Question

The starter motor of a car engine draws a current of 110 A from the battery. The copper wire to the motor is 4.90 mm in diameter and 1.2 m long. The starter motor runs for 0.800 s until the car engine starts.A)How much charge passes through the starter motor? (C)

B)How far does an electron travel along the wire while the starter motor is on?(mm)

Answer 1

Step-by-step explanation:

A.

Q = I*t

Where,

Q = charge

I = current

= 110 A

t = time

= 0.8 s

= 110 * 0.8

= 88 C

B.

The radius of the conductor, r = 4.9/2

= 2.45 mm.

The area of the conductor is:

A = π*r^2

= π*(.00245)^2

= 1.89 x 10^-5 m^2

Charge on an electron, qe = 1.602 × 10⁻¹⁹ C

Density of Copper = 8.80 × 10³ kg/m³

Molar mass of copper is 63.55 g/mol = 0.06355 kg/mol

Avogadro's constant = 6.02 × 10²³ electrons/mol

Number of moles, n = (Density/molar mass) × avogadro's constant

= (8800/0.06355) × 6.02 × 10²³

= 8.342 × 10²⁸ electrons/m³

I = nqAVd

Vd = I/nqA

Vd= 110/[(8.342 × 10²⁸)(1.602 × 10⁻¹⁹)(1.89 × 10⁻⁵)]

= 4.37 x 10^-4 m/s

= 0.437 mm/s

The distance traveled is:

x = v * t

= 0.437 * 0.80

= 0.35 mm.

Answer 2

a) Amount of charge that passes through the starter motor = 88 C

b) Distance travelled by the electrons along the wire while the starter motor is on = 0.174 mm

Step-by-step explanation:

Amount of charge carried that passes through the starter motor, Q = It

I = 110 A

t = 0.8 s

Q = 110 × 0.8 = 88 C

b) now to calculate this velocity, (drift velocity)

I = nqAv

v = I/nqA

v = drift velocity = ?

I = current = 110 A

A = Cross section Area of the wire = πd²/4 =

π(0.0049²)/4 = 3.77 × 10⁻⁵ m²

q = charge on an electron = 1.602 × 10⁻¹⁹ C

n = number of electrons per m³ for Copper

To calculate this,

Density of Copper = 8.80 × 10³ kg/m³, atomic mass of copper is 63.54 g/mol = 0.06354 kg/mol. We can use these two quantities along with Avogadro’s number, 6.02 × 10²³ electrons/mol, to determine n, the number of free electrons per cubic meter.

n = (Density/atomic mass) × avogadro's constant = (8800/0.06354) × 6.02 × 10²³ = 8.342 × 10²⁸ electrons/m³

v = 110/[(8.342 × 10²⁸)(1.602 × 10⁻¹⁹)(3.77 × 10⁻⁵)] = 0.000218 m/s = 0.218 mm/s

Since the starter is on for 0.8 s,

Distance travelled by the electrons in that time = 0.218 × 0.8 = 0.174 mm