A cylindrical tungsten filament 160 cm long with a diameter

A cylindrical tungsten filament 16.0 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 12.5 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 )

NEED PARTS A-C

PLEASE INCLUDE ALL WORK WITH ACTUAL NUMBERS PROVIDED SO I CAN SEE HOW YOU GOT YOUR ANSWER

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

ANSWER: E = _______________ V/m

PART B:What will be its resistance with that field?

ANSWER: R = _______________ omega

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

ANSWER: V= ________________ V

Solution

A. Electric field

E = rho*J

J = I/pi*r^2

rho = rho1*(1 + alpha(T - T0))

E = rho1*(1 + alpha(T - T0))*I/(pi*r^2)

E = 5.25*10^-8*(1 + 0.0045*(120 - 20))*12.5/(3.14*0.00065^2)

E = 0.717 N/C

B. R = rho*L/A

At 120 C resistivity of filament = 7.61*10^-8 ohm.m

R = 7.61*10^-8*0.16/(3.14*0.00065^2) = 9.17*10^-3 ohm

C. potential drop = E*L

V = 0.717*0.16 = 0.115 V

Let me know if you have any doubt.