Question

Problem 3 Copper has 8.5-1028 free electrons per cubic meter. A 71.0 cm length of 12-gauge copper wire that is 2.05 mm in diameter carries 4.85 A of current. (a) How much time does it take for an electron to travel the length of the wire? (b) Repeat part (a) for 6-gauge copper wire (diameter 4.12 mm) of the same length that carries the same current. (c) More generally, how does changing the diameter of the wire that carries a given amount of current affect the drift velocity of the electrons in the wire?

Answer 1

Given: cu has 8.581028 free electrons Im? 2. na 8.5x1028 /m3 Length of an wire a #cm a Illet) Diameter of the wire a 2.05 min = d (led) current in cu wire a 4.85A = Illet) we know that, J a neve. - 0 Ta current density - 7 . Az Area (cross sectional) 32 vd Drift velocity, of an etectron. A J: A. TO 377 (2.0541037mm A. 9 3.3x105 mm 3? Jo hop 32 - 4.85 - 147x100 Alm. 3-3x10-6 from our mis 1.47x06 8.5X1028 x 1.6x1019 - 1.08 X169 mis

w Time taken for an e to travel the length of to wire is to L. 71cm_ - 31x102 1.0 8x10 4 mic 1.08x10 " t: 65.94x10s. thy k t da (b) da 4.22 mm = 4, 12x15² m. As 1654 : 7(4. !2 410-37" = 13.33 X10 m , T . 4.850 I 13,33x10 J = 3.64810 Da Almy 3.64 x 10 vis 3.64x tor Vd. he 8.5810787 1.641619 V . 2.67 X 10 m/s 718.10.2 t 21 cm 2.67810 m/s . 2.67X105 F = 26.59x1095)
c)

As the diameter of wire is increasing, drift velocity is decreasing. In fact, Vd is inversely propotional to square of the diameter of the wire.