Problem-9 The circuit in the following figure can be used to measure the in-car temperature. This circuit is designed to operate between -40 °C and +40 °C. The resistor R₂ is a temperature dependent resistor (RTD). The relation between temperature and resistance (transfer function) can be approximated with the following linear equation: R₂ (T) = Ro(1 + aT), with Ro equal to 100 and a = 0.004/°C. The resistor R₁ has a fixed value (R₁ = Rok). a) Find the output voltage in terms of k, a, and T. b) Find the sensitivity of the sensor for a change in the temperature (i.e., do). Calculate the output voltage for k = 10, V₂ = 24 V, and T is last three digits of your student ID divided by 3. (i.e., if your student ID is 114207036, T == 36 3 VO R₁ www O R₂ v Figure 2 Vo = 12°C)

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Problem-9
The circuit in the following figure can be used to measure the in-car temperature.
This circuit is designed to operate between -40 °C and +40 °C. The resistor R₂ is a temperature
dependent resistor (RTD). The relation between temperature and resistance (transfer function) can be
approximated with the following linear equation: R₂ (T) = Ro(1 + aT), with Ro equal to 100 N and
α= 0.004/°C. The resistor R₁ has a fixed value (R₁ = Rok).
a)
b)
c)
Find the output voltage in terms of k, a, and T.
Find the sensitivity of the sensor for a change in the temperature (i.e., dvo).
dT
Calculate the output voltage for k = 10, Vr = 24 V, and T is last three digits of your
student ID divided by 3. (i.e., if your student ID is 114207036, T = = 12°C)
36
3
V₁O
R₁
www
Figure 2
O
R₂ Vo
O
Transcribed Image Text:Problem-9 The circuit in the following figure can be used to measure the in-car temperature. This circuit is designed to operate between -40 °C and +40 °C. The resistor R₂ is a temperature dependent resistor (RTD). The relation between temperature and resistance (transfer function) can be approximated with the following linear equation: R₂ (T) = Ro(1 + aT), with Ro equal to 100 N and α= 0.004/°C. The resistor R₁ has a fixed value (R₁ = Rok). a) b) c) Find the output voltage in terms of k, a, and T. Find the sensitivity of the sensor for a change in the temperature (i.e., dvo). dT Calculate the output voltage for k = 10, Vr = 24 V, and T is last three digits of your student ID divided by 3. (i.e., if your student ID is 114207036, T = = 12°C) 36 3 V₁O R₁ www Figure 2 O R₂ Vo O
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