Question

If the relaxation time is doubled and the applied electric field is tripled, then the drift speed of electrons:

• A. becomes three times of its initial value
• B. decreases by six times of its initial value
• C. becomes 1.5 times of its initial value
• D. decreases by six times of its initial value

Hint:

Drift velocity is proportional to the relaxation time and electric field. Changes in these factors can significantly impact the drift velocity of electrons.

Answer 1

The Correct Option is B

Step 1: The drift velocity \( v_d \) of electrons is related to the electric field \( E \) and the relaxation time \( \tau \) by the equation: \[ v_d = \mu E \] where \( \mu \) is the mobility of electrons. 

Step 2: The drift velocity is proportional to the product of the relaxation time and the applied electric field. Doubling the relaxation time and tripling the electric field results in: \[ v_d' = \frac{2\tau \times 3E}{\tau E} = 6 \times v_d \] 

Step 3: Thus, the drift velocity decreases by a factor of 6.