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Welcome to our Physics lesson on Appendix: Dependence of Resistance from Temperature of Material, this is the fifth lesson of our suite of physics lessons covering the topic of Electric Resistance. Combinations of Resistors, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
As we explained earlier, resistance of a conductor depends on temperature but this quantity does not appear in the formula of the resistance of a conductor as temperature was assumed as constant. However, we explained that electricity flow is accompanied by a heating effect in the conductor because electrons collide with the atoms of conductor during their flow and as a result, they make these atoms vibrate faster around their equilibrium positions. This brings an increase in the internal energy of atoms, which is nothing else but the average kinetic energy of all particles of a material.
All values of resistance we discussed earlier, are taken at "normal" temperature, i.e. at T = 20°C. This temperature is known as the "reference temperature", Tref and the corresponding resistance of a certain conductor at this temperature is known as the "conductor resistance at reference temperature", Rref. The equation for the resistance R of a conductor at a certain temperature T therefore is
where α is the temperature coefficient of resistance for a given conducting material. It is an intrinsic property of the material itself and is given in tables. (Do not confuse this quantity with the coefficient of linear expansion α we have discussed in the tutorial 13.2 "Thermal Expansion"; they are different concepts). The unit of temperature coefficient of resistance is [K-1] or [1/K].
What is the resistance of a 12 m copper wire at 50°C if its thickness is 4mm2? Take the resistivity of copper as 1.69 × 10-8 Ω ∙ m and the temperature coefficient of resistance for copper as 0.00393 K-1.
Clues:
L = 12 m
T = 50°C
A = 4 mm2 = 4 × 10-6 m2
ρ = 1.69 × 10-8 Ω ∙ m
α = 0.00393 K-1 = 3.93 × 10-3 K-1
Tref = 20°C
R = ?
First, we must find the reference temperature for this copper wire. It is calculated using the formula for the resistance of conductor. We have
Now, we calculate the resistance of the wire at the given temperature. We have:
As you see, the temperature of the copper wire at 50°C is slightly higher than the temperature of the same wire at 20°C.
You have reached the end of Physics lesson 15.2.5 Appendix: Dependence of Resistance from Temperature of Material. There are 5 lessons in this physics tutorial covering Electric Resistance. Combinations of Resistors, you can access all the lessons from this tutorial below.
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