Question

A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will warm her on cold rides. She is using 0.25-mm-diameter copper wire, and she wants a current of 4.3 A in the wire.What length wire must she use?

Answer 1

8.2 m

Step-by-step explanation:

We are given that

Potential difference=
`V=12 V`

Diameter=
`d=0.25 mm`

Radius=
`[r=(d)/(2)=(0.25)/(2)mm=0.125mm=0.125* 10^(-3) m`

`1 mm=10^(-3) m`

Current= I=4.3 A

Resistivity of copper wire of
`\rho=1.68* 10^(-8)\Omega-m`

We have to find the length of wire must she use.

We know that

`R=(V)/(I)`

Using the formula

`R=(12)/(4.3)`ohm

`A=\pi r^2=3.14* (0.125* 10^(-3))=4.91* 10^(-8) m^2`

Using
`\pi=3.14`

`R=\rho(l)/(A)`

`(12)/(4.3)=1.68* 10^(-8)* (l)/(4.91* 10^(-8))`

`l=(12* 4.91* 10^(-8))/(1.68* 10^(-8)* 4.3)`

`l=8.2 m`

Hence, she must use the length of wire =8.2 m