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In this lesson, we will learn how to calculate 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 . 0 6 0 ∘ − 1 C 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 8 2 % of its value at 3 7 ∘ C ?

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 1 0 0 . 0 0 × 1 0 − 8 Ω⋅m.

The temperature coefficient of resistance of nichrome is 0 . 0 0 0 4 0 0 ∘ − 1 C .

What is the rods’s resistance at 2 0 . 0 ∘ C ?

What is the rods’s resistance at 3 7 . 0 ∘ C ?

Q3:

A 12-gauge (2.05 mm diameter) gold wire has a length of 1.00 meter. The resistivity of gold is 2 . 4 4 × 1 0 − 8 Ω⋅m and the resistivity of silver is 1 . 5 9 × 1 0 − 8 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 . 0 0 3 4 ∘ − 1 C . 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 0 . 0 0 3 8 ∘ − 1 C , 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 2 0 . 0 ∘ C and an iron wire has a resistance of 0.525 Ω at the same temperature. The temperature coefficient of resistance of copper is 0 . 0 0 3 9 0 ∘ − 1 C and the temperature coefficient of resistance of iron is 0 . 0 0 6 5 0 ∘ − 1 C . At what temperature do the resistances of the wires equal each other?

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 2 0 ∘ C . Find the length of the filament. Use a value of 5 . 6 0 × 1 0 − 8 Ω⋅m for the resistivity of tungsten at 2 0 . 0 ∘ C .

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 = 1 1 0 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 1 5 ∘ C and 4 0 ∘ C 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 . 0 0 4 0 ∘ − 1 C for the temperature coefficient of resistance of aluminum.

Q8:

Find the change in temperature required to decrease the resistance of a carbon resistor by 2 5 % . Use a value of − 0 . 0 0 0 5 ∘ − 1 C for the temperature coefficient of resistance of carbon.

Q9:

The temperature of a tungsten wire is reduced from 2 5 ∘ C to − 1 5 ∘ C . Find the percent decrease in the wire’s resistance. Use a value of 0 . 0 0 4 5 ∘ − 1 C for the temperature coefficient of resistance of tungsten.

Q10:

An electronic device designed to operate at any temperature in the range − 1 5 . 0 ∘ C to 6 5 . 0 ∘ C 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 . 0 0 0 5 0 ∘ − 1 C 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 . 0 0 % from its value at a temperature of 2 5 . 0 ∘ C . Find the highest temperature at which the resistor can be used. Use a value of 0 . 0 0 0 4 ∘ − 1 C for the temperature coefficient of resistance of nichrome.

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