Cut strands effect on resistance

Discussion in 'General Electronics Chat' started by steveparrott, Feb 21, 2006.

  1. steveparrott

    Thread Starter Active Member

    Feb 14, 2006
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    I'm trying to understand the effect of cutting strands in a multi-stranded wire. For example, take a 10/2 wire with 50 strands of copper wire twisted together inside an insulated sleeve, then cut half the strands (at a point along a wire run). My understanding is that the wire resistance is then equivalent to a wire with only 25 strands.

    If the cut is only a fraction of an inch long, then why doesn't the current jump across to the other strands, effectively bypassing the cut with a miniscule increase in resistance instead of doubling the resistance along the whole run?
     
  2. n9352527

    AAC Fanatic!

    Oct 14, 2005
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    I think that the resistance wouldn't be doubled since there is cross conduction on the strands exactly like you said. Calculating the exact resistance is quite difficult since we have to obtain the cross-strands resistances if they are not negligible. However, the current carrying capability would have been effectively halved since that is dictated by the weakest point along the wire, which would be where half the strands are cut.
     
  3. Gadget

    Distinguished Member

    Jan 10, 2006
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    Kinda like putting a fuse in the line. The resistance wont change to that of a wire made up of an entire length of fine fuse wire, but the current capacity will.
     
  4. steveparrott

    Thread Starter Active Member

    Feb 14, 2006
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    I guess I'm really showing my ignorance here. What you said about the current capacity being the important factor makes sense.

    But I did have a confusing conversation with someone who said that currents travel in a circular or spiral fashion along the outsides of the strands, so when a strand is cut, the current doesn't jump over to the other strands. Does this make any sense?
     
  5. n9352527

    AAC Fanatic!

    Oct 14, 2005
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    It is called skin effect and happens only with AC current. Have a look at that Wiki page to get an idea on how the frequency affects current density, skin depth and resistance.
     
  6. steveparrott

    Thread Starter Active Member

    Feb 14, 2006
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    Thanks for the reference. I slogged through the wiki explanation as best I could. I"ll put what I've got from this into my own words and would greatly appreciate if you could correct what I get wrong. By the way, I'm just considering 12V AC current here since I'm trying to apply this to low voltage lighting circuits.

    A 12 gauge landscape lighting wire has 65 strands of 0.01" diameter each. Each of these strands transmits current in two ways – along the inside of the solid strand and along the skin of the strand. The resistance to the flow of energy is less inside the strand (it flows more easily) and greater along the skin (the resistance to flow is greater).

    If, at some point in the wire run, some strands are cut, the electricity flowing through these cut strands is (roughly speaking) looking for somewhere to go. The current flowing through the center of the cut strands will try to migrate through the strand skins and move over to the other strands, but the skin resistance blocks (to a great extent) this migration. The current moving along the surface of the cut strands may be somewhat more successful migrating across to the other strands, but there would be significant resistance in this migration also.

    The result is that the combined resistance along the entire stranded wire is increased and the capacity for the wire to contain the current is decreased.

    Putting this into a practical example, if when a stranded 12 gauge wire is stripped then twisted into a wire nut, 10 of the 65 strands are cut, then the resistance and capacity of that entire wire run would approximate that of a 55 strand wire. Even though those 10 strands were only cut at one point, they are effectively wasted for the entire length of the run.
     
  7. steveparrott

    Thread Starter Active Member

    Feb 14, 2006
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    I'd like to add one more attempted explantion about what happens in a wire nut even when the strands are not cut.

    When wire nuts are used to make a connection between two wires, only a portion of the skins of the strands are in contact with each other. There is a meaurable resistance imposed on a current as it passes from one strand to another through the skins.

    An effective way to eliminate this resistance is to solder the entire connection. This, in effect, allows current to move from strands to the solid metal section then back to the strands – thus eliminating the need for the current to migrate through the strand skins.

    [A final question, does the increased resistance factor in a 12v AC wire nut connection present more of a problem than with a 120V AC wire nut connection? I'm asking this because voltage loss is a big factor with low voltage.]
     
  8. Erin G.

    Senior Member

    Mar 3, 2005
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    Skin effect is usually negligable in stranded wire. In fact, it's one of the primary reasons the industry developed stranded wire. The current will tend to flow around the skins of the individual strands, not just the strands on the outside of the total conductor, which I think is your (mis)understanding to this point. As a result, there is no "real" (measurable) skin effect occuring in a stranded wire.

    If you can get a copy of "Uglies Electrical Reference Guide" (or similar guide) in which both stranded and solid wires are listed, you would notice that for the same gage wire, the stranded is always rated at a slightly higher ampacity than the solid depending on insulation, (ie THHN would be a fraction higher than THHW).

