Question

When the starter motor on a car is engaged, there is a 310 A current in the wires between the battery and the motor. Suppose the wires are made of copper and have a total length of 1.0 m.

What minimum diameter can the wires have if the voltage drop along the wires is to be less than 0.55 V? (answer in mm)

Answer 1

Diameter will be 351.42 mm

Step-by-step explanation:

We have given current flowing in the copper wire i = 310 A

Voltage drop across the wire V = 0.55 volt

We know that resistance is given by
`R=(V)/(i)=(0.55)/(310)=0.00177\Omega`

Length of the copper wire l = 1 m

Resisitivity of the copper wire
`\rho =1.72* 10^(-8)\Omega m`

We know that resistance
`R=(\rho l)/(A)`

`0.00177=(1.72* 10^(-8)*  1)/(A)`

`A=969.4545* 10^(-8)m^2`

As area
`A=\pi r^2`

`3.14* r^2=969.4545* 10^(-8)`

`r=17.57* 10^(-4)m`

So diameter
`d=17.57* 10^(-4)* 2=35.142* * 10^(-4)m` = 351.42 mm