Final answer:
To calculate the temperature of the 10kΩ NTC thermistor, use the Steinhart-Hart equation T = 1/(1/T_0 + 1/β * ln(R/R_0)). First, calculate the thermistor resistance using the voltage divider equation R = (V_thermistor/(V_supply - V_thermistor)) * R_fixed. Then, plug the values into the Steinhart-Hart equation to find the temperature T.
Step-by-step explanation:
To calculate the temperature of the thermistor, we can use the Steinhart-Hart equation:
T = \frac{1}{\frac{1}{T_0} + \frac{1}{\beta} \cdot ln(\frac{R}{R_0})}
Where T is the temperature of the thermistor, T_0 is the reference temperature (25°C in this case), \beta is the thermistor constant (3800 in this case), R is the thermistor resistance (calculated using the voltage divider equation), and R_0 is the resistance at the reference temperature (10kΩ in this case).
Using the voltage divider equation, we can calculate the thermistor resistance:
R = \frac{V_{thermistor}}{V_{supply} - V_{thermistor}} \cdot R_{fixed}
Given that V_{thermistor} is 2.5V, V_{supply} is 5V, and R_{fixed} is 10kΩ, we can calculate R to be 5kΩ. Plugging the values into the Steinhart-Hart equation, we can calculate the temperature T to be approximately 39.17°C.