To determine the current through the conductor at 1200°C, we need to use the concept of temperature coefficient of resistance. The temperature coefficient of resistance is a measure of how the resistance of a material changes with temperature.
Assuming the temperature coefficient of resistance for the conductor is known, we can use the following formula:
R2 = R1 * (1 + α * ΔT)
where: R1 is the initial resistance of the conductor at temperature T1, R2 is the final resistance of the conductor at temperature T2, α is the temperature coefficient of resistance, and ΔT is the change in temperature (T2 - T1).
Since the current through a conductor is inversely proportional to its resistance (assuming the voltage remains constant), we can use the formula:
I2 = I1 * (R1 / R2)
Given that the current at 0°C is 1 A and at 100°C is 0.7 A, we'll use these values to find the temperature coefficient of resistance and then calculate the current at 1200°C.
Let's assume the initial temperature is 0°C, the initial current is 1 A, and the final temperature is 100°C, with a current of 0.7 A. Plugging these values into the formulas:
R2 = R1 * (1 + α * ΔT) 0.7 = 1 * (1 + α * 100)
Simplifying the equation: 0.7 = 1 + 100α 100α = 1 - 0.7 100α = 0.3 α = 0.3 / 100 α = 0.003
Now we can calculate the current at 1200°C: ΔT = 1200 - 100 = 1100°C
R2 = R1 * (1 + α * ΔT) R2 = 1 * (1 + 0.003 * 1100) R2 = 1 * (1 + 3.3) R2 = 1 * 4.3 R2 = 4.3 Ω
I2 = I1 * (R1 / R2) I2 = 1 * (1 / 4.3) I2 ≈ 0.233 A
Therefore, the current through the conductor at 1200°C would be approximately 0.233 A.