A cylindrical tungsten filament 17.0 cm long with a diameter of 1.10 mm is to be

Question

A cylindrical tungsten filament 17.0 cm long with a diameter of 1.10 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 13.5 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 )

A)What will be the maximum electric field in this filament?

Express your answer using two significant figures.

B)What will be its resistance with that field?

Express your answer using two significant figures.

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

Express your answer using two significant figures.

Explanation / Answer

Current density J = current/area = E /rho

where rho is ressitivity, here it is rho t = rho (1+ A dT)

Rho t = (5.25 e -8 * (1+ 0.0045 *(120-20)))

Rhot = 7.61 e -8 ohm m

so

E lectric field E = I rhot/A = 13.5 * 7.61 e -8/(3.14*0.55 e-3 * 0.55 e-3)

E = 1.08 V/m =---------------------<<<<<<<<<<<<<Answer to part A

-------------------------------------

Vmax = EL = 1.08 * 0.17 = 0.183 Volts -------<<<<<<<<<<Answer to part C

from ohms law V = IR

R = V/I = 0.183/13.5 = 0.0136 ohms ----<<<<<<<<<<Answer to part B

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