Common light bulbs have a mental filament made of tungsten and when a current passes through it, it radiates visible light, as well as heat. If initially the filament's resistance is 2.45 ohm (6%) at 20 degrees Celsius and the temperature coefficient of resistivity α is 0.004403/degrees Celsius, what is its resistance at 40 degrees Celsius? And at 60 degree Celsius? (include the uncertainty of the result)

Question

Common light bulbs have a mental filament made of tungsten and when a current passes through it, it radiates visible light, as well as heat. If initially the filament's resistance is 2.45 ohm (6%) at 20 degrees Celsius and the temperature coefficient of resistivity α is 0.004403/degrees Celsius, what is its resistance at 40 degrees Celsius? And at 60 degree Celsius? (include the uncertainty of the result)

As the filament's temperature increases, does its resistance stay the same, increase or decrease?

Answer 1

It increases with increasing temperature.

http://en.wikipedia.org/wiki/Resistivity

Answer 2

To determine the resistance of the filament at different temperatures, we need to use the formula for temperature-dependent resistance:

R2 = R1 * (1 + α * (T2 - T1))

Where:
R2 is the resistance at the second temperature (40 or 60 degrees Celsius, in this case)
R1 is the resistance at the first temperature (20 degrees Celsius)
α is the temperature coefficient of resistivity (0.004403/degrees Celsius)
T2 is the second temperature
T1 is the first temperature (20 degrees Celsius)

Let's calculate the resistance at 40 degrees Celsius:

R2 = 2.45 ohm * (1 + 0.004403/°C * (40°C - 20°C))
R2 = 2.45 ohm * (1 + 0.004403/°C * 20°C)
R2 = 2.45 ohm * (1 + 0.08806)
R2 = 2.45 ohm * 1.08806
R2 = 2.66337 ohm

Now, to calculate the uncertainty of the result, we need to calculate the absolute uncertainty of the initial resistance:

Absolute uncertainty = R1 * (uncertainty percentage / 100)
Absolute uncertainty = 2.45 ohm * (6 / 100)
Absolute uncertainty = 0.147 ohm

So, the resistance at 40 degrees Celsius is approximately 2.66337 ohm with an uncertainty of 0.147 ohm.

Similarly, let's calculate the resistance at 60 degrees Celsius:

R2 = 2.45 ohm * (1 + 0.004403/°C * (60°C - 20°C))
R2 = 2.45 ohm * (1 + 0.004403/°C * 40°C)
R2 = 2.45 ohm * (1 + 0.17612)
R2 = 2.45 ohm * 1.17612
R2 = 2.88326 ohm

Again, we calculate the absolute uncertainty:

Absolute uncertainty = R1 * (uncertainty percentage / 100)
Absolute uncertainty = 2.45 ohm * (6 / 100)
Absolute uncertainty = 0.147 ohm

So, the resistance at 60 degrees Celsius is approximately 2.88326 ohm with an uncertainty of 0.147 ohm.

As for the second part of your question, as the filament's temperature increases, its resistance increases. This phenomenon is known as positive temperature coefficient, where the electrical resistance of a material increases with an increase in temperature.