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 0.20-mm-diameter copper wire, and she wants a current of 3.9 A in the wire.

Part A

What length wire must she use?

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 0.20-mm-diameter copper wire, and she wants a current of 3.9 A in the wire.

Part A

What length wire must she use?

Explanation / Answer

from ohms law

v = iR

R = v/i = 12/3.9 = 3.08 ohm

from the relation R = rho*l/A

rho = resistivity of copper = 1.72*10^-8 ohm-m

A = 3.14*0.2^2*10^-6/4 = 3.14*10^-8 m^2

length (l) = 3.08*3.14*10^-8/1.72*10^-8 = 5.62 m

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