To find the resistance of the filament at 40 degrees Celsius and 60 degrees Celsius, we can use the temperature coefficient of resistivity (α) and the initial resistance value. The temperature coefficient of resistivity measures how the resistivity of a material changes with temperature.
First, let's calculate how much the resistance changes (ΔR) between the initial temperature and the desired temperature using the equation:
ΔR = α * R_initial * ΔT
where ΔT is the change in temperature. In this case, ΔT = 40°C - 20°C = 20°C for the first calculation, and ΔT = 60°C - 20°C = 40°C for the second calculation.
1. Calculate the resistance at 40 degrees Celsius:
ΔR = 0.004403 * 2.45 Ω * 20°C = 0.217 Ω
Resistance at 40°C = R_initial + ΔR = 2.45 Ω + 0.217 Ω = 2.67 Ω
2. Calculate the resistance at 60 degrees Celsius:
ΔR = 0.004403 * 2.45 Ω * 40°C = 0.434 Ω
Resistance at 60°C = R_initial + ΔR = 2.45 Ω + 0.434 Ω = 2.89 Ω
Now, let's discuss how the resistance changes with temperature. Generally, as the temperature of the filament increases, its resistance also increases. This is because at higher temperatures, the atoms in the filament vibrate more vigorously, which increases the chances of collisions with the moving electrons. These collisions impede the flow of current, resulting in an increased resistance.
To recap:
Resistance at 40 degrees Celsius = 2.67 Ω (with an uncertainty of 6%)
Resistance at 60 degrees Celsius = 2.89 Ω (with an uncertainty of 6%)