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 0.22-mm-diameter copper wire, and she wants a current of 3.9 A in the wire.
What length wire must she use?

Answer 1

Answer:

Length of the wire, l = 6.78 meters

Explanation:

It is given that,

Voltage of the motorcycle, V = 12 V

Diameter of the copper wire, d = 0.22 mm

Radius, r = 0.11 mm = 0.00011 m

Current in the wire, I = 3.9 A

Resistivity of the copper wire, $\rho=1.72\times 10^{-8}\ \Omega -m$

The resistance of wire is calculated using Ohm's law as :

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

$R=\dfrac{12\ V}{3.9\ A}$

R = 3.07 ohms

Resistance of wire in terms of length is given by :

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

$l=\dfrac{RA}{\rho}$

$l=\dfrac{3.07\times \pi \times (0.00011)^2}{1.72\times 10^{-8}}$

l = 6.78 meters

So, the length of the wire is 6.78 meters. Hence, this is the required solution.

Answer 2

Length of wire she must use is mathematically given as

l=6.78m

Length of wire

Question Parameters:

Generally the equation for the Ohms law  is mathematically given as

V=IR

Therefore

R=V/I

R=12/3.9

r=3.07ohms

Resistance

R=dl/A

l=RA/d

$l=3.07*\pi*(0.00011)^2/1/.72*10^-8$

l=6.78m

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