Problem 31.40 When you step on the brake pedal in your car, charge carriers flow

Question

Problem 31.40

When you step on the brake pedal in your car, charge carriers flow from the battery to the rear brake lights. Suppose the wire connecting the switch at the pedal to the brake lights is made of copper and has a diameter of 1.2 mm .

Part A

If the current through the wire is 2.5 A , how long on average does it take an electron to travel from the switch at the pedal to one of the brake lights? The number density of free electrons in copper is n = 8.4 ×1028 electrons/m3.Suppose that the length of the wire is 3 m.

Explanation / Answer

here,

I= 2.5 A

diameter of the wire , d = 1.2 mm

radius , r = 0.6 *10^-3 m

density of free electron in the copper , n = 8.4 * 10^28 electrons / m^3

length of wire , l = 3 m

drift speed , vd = I/(n*e*A)

vd = 2.5 /(8.4 * 10^28 * 1.6 *10^-19 * pi * 0.6^2 * 10^-6)

vd = 0.0001646 m/s

time taken , t = l/vd

t = 18226 s

t = 5.06 hours

the time taken is 5.06 hr

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