# Resistance = resistivity * L/A...

Discussion in 'Homework Help' started by dtvonly, Jun 2, 2014.

1. ### dtvonly Thread Starter Member

Dec 14, 2012
43
0
Hi. the equation R=resistivity * (L/A) does make the resistance directly proportional to the length. It also make it inversely proportional to the cross sectional area. this does not make sense to me. Given the same wire and length, the bigger (cross sectional area) wire should have a larger resistance. But according to the equation, this works in reverse. Common sense doesn't "make" sense. I am a little confuse. please clarify. Thanks.

2. ### timwhite Member

Apr 10, 2014
50
7
Common sense cannot really be applied to this case because electrons don't flow like we would think.

This quote from the Wiki page on resistivity explains this reasonably well:

3. ### tshuck Well-Known Member

Oct 18, 2012
3,531
675
A larger cross-sectional area means more chances for electrons to move in the direction imposed by the applied stimulus/voltage.

Perhaps you could explain why the larger cross-section "should" have a larger resistance?

4. ### Sparky49 Well-Known Member

Jul 16, 2011
835
417
Think of the wire as a water pipe, and the current as water flowing through the pipe. If you make the pipe's A smaller, it's going to be harder to get the same amount of water through in the same time. If you make it bigger, then the same amount of water can be pumped through, with less effort.

Technically, this analogy isn't 100% accurate, but the results are the same.

5. ### WBahn Moderator

Mar 31, 2012
18,079
4,917
Can you articulate why the larger diameter wire should have more resistance?

Imagine taking a small insulated wire that is, say, 1m long and, for discussion purposes, has a resistance of 100Ω. This is simply a resistor, right. Now, take two of these resistors and put them in parallel. Does it make sense that, like any two identical resistors in parallel that the net resistance is half, or 50Ω in this case? Now take 1000 of these resistors (wires) and put them in parallel. The net resistance would be 0.1Ω, right? Now imagine simply removing the insulation and putting all the wires up against each other. The result is really nothing more than a stranded wire made up of 1000 strands with the overall wire having 1000 times the area of a single strand and 1/1000 the resistance of a single strand. Now just imagine a solid wire that has the same 1000x the area as being 1000 individual wires, perhaps hexagonal in cross section, all butted up against each other.

6. ### WBahn Moderator

Mar 31, 2012
18,079
4,917
Why can't common sense be applied to this case. It works just fine.

7. ### crutschow Expert

Mar 14, 2008
13,472
3,361
If by "common sense" you mean a larger wire would have more resistance, then, by that logic, you could use an infinitesimally small wire to carry thousands of amps with little resistive power loss and power lines could be microscopic in size. Since that's obviously not the case, then it would seem your common sense meter needs some recalibration.