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A metal wire is subjected to a constant potential difference. When the temperature of the metal wire increases, the drift velocity of the electron in it
A) Increases, thermal velocity of the electron increases
B) Decreases, thermal velocity of the electron increases
C) Increases, thermal velocity of the electron decreases
D) Decreases, thermal velocity of the electron decreases



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Last updated date: 16th Jul 2024
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Answer
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Hint:The question is from Current, Resistance and Electricity part of the physics. Using concepts of drift velocity we can find the correct option. Drift velocity is the average velocity attained by charged particles, (electrons) in a material due to an electric field (\[\overrightarrow E \]). The SI unit of drift velocity is the same as velocity which is m/s.


Complete answer:
Mobility (\[\mu \]) of an electron is the drift velocity of an electron for a unit electric field (\[E\]). The equation for mobility is given below.
\[\mu = \dfrac{{{v_d}}}{E}\]
Equation of mobility (\[\mu \]) of an electron can also be written as,
$\mu = \dfrac{{e\tau }}{m}$
e = charge of an electron
m = mass of charge
$\tau $= relaxation time.
$\dfrac{{e\tau }}{m} = \dfrac{{{v_d}}}{E}$

From the above equation, we can find that the drift velocity is directly proportional to relaxation time.
When the temperature of the metal wire increases, the kinetic energy (KE) of the electron will increase. That causes an increase in the number of electron collisions. The increase in collisions will cause the relaxation time ($\tau $) to decrease. Drift velocity and relaxation time are directly proportional to each other. Hence the drift velocity will decrease.

When the temperature of the metal wire increases, the kinetic energy (KE) of the electron will increase. Hence the thermal velocity of the electron will increase.

So, the correct option is Option (B) Decreases, thermal velocity of the electron increases.






Note: The drift velocity and current flowing through the conductor both increase as the intensity of the electric field increases. Drift velocity is directly proportional to electric field intensity.