Physics · Electric current: drift velocity, mobility and their relation with electric current
Two wires each of radius of cross section but of different materials are connect
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:
- A. 1: 2
- B. 2: 1
- C. 4: 1
- D. 1: 4
Step-by-step solution
In a series connection, the current I is the same through both wires. Current I = n e A v_d, where n is charge carrier density, A is cross-sectional area (same for both wires due to equal radius), e is electron charge (constant), and v_d is drift velocity. Thus, n1 v_d1 = n2 v_d2, implying v_d1 / v_d2 = n2 / n1. Given n1 : n2 = 1 : 4, we have n2 / n1 = 4, so the ratio of drift velocities is 4:1.
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