What will be the maximum electric field in this filament?

A cylindrical tungsten filament 14.0 cm long with a diameter of 1.30 mm is to be used in a machine for which the temperature will range from room temperature (20 ∘C) up to 120 ∘C. It will carry a current of 11.5 A at all temperatures ( Resistivity of tungsten at 20 ∘C is 5.25×10^−8 Ω⋅m , the 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 its resistance with that field?

R=__

Part C

What will be the maximum potential drop over the full length of the filament?

V =__

1 Answer

  • 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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