A cylindrical tungsten filament 13.5 cm long with a diameter of 0.50 mm is to be

Question

A cylindrical tungsten filament 13.5 cm long with a diameter of 0.50 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 11.0 A at all temperatures (consult tables [a] and [b] below).

(a) What will be the maximum electric field in this filament?
_______ V/m

(b) What will be its resistance with that field?
________

(c) What will be the maximum potential drop over the full length of the filament?
______________ V

[a] [b] Resistivities at Room Temperature ( 20 °C) Substance p(0.m) Substance p(2. m) Conductors Metals 3.5 X 10-5 0.60 2300 Silver Copper Gold Aluminum Tungsten Steel Lead Mercury Manganin (Cu 84%, Mn 12%, Ni 4%) Constantan (Cu 60%, Ni 40%) Nichrome 1.47 X 10-8 1.72 x 10-8 2.44 x 10-8 2.75 X 10-8 5.25 X 10-8 20 X 108 22 x 108 95 x 10-8 44 x 10-8 49 x 10-8 100 x 10-8 Semiconductors Pure carbon (graphite) Pure germanium Pure silicon Insulators Amber Glass Lucite Mica Quartz (fused) Sulfur Teflon Wood 5X 1024 101-1014 >1013 10"-1015 75 x 1016 1015 >1013 108-1011 Alloys

Explanation / Answer

(A) E will be maxium when V is maximum that will be when R is maxiumum.

R = R0 [1 + alpha deltaT ]

R = (5.25 x 10^-8 x 0.135 / (pi (0.50 x 10^-3/2)^2))[1 + (0.0045)(120-20)]

R = 0.0523 ohm

V = I R = 0.576 Volt

E = V/m = 4.26 V/m

(B) R = 0.0523 ohm

(C) V = 0.576 Volt

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