How long does it take electrons to get from a car battery to the starting motor?

Question

How long does it take electrons to get from a car battery to the starting motor? Assume the current is 385 A and the electrons travel through a copper wire with cross-sectional area 0.30 cm^2 and length 0.90 m. The number of charge carriers per unit volume of copper is 8.49 times 10^28 m^-3. (a) Find the drift velocity (b) How long would it take an electron to go from the starter to the battery? (c) If it only takes 3 seconds to start the car, how many electrons are used? (how many pass through the starter?)

Explanation / Answer

The concentration of electron/volume, n = 8.5 x 1028 /m3

a) The drift velocity of the electron,  v = I / ne A

v = 385 / (8.5 x 1028 x 1.6 x 10-19 x 0.30 x10-4) = 9.44 x 10-4 m/s

b) The time required, t = L / v = 0.90 / 9.44 x 10-4 = 953.766 s

c) q = n e = I t

=> n = I t / e = (385 x 3) / (1.6 x 10-19) = 7.22 x 1021

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