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Two wires each of radius of cross section \( r \) but of different materials are connected together end to end (in series). If the densities of charge carriers in the two wires are in the ration \( 1: 4, \) the drift velocity of electrons in the two wires will be in the ratio:

1. 1: 2
2. 2: 1
3. 4: 1
4. 1: 4

Correct answer: 4: 1

Solution

Since the wires are in series, the same current flows through both. With equal cross-sectional area, drift velocity satisfies \(v_d = \frac{I}{nAe}\), so it is inversely proportional to carrier density. Therefore, if the densities are in the ratio 1:4, the drift velocities are in the ratio 4:1.

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