Replacing a wire resistor with another of the same material and length but with three times the diameter will have the effect of changing the resistance by what factor?
A)1/3
B)1/9
C)3
D)9

Question

Quizplus · Accepted Answer

The resistance of a wire is proportional to its length divided by its cross-sectional area. If the length and material remain constant but the diameter is tripled, the cross-sectional area increases by a factor of 9 (since area is proportional to diameter squared). Thus, the resistance will decrease by a factor of 9, which is the reciprocal of 1/9. Therefore, the resistance will change by a factor of 1/9 if the wire diameter is tripled.

Replacing a Wire Resistor with Another of the Same Material