Question

(A) The drift velocity of electrons decreases with the increase in the temperature of conductor.
(B) The drift velocity is inversely proportional to the area of cross-section of given conductor.
(C) The drift velocity does not depend on the applied potential difference to the conductor.
(D) The drift velocity of electron is inversely proportional to the length of the conductor.
(E) The drift velocity increases with the increase in the temperature of conductor.

Choose the correct answer from the options given below

• (A) and (B) only
• (A) and (D) only
• (B) and (E) only
• (B) and (C) only

Answer 1

The Correct Option is A

Let's analyze each statement to determine which ones are correct regarding the drift velocity of electrons in a conductor.

1. Statement (A): The drift velocity of electrons decreases with the increase in the temperature of the conductor.
   • Drift velocity (\(v_d\)) is defined as the average velocity attained by charged particles, such as electrons, due to an electric field.
   • It is given by the formula: \(v_d = \frac{eE}{m}\tau\), where \(e\) is the charge of an electron, \(E\) is the electric field, \(m\) is the mass of an electron, and \(\tau\) is the mean time between collisions.
   • As temperature increases, the lattice vibrations increase, leading to a decrease in \(\tau\). Thus, drift velocity decreases.
   • This statement is correct.
2. Statement (B): The drift velocity is inversely proportional to the area of cross-section of the given conductor.
   • Drift velocity can be expressed using the equation: \(I = nAev_d\), where \(I\) is the current, \(n\) is the number density of electrons, \(A\) is the cross-sectional area, and \(e\) is the electron charge.
   • From this, \(v_d = \frac{I}{nAe}\), showing that drift velocity is indeed inversely proportional to the cross-sectional area \(A\).
   • This statement is correct.
3. Statement (C): The drift velocity does not depend on the applied potential difference to the conductor.
   • The drift velocity is influenced by the electric field \(E\), which is related to the potential difference across the conductor. Hence, it does depend on the applied potential difference.
   • This statement is incorrect.
4. Statement (D): The drift velocity of electron is inversely proportional to the length of the conductor.
   • Drift velocity does not directly depend on the length of the conductor but rather on the electric field and other properties like potential difference.
   • This statement is incorrect.
5. Statement (E): The drift velocity increases with the increase in the temperature of the conductor.
   • As discussed in statement A, the drift velocity decreases due to increased lattice vibrations at higher temperatures.
   • This statement is incorrect.

Therefore, the correct answer is: (A) and (B) only.