# Worksheet: Effect of Temperature on Resistivity

In this worksheet, we will practice calculating the change in the resistivity of a material given its temperature coefficient of resistance.

**Q1: **

A digital medical thermometer contains a thermistor that has a temperature coefficient of resistance of when it is at the same temperature as a patient. What is a patient’s temperature if the thermistor’s resistance at that temperature is of its value at ?

**Q2: **

A nichrome rod that is 3.00 mm long with a
cross-sectional area of 1.00 mm^{2} is used for a digital thermometer.

The resistivity of nichrome is Ω⋅m.

The temperature coefficient of resistance of nichrome is .

What is the rods’s resistance at ?

- A Ω
- B Ω
- C Ω
- D Ω
- E Ω

What is the rods’s resistance at ?

- A Ω
- B Ω
- C Ω
- D Ω
- E Ω

**Q3: **

A 12-gauge (2.05 mm diameter) gold wire has a length of 1.00 meter. The resistivity of gold is Ω⋅m and the resistivity of silver is Ω⋅m.

What would be the length of a silver 12-gauge wire with the same resistance as a 1.00 m long 12-gauge gold wire?

The temperature coefficient of resistance of gold is . What is the resistance of a 1.00 m length of 12-gauge gold wire at the temperature of boiling water?

Consider a silver 12-gauge wire that has the same resistance as a 1.00 m length of 12-gauge gold wire. If the temperature coefficient of resistance of silver is , what is the resistance of this silver wire at the temperature of boiling water?

**Q4: **

A copper wire has a resistance of 0.500 Ω at and an iron wire has a resistance of 0.525 Ω at the same temperature. The temperature coefficient of resistance of copper is and the temperature coefficient of resistance of iron is . At what temperature do the resistances of the wires equal each other?

- A
- B
- C
- D
- E

**Q6: **

A heater is being designed that uses a coil of 14-gauge (1.63 mm diameter) nichrome wire to dissipate 300 W using a voltage of V. How long should the engineer make the wire if the resistivity of nichrome is 1.5 µΩ⋅m?

**Q10: **

An electronic device designed to operate at any temperature in the range to contains resistors made of pure carbon. Determine the factor by which the resistance of the resistors increases from the bottom to the top of the device’s operating temperature range. Use a value of for the temperature coefficient of resistance of pure carbon.