Question

Consider two conducting wires A and B of the same diameter but made of different materials joined in series across a battery. The number density of electrons in A is 1.5 times that in B. Find the ratio of drift velocity of electrons in wire A to that in wire B.

Answer 1

Since wires are connected in series, therefore some current will flow in the two wires.

we know that,

\(I = neAv_d \)

\(\therefore \ I_A = I_B \Rightarrow n_AeA_A \times \left(\vec v_d\right)_A = n_BeA_B \times \left(\vec v_d\right)_B\) 

Given \(n_A = 1.5 n_B, \ A_A = A_B\)

\(\therefore \ 1.5n_B \times \left(\vec v_d\right)_A = n_B \times \left(\vec v_d\right)_B\)  

\(\frac{\left(\vec v_d\right)_A}{\left(\vec v_d\right)_B} = \frac{1}{1.5} = \frac{2}{3}\)