How long does it take electrons to get from a car battery to the starting motor? Assume the current is 280 A and the electrons travel through a copper wire with cross-sectional area 0.44 cm2 and length 0.85 m. The number of charge carriers per unit volume is 8.49 ✕ 1028 m-3.

Answer:1.86*10^ (-22) seconds

Explanation:

The copper wire has a cross sectional area (CSA) of 0.44cm² and a length of 0.85m ... we first need to convert the (CSA) to m². To do this 0.44cm² is divided by 10000 (since 100cm make 1m) ... 0.44/10000=0.000044m² ...

Volume=CSA * length

Volume=0.000044m²*0.85m

Volume (m³) = 0.0000374m³

Therefore, the total charge carriers is the product of the volume and the charge per unit volume

Total charge carriers = 0.0000374m³ * 8.48*1028m^ (-3)

Total charge carriers = 0.3260charge carriers

Recall however, that the charge per unit charge carrier is 1.60*10^ (-19)

Therefore, the total charge on the copper wire is=

1.60*10^ (-19) coulombs*0.3260

Total quantity of charge=5.216*10^ (-20) coulumbs

And Quantity of charge (Q) = current (I) * time (t)

Time={5.216*10^ (-20) }C/280A

Time=1.86*10^ (-22) seconds

Given:

Current, i = 280 A

Cross-sectional area, A = 0.44 cm^2

Converting from cm^2 to m^2,

0.44 cm^2 * (1 m) ^2 / (100 cm) ^2

= 0.44 * 10^-4 m^2

Length, L = 0.85 m

Number of charge carriers per unit volume, nv = 8.49 ✕ 10^28 m^-3

Current density, J = nv * q * v

I/A = nv * q * v

I = nv * A * q * (L/t)

t = (nv * A * q * L) / I

= (8.49 ✕ 10^28 * 0.44 * 10^-4 * 1.602 * 10^-19 * 0.85) / 280

= 1816.7 s

Since 60 seconds = 1 minute

= 30.28 minutes