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 4.0 a in the wire. what length wire must she use?

Answer 1

The length of copper wire this motorcyclist must use is equal to 8.56 meters.

Given the following data:

• Voltage of the motorcycle, V = 12 V

• Diameter of the copper wire, d = 0.25 mm

• Current in the wire, I = 4.0 A

Radius, r = diameter/2 = 0.12.5 mm = 0.000125 m.

Resistivity of the copper wire, ρ = 1.72 × 10⁻⁸ Ω-m.

How to determine the resistance?

By applying Ohm's law, the resistance of this copper wire can be calculated  by using this formula:

R = V/I

R = 12/4

Resistance, R = 3 Ohms.

Mathematically, the resistance of any conductor (wire) in terms of length is given by this formula:

Length = RA/ρ

Length = Rπr²/ρ

Length = [3 × 3.142 × (0.000125)²]/1.72 × 10⁻⁸

Length = 14.73 × 10⁻⁷/1.72 × 10⁻⁸

Length = 8.56 meters.

Read more on resistance and length here: brainly.com/question/13930397

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