Question

How long does it take electrons to get from a car battery to the starting motor? Assume the current is 300 A and the electrons travel through a copper wire with cross-sectional area 0.21 cm2 and length 0.85 m.The number of charge carriers per unit volume is 8.49 $ 1028 m#

Answer 1

Answer:

808.25 seconds

Explanation:

From the relation, $Velocity = \frac{Length}{time}$

If t = time

v = velocity

l = length

$t = \frac{l}{v}$

The current density, J, of a charge is given by:

$J = nqv..........................(1)\\J = \frac{I}{A} ................(2)$

Where number of charge carriers per unit volume n = 8.49 * 10²⁸

Charge of the electron, q = 1.6 * 10⁻¹⁹

Cross sectional area of the wire, A = 0.21 cm² = 0.000021 m²

Equating (1) and (2)

$nqv = \frac{I}{A} \\v = \frac{I}{nqA}$

Since t = l/v.......(3)

Put the formula for v into equation (3)

$t = \frac{nqAl}{I} \\t = \frac{8.49*10^{28}*1.6 *10^{-19}* 2.1 * 10^{-5} * 0.85}{300}$

t = 808.25 seconds