Question

On increasing the temperature of a conductor, for free electrons ______ increases.

• A. drift velocity
• B. mobility
• C. relaxation time
• D. thermal speed

Hint:

Higher temperature $\rightarrow$ More "chaos" (Thermal Speed) $\rightarrow$ More collisions $\rightarrow$ Lower Relaxation Time $\rightarrow$ Higher Resistance.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Temperature is a measure of the average kinetic energy of particles. As temperature increases, electrons move faster randomly.
Step 2: Formula Application:
Root Mean Square (RMS) thermal speed $v_{rms} = \sqrt{\frac{3k_BT}{m}}$.
Step 3: Explanation:
1. Thermal speed increases with $\sqrt{T}$. 2. Relaxation time ($\tau$) decreases because more frequent collisions occur. 3. Mobility ($\mu = \frac{e\tau}{m}$) decreases because $\tau$ decreases. 4. Drift velocity ($v_d = \mu E$) decreases for a constant electric field.
Step 4: Final Answer:
Only thermal speed increases.