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

Answer:

8.2 m

Explanation:

We are given that

Potential difference=$V=12 V$

Diameter=$d=0.25 mm$

Radius=$[r=\frac{d}{2}=\frac{0.25}{2}mm=0.125mm=0.125\times 10^{-3} m$

$1 mm=10^{-3} m$

Current= I=4.3 A

Resistivity of copper wire of$\rho=1.68\times 10^{-8}\Omega-m$

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

We know that

$R=\frac{V}{I}$

Using the formula

$R=\frac{12}{4.3}$ohm

$A=\pi r^2=3.14\times (0.125\times 10^{-3})=4.91\times 10^{-8} m^2$

Using $\pi=3.14$

$R=\rho\frac{l}{A}$

$\frac{12}{4.3}=1.68\times 10^{-8}\times \frac{l}{4.91\times 10^{-8}}$

$l=\frac{12\times 4.91\times 10^{-8}}{1.68\times 10^{-8}\times 4.3}$

$l=8.2 m$

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