How how does the resistance of a conductor change if it is temperature is increased?
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One of the factors that affects the resistivity of a metallic conductor is the temperature. As the temperature increases, the ions vibrate with greater amplitude. Because of this, the ions and the electrons are more likely to collide and the electron finds it more difficult to move through the conductor. Since there is an impede in the electron flow as the temperature increases, the resistivity of metallic conductor increases. This relationship is shown in the formula of temperature dependence of resistivity which is:
where
is the resistivity at some temperature T (in Celsius degrees),
is the resistivity at some reference temperature T0 (usually taken to be 20°C) and
is a parameter called the temperature coefficient of resistivity.
Moreover, resistivity of a conductor is directly proportional to its resistance as shown in the formula:
Isolating the resistivity of the conductor, it becomes:
Plugging this to the formula of temperature dependence of resistivity, the equation becomes:
And this simplifies to:
Notice that the resistance of the conductor is proportional to the temperature change.
Therefore, as the temperature of the conductor increases, its resistance increases.
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The resistance of a conductor increases with an increase in temperature because the thermal velocity of the free electrons increases as the temperature increases. This results in an increase in the number of collisions between the free electrons.
If we raise the temperature of the metallic conductor, the resistance will increase.
What happens in the case of a conductor is that as the temperature rises, the ions within the metal conductor gain energy and begin to oscillate around their mean positions.
All of these oscillating ions collide with electrons, causing resistance to increase.
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