A motorcyclist is making an electric vest that, when connected to the motorcycle

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 0.23-mm-diameter copper wire, and she wants a current of 3.8 A in the wire. You may want to review ( pages 708 - 712) . For help with math skills, you may want to review: Rearrangement of Algebraic Expressions For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Electrical measurements of soil properties.

What length wire must she use?

Explanation / Answer

Use Ohm's Law:

V = I * R
12V = 3.8A * R

You need enough wire to create a total of 3.15 ohms of resistance.

you need the resistance of .23mm diameter copper wire. Wikipedia defines .227mm copper wire at 426.9 ohms per thousand meters.

Simple ratio: 3.15/L = 426.9/1000 Solve for L.
L = 7.378m of wire

Like I said, this needs to reference the tables in your book. Wikipedia's resistance may not perfectly match the copper wire you are working with.

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