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 0.060C 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 82% of its value at 37C?

Q2:

A nichrome rod that is 3.00 mm long with a cross-sectional area of 1.00 mm2 is used for a digital thermometer.

The resistivity of nichrome is 100.00×10 Ω⋅m.

The temperature coefficient of resistance of nichrome is 0.000400C.

What is the rods’s resistance at 20.0C?

  • A 2 . 0 0 × 1 0 Ω
  • B 3 . 0 0 × 1 0 Ω
  • C 2 . 5 0 × 1 0 Ω
  • D 1 . 5 0 × 1 0 Ω
  • E 3 . 5 0 × 1 0 Ω

What is the rods’s resistance at 37.0C?

  • A 3 . 5 3 × 1 0 Ω
  • B 2 . 0 2 × 1 0 Ω
  • C 1 . 5 6 × 1 0 Ω
  • D 2 . 5 5 × 1 0 Ω
  • E 3 . 0 2 × 1 0 Ω

Q3:

A 12-gauge (2.05 mm diameter) gold wire has a length of 1.00 meter. The resistivity of gold is 2.44×10 Ω⋅m and the resistivity of silver is 1.59×10 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 0.0034C. What is the resistance of a 1.00 m length of 12-gauge gold wire at the temperature of boiling water? Assume the wire was at room temperature 25C.

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 0.0038C, what is the resistance of this silver wire at the temperature of boiling water? Assume the wire was at room temperature 25C.

Q4:

A copper wire has a resistance of 0.500 Ω at 20.0C and an iron wire has a resistance of 0.525 Ω at the same temperature. The temperature coefficient of resistance of copper is 0.00390C and the temperature coefficient of resistance of iron is 0.00650C. At what temperature do the resistances of the wires equal each other?

  • A 2 . 7 7 C
  • B 3 . 6 1 C
  • C 3 . 1 5 C
  • D 3 . 3 9 C
  • E 2 . 9 1 C

Q5:

The tungsten filament of light bulb has a 0.100 mm diameter. The filament has a resistance of 0.20 Ω at a temperature of 20C. Find the length of the filament. Use a value of 5.60×10 Ω⋅m for the resistivity of tungsten at 20.0C.

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=110 V. How long should the engineer make the wire if the resistivity of nichrome is 1.5 µΩ⋅m?

Q7:

The air temperature in a town varied between 15C and 40C on a certain summer day. Find the percentage change in the resistance of an exposed aluminum wire in the town during such a day. Use a value of 0.0040C for the temperature coefficient of resistance of aluminum.

Q8:

Find the change in temperature required to decrease the resistance of a carbon resistor by 25%. Use a value of 0.0005C for the temperature coefficient of resistance of carbon.

Q9:

The temperature of a tungsten wire is reduced from 25C to 15C. Find the percent decrease in the wire’s resistance. Use a value of 0.0045C for the temperature coefficient of resistance of tungsten.

  • A 2 0 %
  • B 3 8 %
  • C 6 . 0 %
  • D 1 5 %
  • E 1 8 %

Q10:

An electronic device designed to operate at any temperature in the range 15.0C to 65.0C 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 0.00050C for the temperature coefficient of resistance of pure carbon.

Q11:

A resistor made of nichrome wire is used in an application where the resistor’s resistance must not change more than 5.00% from its value at a temperature of 25.0C. Find the highest temperature at which the resistor can be used. Use a value of 0.0004C for the temperature coefficient of resistance of nichrome.

Q12:

A copper wire at a temperature of 20.0C has a resistance 𝑅. At what temperature will the wire have a resistance 𝑅, where 𝑅=2𝑅, assuming that any changes in the wire’s dimensions due to thermal expansion are negligible? Use a value of 0.00390C for the temperature coefficient of resistance of copper.

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