Two conducting wires X and Y of the same diameter but different materials are joined in series across a battery. If the number density of electrons in X is twice that in Y, find the ratio of the drift velocity of electrons in the two wires.

In the series arrangement, the current remains the same – 

\(i_x = i_y\)

For the same diameter, the cross-sectional area will remain the same.

Therefore, \(\begin{array}{l}n_{x} eAv_{x} = n_{y}eAv_{y}\end{array}\)

\(= \begin{array}{l} \frac{v_{x}}{v_{y}} \end{array}\)

\(=\begin{array}{l} \frac{n_{y}}{2n_{y}}\end{array}\)

= 1/2

Therefore, \(\begin{array}{l}v_{x} : v_{y} = 1:2\end{array}\)

Read More: Drift Velocity

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