A cylindrical tungsten filament 13.0 cm long with a diameter of 1.00 mm is to be

Question

A cylindrical tungsten filament 13.0 cm long with a diameter of 1.00 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 13.0 A at all temperatures ( Resistivity of tungsten at 20 C is 5.25×108m , the temperature coefficient of resistivity at 20 C is 0.0045 C1 )

Part A

What will be the maximum electric field in this filament?

Part B

What will be its resistance with that field?

Part C

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

Explanation / Answer

A.

resistivity = rho = E/J

E = rho*J

E = rho0*(1 + alpha*(T - T0))*J

J = i/A

Using the given values:

E = 5.25*10^-8*(1 + 0.0045*(120 - 20))*13/(pi*0.0005^2)

E = 1.26 N/C

C.

Vmax = E*d

Vmax = 1.26*0.13 = 0.1638 V

B.

R = V/I

R = 0.1638/13 = 0.0126 = 12.6*10^-3 ohm

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