Question

Two conductors, made of the same material have equal lengths but different cross-sectional areas A₁ and A2 (A₁ > A₂). They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.

Answer 1

Drift velocity is given by

\(\text{v}_{d} = \frac{-eE}{m}τ\)

where,

e \(\rightarrow \) is electronic charge having value 1.6 × 10^–19 C

E \(\rightarrow\) is electric field across the conductor.

Since \(E = \frac{V}{l}\), V is same across both conductor and l is also same for both

\(\tau \rightarrow \) it is mean relaxation time depends upon the temperature and material but both temperature and material are same for both conductor

\(m \rightarrow \) mass of electron which is constant therefore v_d will be same in both the conductors

Hence, v_d is equal for both the conductors.