
Thomas H. answered 02/14/20
Mathematics Tutor
For question 1, you start with the formula for resistance, R=ρ(L/A) where ρ is the resistivity of the material with which the wire is composed, L is the length of the wire and A is the cross-sectional area of the wire. Increasing the thickness of the wire, by definition, increases the cross-sectional area, A. Barring anything else happening, the resistivity and length will remain the same; since A is in the denominator of the expression, as it getting bigger, the resistance, R will get smaller.
As for question 2, I'm not sure what the text has in mind for the correct answer; electromotive force, despite the presence of force in the name, actually refers to a potential difference. Two examples where the concept of electromotive force are a) the potential difference between the positive and negative terminals of a battery and b) the potential difference induced by a change in magnetic flux as described by Faraday's Law.
Going back to the question itself, if for instance you attached the wire to the two ends of the battery, there will be strictly speaking a potential difference (or a voltage) between the two ends of the wire and current (which can be measured by among other units, Amperes) will flow through the wire. From that point of view d) (all of the above) sounds like the correct answer, but again I'm not sure what the text is getting at there..
Thomas H.
Arturo, I apologize for my belated thanks, but thank you for clarifying it for me. All the Best! Tom03/16/20