# Temperature Coefficient of Resistance

## Basic Electricity

• #### Question 1

It is a common phenomenon for the electrical resistance of a substance to change with changes in temperature. Explain how you would experimentally demonstrate this effect.

• #### Question 2

An electronics instructor wants to demonstrate to his students the effect of electrical resistance changing with temperature. To do this, he selects a carbon resistor about 3 centimeters in length and 5 millimeters in diameter, black in color, with a wire at each end, and connects it to an ohmmeter. Whenever he grasps the resistor between his fingers, the ohmmeter instantly responds by showing a greatly reduced resistance.

What is wrong with this experiment?

• #### Question 3

If we were to plug an electric saw into a very long extension cord, and then plug the other end of the cord into a power receptacle, we would notice a decreased level of performance from the saw, as compared with how it performs when directly plugged into the same receptacle (with no extension cord).

Determine if the saw’s performance becomes better or worse as the ambient temperature increases, and explain your answer.

• #### Question 4

The electrical resistance of a conductor at any temperature may be calculated by the following equation:

$$R_T=R_r+R_r\alpha T-R_r\alpha T_r$$

Where,

RT = Resistance of conductor at temperature T

Rr = Resistance of conductor at reference temperature Tr

α = Temperature coefficient of resistance at reference temperature Tr

Simplify this equation by means of factoring.

• #### Question 5

Write an equation solving for the temperature of a conductor (T), given its resistance at that temperature (RT), its resistance at a standard reference temperature (Rr @ Tr), and its temperature coefficient of resistance at that same reference temperature (α @ Tr).

• #### Question 6

Precision wire-wound resistors are often made of a special metal alloy called manganin. What is it about this alloy that makes it preferable for use in precision resistor construction?

• #### Question 7

A length of copper wire (α = 0.004041 at 20o C) has a resistance of 5 ohms at 20 degrees Celsius. Calculate its resistance if the temperature were to increase to 50 degrees Celsius.

Now, take that calculated resistance, and that new temperature of 50o C, and calculate what the resistance of the wire should go to if it cools back down to 20o C. Treat this as a separate problem, working through all the calculations, and don’t just say “5 ohms” because you know the original conditions!

• #### Question 8

Calculate the resistance of each of these specimens, given their resistance at the reference temperature (Rr @ Tr), and their present temperatures (T):

• Specimen 1: Copper ; Rr = 200 Ω @ Tr = 20oC ; T = 45oC ; RT =
• Specimen 2: Copper ; Rr = 10 kΩ @ Tr = 20oC ; T = 5oC ; RT =
• Specimen 3: Aluminum ; Rr = 1,250 Ω @ Tr = 20oC ; T = 100oC ; RT =
• Specimen 4: Iron ; Rr = 35.4 Ω @ Tr = 20oC ; T = −40oC ; RT =
• Specimen 5: Nickel ; Rr = 525 Ω @ Tr = 20oC ; T = 70oC ; RT =
• Specimen 6: Gold ; Rr = 25 kΩ @ Tr = 20oC ; T = 65oC ; RT =
• Specimen 7: Tungsten ; Rr = 2.2 kΩ @ Tr = 20oC ; T = −10oC ; RT =
• Specimen 8: Copper ; Rr = 350 Ω @ Tr = 10oC ; T = 35oC ; RT =
• Specimen 9: Copper ; Rr = 1.5 kΩ @ Tr = −25oC ; T = −5oC ; RT =
• Specimen 10: Silver ; Rr = 3.5 MΩ @ Tr = 45oC ; T = 10oC ; RT =
• #### Question 9

A spool of #10 AWG aluminum wire is 500 feet long. If the ambient temperature is 80o F, what is its end-to-end electrical resistance? Explain all the calculations necessary to solve this problem. 