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 0.250 cm2 and length 0.900 m. The number of charge carriers per unit volume is 8.49 × 1028 m-3.

Answer 1

Answer:

16.98 minutes

Explanation:

We are given that

Current,I=300 A

Area, A=0.250 square cm=$0.250\times 10^{-4} m^2$

$1 cm^2=10^{-4} m^2$

Length of wire,d=0.9 m

Number of charge carriers per unit volume=$n=8.49\times 10^{28} m^{-3}$

$1 e=1.6\times 10^{-19} C$

We know that

$t=\frac{ne Ad}{I}$

Using the formula

$t=\frac{8.49\times 10^{28}\times 1.6\times 10^{-19}\times 0.25\times 10^{-4}\times 0.9}{300}$

$t=1018.8 s=\frac{1018.8}{60}=16.98 minute$

Answer 2

Answer:

Explanation:

current, i = 300 A

Area of crossection, A = 0.250 cm² = 0.250 x 10^-4 m²

length, l = 0.9 m

number of electrons per unit volume, n = 8.49 x 10^28 /m³

let v be the drift velocity and t be the time taken by the electrons

i = n e A v

300 = 8.49 x 10^28 x 1.6 x 10^-19 x 0.25 x 10^-4 x v

v = 8.84 x 10^-4 m/s

Time, t = distance / velocity

t = 0.9 / (8.84 x 10^-4)

t = 1018.8 s

t = 17 minutes