the temperature coefficient of resistivity for a thermistor in a digital thermometer used to measure the temperature of a sick patient is -6×10^-2 C If the resistance of the thermistor decreases by 15% relative to its value at normal body temperature of 37°C what is the patient's temperature
To determine the patient's temperature using the information provided, we can use the formula for the temperature coefficient of resistivity and the percentage change in resistance.
Let's break down the steps to calculate the patient's temperature:
Step 1: Convert the temperature coefficient from percent to decimal:
The temperature coefficient given is -6×10^-2 C, which already is in decimal form.
Step 2: Calculate the change in resistance:
The resistance of the thermistor decreases by 15% relative to its value at 37°C. To calculate the change in resistance, multiply the resistance at 37°C by the percentage change:
Change in Resistance (ΔR) = -15% * Resistance at 37°C
Step 3: Calculate the change in temperature:
We can use the formula for the temperature coefficient of resistivity to relate the change in resistance to the change in temperature:
ΔR/R = Temperature Coefficient * ΔT
Rearranging the formula, we can solve for ΔT:
ΔT = ΔR / (R * Temperature Coefficient)
Step 4: Calculate the patient's temperature:
To find the patient's temperature (T), add the change in temperature (ΔT) to the normal body temperature of 37°C:
Patient's Temperature = 37°C + ΔT
Let's plug in the values and calculate the patient's temperature:
Step 1:
Temperature Coefficient (α) = -6×10^-2 C
Step 2:
Change in Resistance (ΔR) = -15% * Resistance at 37°C
Step 3:
ΔT = ΔR / (R * α)
Step 4:
Patient's Temperature = 37°C + ΔT
By following these steps and plugging in the appropriate values, you can calculate the patient's temperature based on the given information.