Question

The starter motor of a car engine draws a current of 180A from the battery. The copper wire to the motor is 5.40mm in diameter and 1.2 m long. The starter motor runs for 0.960s until the car engine starts. How much charge passes through the starter motor? How far does an electron travel along the wire while the starter motor is on?

Answer 1

The first part is easy, while the second part istedious.

PART A>>>>     Q = I t   = (150 Coul/sec) ( 0.8sec) = 120 Coulombs.   final answer.

PART B>>>   We first need to calculate thedrift velocity of electrons in a Cu wire.

You will need to look and use the density of Cu = 8.95 g /cm³ and the atomic mass

of Cu = 63.5 g/ mole.

The volume of 1 mole of Cu is   63.5g/mole   / 8.95 g/cm³  =    7.09 cm³ / mole.

Assuming that there is 1 free electron in each Cu atom,

the density of electrons in Cu is    n= (6.02E23 electrons) / 7.09 cm³  = 8.48E22 e/cm³

converting this electron density to units ofelectrons/m³ , we get   8.48E28.

Now, the drift velocity v = I / ( n q A) ,where we know I, n, and q , but need to find the crosssectional area A of the given wire.

A = ? (0.005 m)² / 4 = 1.96E-5 m²

Thus,   drift v =   (150) / [(8.48E28) (1.60E-19) (1.96E-5)] = 5.64E-4 m/s

PLEASE CHECK AND VERIFY ALL OF MY CALCULATOR WORK

Distance traveled by electrons = v t   =   (5.64E-4 m/s) (0.8 sec)  = 4.51E-4 m or 0.45 mm.