Respuesta :
Answer:
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
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
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.
