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Effect of Temperature on Drift Velocity
In this article, we will discuss the effects of temperature on drift velocity in conductors.
Introduction to Drift Velocity
Drift velocity ($v_d$) is the average velocity attained by free charge carriers, like electrons, in a conductor due to an applied electric field.
The equation for drift velocity is:
$$v_d = \frac{I}{nAe}$$
where:
- $I$ is current,
- $n$ is the number of free charge carriers per unit volume,
- $A$ is the cross-sectional area, and
- $e$ is the charge of an electron.
Effect of Temperature on Atomic Vibrations
As temperature rises, atoms in the conductor vibrate more vigorously. This is because the temperature is directly proportional to the kinetic energy of the atoms, causing increased atomic vibrations with higher temperatures.
Impact of Increased Atomic Vibrations on Electron Movement
The increased atomic vibrations due to higher temperature lead to more frequent collisions between free electrons and atoms. Each collision disrupts the motion of the electron, causing it to scatter and lose some of its energy.
Effect on Drift Velocity
The more frequent scattering events mean that, on average, an electron will not get as far in a given time, reducing its drift velocity. Therefore, the drift velocity decreases with an increase in temperature.
This can be reasoned from the drift velocity formula as well. The current $I$ decreases due to increased resistance with temperature (from Ohm’s law, $V = IR$), and since $v_d$ is directly proportional to $I$, the drift velocity decreases.
What happens when the temperature is decreased?
The atoms in the conductor vibrate less as the temperature decreases. This means there are fewer collisions between the atoms and the free electrons moving through the conductor. With fewer collisions, the electrons maintain their direction and speed for a longer average time.
This increases the electron’s mobility (its ability to move through the conductor), and consequently, the drift velocity increases. This is because the electrons, on average, can move further in a given time with fewer collisions to impede their progress.
So, in simple terms, when the temperature of a conductor decreases, the drift velocity of the electrons in the conductor increases due to a decrease in the frequency of collisions with the now less vigorously vibrating atoms.
Conclusion
Thus, in a conductor, the rise in temperature leads to increased atomic vibrations, causing more frequent collisions between atoms and free electrons. This results in a decrease in the average drift velocity of the electrons in the conductor. This effect is important in understanding the electrical properties of materials and has implications for the design and operation of many electronic devices.