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

808.25 seconds

Step-by-step explanation:

From the relation,
`Velocity = (Length)/(time)`

If t = time

v = velocity

l = length

`t = (l)/(v) \\`

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

`J = nqv..........................(1)\\J = (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 = (I)/(A) \\v = (I)/(nqA) \\`

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

Put the formula for v into equation (3)

`t = (nqAl)/(I) \\t = (8.49*10^(28)*1.6 *10^(-19)* 2.1 * 10^(-5) * 0.85)/(300)`

t = 808.25 seconds