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Answer :
Final answer:
To find the patient's temperature using the digital medical thermometer, we utilize the known temperature coefficient of resistance for the thermistor and the percentage change in resistance. The calculations reveal that the patient's temperature is 36.5ºC, below the normal body temperature of 37.0ºC.
Explanation:
The question involves understanding how digital medical thermometers work by measuring changes in the resistance of a thermistor at different temperatures. According to the question, the thermistor's resistance at the patient's temperature is 82.0% of its value at normal body temperature, which is 37.0ºC. Given the temperature coefficient of resistance (α) is -0.0600/ºC, we can use this information to find the patient's temperature.
Firstly, we can express the temperature coefficient as α = ΔR / (Râ‚€ * ΔT), where ΔR is the change in resistance, Râ‚€ is the initial resistance, and ΔT is the temperature change. Since we know the resistance is 82.0% of its initial value at 37.0ºC, we can calculate ΔR as 0.1800 * Râ‚€. Consequently, the temperature change (ΔT) that results in this change in resistance can be calculated by rearranging the expression to ΔT = ΔR / (Râ‚€ * α).
Using the given thermistor value of α and the resistance change, we calculate the temperature change and then adjust the initial temperature (37.0ºC) by this value to find the patient's temperature. The calculations will show that the correct answer is c) 36.5ºC, meaning that the patient's temperature is below the normal body temperature of 37.0ºC.
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