Question

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 1.3 mm .

Part A

If the current through the wire is 2.0 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 isn = 8.4 ×1028 electrons/m3. Suppose that the length of the wire is 3 m.

Answer 1

Given that,

diameter of the wire = d = 1.3mm, so radius = 1.3/2 = 0.65mm = 0.00065 m

Current = I = 2 A ; length = L = 3 m ; free electron density = n = 8.4 x 10²⁸ electrons / m³

Area = A = pi r2 = 3.14 x (0.00065)² = 1.33 x 10^-6 m²

We need to find the time that the electron take in reaching from switch to brake lights. Let it be"t".

we know that, the drift velocity is given by:

Vd = I / n A e

Vd = 2 /   8.4 x 10²⁸ x 1.33 x 10^-6 m² x 1.6 x 10^-19 = 0.0011 m/s

We know that, speed = distance/time = > time = distance/speed

t = L / Vd = 3/0.0011 = 2727.3 sec.

Hence, time = t = 2727.3 sec