A constant voltage is applied across a wire of non-uniform area of cross-section. Which of the following quantity is independent of the cross-section?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Drift speed
The drift speed of the free electrons is set by the electric field that drives them and by the relaxation time of the material:
\( \displaystyle v_d = \frac{eE\tau}{m} \)
With a constant voltage V across a wire of length l, the driving field is taken as \( E = V/l \), so
\( \displaystyle v_d = \frac{eV\tau}{ml} \)
This expression contains the voltage, the length and the properties of the material, but not the area of cross-section. The current itself, \( I = neAv_d \), does depend on the area A.