A carbon resistor is to be used as a thermometer. On a winter day when the temperature is 4.0°C, the resistance of the carbon resistor is217.3Ω. What is the temperature on a spring day when the resistance is215.8Ω? (Take the reference temperatureT0to be4.0°C.)

Short Answer

Expert verified

The temperature on a spring day when the resistance is 215.8Ωis17.80°C

Step by step solution

01

Determine the formula to find the resistance

Use the resistance dependence temperature formula

RT=R01+αT-T0RTR0-1=αT-T0RTR0-1/α=T-T0T=RTR0-1α+T0

02

Determine the temperature on a spring day when resistance is 215.8Ω

Use the formula found above

T=RTR0-1α+T0

Substitute the given values

T=21,88Q217.3Ω-1-0.0005°C+4.0°CT=13.80°C+4.0°CT=17.80°C

Here, αis negative because the resistance of the carbon rod decreases as the temperature increases.

Therefore, the temperature on a spring day when the resistance is 215.8Ωis 17.80°C

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