A platinum resistance thermometer uses the change in R to measure temperature. Suppose R0=50 ohm at T0= 20°C. Temperature coefficient of resistance for platinum is 3,92×10-³ (°C)-¹ in this Temperature range. What is R when T=50,0°C?
To calculate the resistance (R) at a certain temperature (T), we can use the formula:
R = R0 * (1 + α * (T - T0))
Where:
R0 = resistance at a reference temperature (T0)
α = temperature coefficient of resistance
T = temperature at which we want to calculate the resistance
Given:
R0 = 50 ohm
T0 = 20°C
α = 3.92×10^-3 (°C)^-1
T = 50.0°C
Substituting the values into the formula:
R = 50 * (1 + 3.92×10^-3 * (50 - 20))
R = 50 * (1 + 3.92×10^-3 * 30)
R = 50 * (1 + 0.1176)
R = 50 * 1.1176
R ≈ 55.88 ohm
Therefore, the resistance (R) at a temperature of 50.0°C is approximately 55.88 ohm.