Question

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

Step-by-step explanation:

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

Answer 2

Answer:1.86×10^(-22)seconds

Step-by-step 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