Final answer:
To calculate the bridge voltage at 55°C for the RTD in a quarter bridge circuit, the resistance at the target temperature is first found using the temperature-resistance formula, and then voltage division is applied considering a 10V power supply. The calculated bridge voltage is approximately 5.42V.
Step-by-step explanation:
The question revolves around the calculation of the bridge voltage of an RTD (Resistance Temperature Detector) in a quarter bridge circuit. To find the bridge voltage at 55°C, we can use the formula for the resistance of an object considering the temperature change:
R = Ro(1 + αΔT)
Where:
- Ro is the original resistance at 0°C (120Ω in this case),
- α is the temperature coefficient of resistance (0.0032 Ω/Ω/°C),
- ΔT is the change in temperature from the reference point, which is 55°C - 0°C = 55°C.
Substituting the given values into the formula:
R = 120Ω(1 + 0.0032Ω/Ω/°C × 55°C) = 120Ω(1 + 0.176) = 120Ω × 1.176 = 141.12Ω
Since the RTD is part of a quarter bridge circuit with 120Ω matched resistors, the voltage across the RTD can be calculated using voltage division:
V_RTD = (R/(R + Ro)) × V_supply
Where V_supply is 10V. Substituting the values:
V_RTD = (141.12Ω / (141.12Ω + 120Ω)) × 10V ≈ 5.42V
Therefore, the bridge voltage at a temperature of 55°C is approximately 5.42V.