It is necessary to double the length of a wire, but the resistance of the wire...

It is necessary to double the length of a wire, but the resistance of the wire needs to remain APPROXIMATELY the same. If the wire is initially 22 gauge, what gauge of wire should be used to accomplish this?

Solutions

Expert Solution

Resistance, R = ( * L) / A ...(1)
Where is the resistivity of the wire, L is the length of the wire and A is the area of the wire.

L becomes 2L but resistance remains the same
R = ( * 2L) / Anew ...(2)
Where Anew is the new area of the wire

(1) / (2) gives
1 = Anew / (2 * A)
2 = Anew / A
2 = Rnew2 / R2
Where Rnew and R are the radius of the new and old wire respectively.
2 = (Rnew/R)2
Taking square root on both the sides,
= Rnew/R
Rnew = 1.414 * R
Dnew = 1.414 * D
Where Dnew is the diameter of the new wire and D is the diameter of the old wire

According to American wire gauge system, 22 gauge corresponding to a diameter of 0.644 mm
Diameter of new wire, Dnew = 0.644 * 1.414
= 0.911 mm
This corresponds to 19 gauge wire

genius_generous answered 1 year ago

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