045°C⁻¹.
Part A
What will be the maximum electric field in this filament?
E = __
Part B
What will be the resistance of the filament at that maximum electric field?
R = __
Part C
What will be the maximum potential drop across the full length of the filament?
V = __
1 Answers
Feb 01, 2025
ρ = ρ'(1 + α(T - T'))
ρ = 5.26 × 10^-8 (1 + 0.0045(120 - 20))
ρ = 5.26 × 10^-8 (1 + 0.45)
ρ = 5.26 × 10^-8 × 1.45
ρ = 7.627 × 10^-8 Ωm
R = ρ L / A
R = (7.627 × 10^-8 × 0.14) / ( π × (1.3/2 × 10^-3)^2)
R = 0.0080 Ω
V = iR
V = 11.5 × 0.0080
V = 0.092V
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