For any material of resistivity p, the resistance of a circuit element made of that material is given by the equation: R = pL A Where A is the cross-sectional area of the circuit element and L is its length. Thus, altering a wire's length or area would change it's resistance, and—since conductivity is simply the reciprocal of resistivity—so would altering its conductivity. Ductility, on the other hand, is a measure of a material's ability to be stretched without breaking. Since ductility is not related to electrical resistance, (C) is correct.
Expert Approach:
Since I'm being asked what would NOT affect resistance, there's no way to know in advance precisely what the correct choice will look like, but I can orient myself by thinking about the factors that DO affect resistance, such as a material's inherent resistivity, as well as the length and cross-sectional area of the resistor—all described by the equation R = pL / A. Any answer choice that modifies one of these variables will be incorrect. This allows me to quickly eliminate choices (A) and (B). I don't know what ductility (the ability of a metal to be drawn into wires or filaments) has to do with resistance, so I'm pretty sure (C) is the answer, but just to confirm, I check out (D), and then I'm be absolutely certain, since conductivity is simply the reciprocal of resistivity.If I didn't remember the actual equation for resistivity, I could still get to the right answer here by thinking qualitatively. I know that resistance is a measure of how much a circuit element interferes with the flow of electrons. And certainly a longer wire (A), forcing the electrons to travel further, should impede flow more than a shorter one, while a thicker wire (B), providing more pathways along which electrons can travel, should impede flow less than a thinner one. Likewise, the very word "conductivity" (D) is self-evidently related to "resistance." On the other hand, ductility (C) describes how easily a material can be stretched, and there's no reason to think that more stretchable materials are either more or less able to conduct electricity. Even if I had never seen the word "ductility" before, I would choose (C), since the other three options all do sensibly relate to resistance.
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