Question

The starter motor of a car engine draws a current of 170 A from the battery. The copper wire to the motor is 4.60 mm in diameter and 1.2 m long. The starter motor runs for 0.930 s until the car engine starts How much charge passes through the starter motor?

Answer 1

The charge that passes through the starter motor is
`\Delta Q=158.1 C`.

Step-by-step explanation:

Known Data

• Avogadro's Number
  `N_(A)=6.02x10^(23)`
• Current,
  `I=170A=170(C)/(s)`
• Charge in an electron,
  `q=1.60x10^(-19)C`
• Time,
  `\Delta t=0.930s`
• Diameter,
  `d=4.60mm=0.0046m`
• Transversal Area,
  `A=((d)/(2))^(2) \pi=((0.0046m)/(2))^(2) \pi=1.66x10^(-5) m^(2)`
• Volume,
  `V=Length*A=(1.2m)(1.66x10^(-5) m^(2))=1.99x10^(-5) m^(3)`

First Step: Find the number of the electrons per unit of volume in the wire

We use the formula
`n=(N_(A))/(V)= (6.02x10^(23) electrons)/(1.99x10^(-5) m^(3)) =3.02x10^(28)el/ m^(3)`.

Second Step: Find the drag velocity

We can use the following formula
`v_(d)=(I)/(nqA)=(170C/s)/((3.02x10^(28)m^(-3))(1.60x10^(-19)C)(1.66x10^(-5) m^(2)))  =2.11x10^(-3) m/s`

Finally, we use the formula
`\Delta Q=(nAv_(d)\Delta t)q=(3.02x10^(28) m^(-3))(1.66x10^(-5) m^(2))(2.11x10^(-3) m/s)(0.930s)(1.60x10^(-19)C)=158.1 C`.