Question

The starter motor of a car engine draws a current of $150\mathrm{A}$from the battery. The copper wire to the motor is $5.0\mathrm{mm}$in diameter and $1.2\mathrm{m}$long. The starter motor runs for $0.80\mathrm{s}$until the car engine starts.

a. How much charge passes through the starter motor?

b. How far does an electron travel along the wire while the starter motor is on?

Short answer

a. The amount of charge that passes through the starter motor is $120C.$

b. The electron travels along the wire while the starter motor on is 0.45mm

Step-by-step solution

Given Information (Part a)

Current $=150A$

Copper wire diameter$=5.0mm$

Copper wire length$=1.2m$

Time$=0.8s$

Explanation (Part a)

The charge passing through the current is,

$I=\frac{q}{t}\Rightarrow q=It.$

Substitute the values,

$q=150A\times 0.8s$

$q=120\mathrm{C}$

Final Answer (Part a)

Hence, the amount of charge that passes through the starter motor is$120C.$

Given Information (Part b) 

Current$=150\mathrm{A}$

Copper wire diameter$=5.0\mathrm{mm}$

Copper wire length$=1.2\mathrm{m}$

Time$=0.8\mathrm{s}$

Explanation (Part b) 

To find the drift speed relation,

$I=n_e{Aev}_d.$

The drift speed is,

$v_d=\frac{I}{n_{e}Ae}=\frac{4I}{\pi e{n}_e{D}^2}$

The distance traveled will be,

$d=v_{d}t=\frac{4It}{\pi e{n}_e{D}^2}$

Substitute the values,

localid="1649138659827" $d=\left(\frac{4\times 150A\times 0.8s}{\pi \times 1.6\times {10}^{-19}C\times 8.5\times {10}^{28}e\times 0.005m^2}\right)$

localid="1649138674698" $d=4.5\times {10}^{-4}\mathrm{m}$

Final Answer (Part b) 

The electron travels along the wire while the starter motor on is$0.45mm.$