Question

A tungsten filament with 5.00 mV applied across it has a current of 1.35 mA and a temperature of 20.0 degrees C. When 5.00 V are applied across the filament, it has a current of 0.250 A. (a) What is the temperature of the tungsten filament with 5.00 V across it? (Tungsten has a resistivity of 5.60 x 10-8 W m at 20.0 degrees C, and a temperature coefficient of resistivity of 4.50 x 10-3 degrees C-1.) (b) If the filament has a length of 1.00 cm at 20.0 oC, what is its cross-sectional area at that temperature?

Answer 1

When applied Voltage = 5.00 mV and current = 1.35 mA, at Temperature of 20 C

Resistor of filament will be

R0 = V/i = 5 mV/(1.35 mA) = 3.70 ohm

When applied Voltage = 5.00 V and current = 0.250A

Resistor of filament will be

R = V/i = 5 V/(0.250 A) = 20 ohm

Relation between temperature and resistance is given by:

R = R0*(1 + alpha*dT)

R0 = resistance at 20 C = 3.70 ohm

R = resistance at T temperature = 20 ohm

alpha = temperature coefficient = 4.5*10^-3 /C

20 = 3.70*(1 + 4.5*10^-3*(T - 20))

T - 20 = (20 - 3.70)/(3.70*4.5*10^-3)

T = 20 + (20 - 3.70)/(3.70*4.5*10^-3)

T = 998.98 C

Part B.

At 20 C

R0 = rho*L/A

A = rho*L/R0

A = 5.6*10^-8*1*10^-2/3.70

A = 1.51*10^-10 m^2

Please Upvote.