    With regard to using solder connections; Though it makes a great connection and reduces resistance from really-low to super-low, it is a NEC code violation to use only solder to make a connection for 120VAC. If the line is overloaded and overheats, the solder can melt, breaking the connection and creating a shock / fire hazard.

    Just so you know, at my job we wire motors ranging from 30VAC to 480VAC every day using wire nuts.

    If you're just transfering power from one place to another, most of the time a good wire nut connection is just fine, even at 12VAC. Wire nuts become unacceptable when you start transfering signal voltages, such as in a 0 to 5 volt analog control circuit. That's when it's time for terminal blocks or solder.

    I hope this helps.
     
  9. windoze killa

    AAC Fanatic!

    Feb 23, 2006
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    My turn.

    Firstly what some of you have said about skin effect is correct. It is only found when using and AC current BUT at low frequencies that seem to be talked about here it can be considered negligable. Skin effect only really comes in to effect at frequencies above say 1MHz. Althought this is a generalisation it is a good guide.

    Now on to the resistance of the wire problem. Consider the wire as a multi lane freeway. A four lane freeway can carry four lanes of traffic. If you come to a bridge that has 3 lanes cut you will now only have a 1/4 of the traffic flow. So the resistance to the traffic flow has gone up. This analogy can be applied to wire. The cars can't just jump the gap and continue.

    Hope this helps
     
  10. n9352527

    AAC Fanatic!

    Oct 14, 2005
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    In 50Hz or 60Hz AC wiring where the wire diameter is less than 9mm or so, the skin effect is negligible regardless whether the wire is solid or multi-strands. The reason is that the skin depth (where difference in current density starts to occur) is about 8 to 9mm or so. Wires with diameter less than the skin depth do not suffer from this effect.

    Wire consisting of _uninsulated_ multiple strands do not as such mitigate the skin effect. It is considered as one solid wire with fill factor of less than one where the current would tend to flow on the outer skin of the _bundled_ wire and not on the skin of individual strand.

    There is a special type of wire, called Litz wire, that is used when skin effect is detrimental. This has multiple _insulated_ strands.

    I think you meant to say the other way around.

    Because the skin effect is negligible if the wire is less than 9mm or so at 60Hz, there would be no significant difference in current density across the wire profile. The strands are not insulated so the wire is considered as one bundle.

    The cross-strand resistance and thus current carrying capability would depend on contact area between strands. I don't think there would be significant resistance across the strands and therefore cross conduction would happen if some strands are cut.

    The resistance along the cut would increase, but this would only cause minimal increase to the overall wire resistance. Current carrying capability, however would decrease as you said.

    <!--QuoteBegin-steveparrott
    @Feb 23 2006, 04:18 PM
    Putting this into a practical example, if when a stranded 12 gauge wire is stripped then twisted into a wire nut, 10 of the 65 strands are cut, then the resistance and capacity of that entire wire run would approximate that of a 55 strand wire. Even though those 10 strands were only cut at one point, they are effectively wasted for the entire length of the run.
    [post=14298]Quoted post[/post]​
    [/quote]

    You are right on the current carrying capability wasted length, but the resistance would not approx. to 55 strands.

    This is a more detailed explanation of skin effect in multi-stranded uninsulated wire. Quite extensive 6 pages explanation.
     
  11. steveparrott

    Thread Starter Active Member

    Feb 14, 2006
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    Great info guys, I really appreciate the help.

    I'm getting that (for 12V AC and stranded cnductors):

    1. Skin effect is negligable and I can discard that from my consideration.

    2. Cross migration across strands is not a significant issue either (though I still have a niggling doubt about that since we have the stacked log issue with strands only touching each other at points). (Clarification on the significance of that factor, please).

    3. Resistance may be increased slightly by a single cut in some strands, but it will not be significantly higher than the resistance of the uncut stranded wire.

    4. Most significantly, cut strands result in a situation where the entire wire run has a reduced amperage capacity equal to the capacity of the uncut strands.

    3. The highway analogy seems most useful in looking at strands as lanes in a highway. When you lose two lanes (strands) all the cars (electrons) need to funnel into the remaining lanes (strands). This doesn't create a problem if the flow of traffic (cars per area travelling at a certain speed - or amperage (?)) is low. But if the traffic increases to a point where the bottleneck slows everyone down (amperage exceeds wire rating), then road rage (heat) gets out of control (insulation melts) and all hell breaks loose (circuit fails).

    Am I getting close?
     
  12. windoze killa

    AAC Fanatic!

    Feb 23, 2006
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    Point 2 in your message, although the strands are only touching at a small part of their suface area and we have determined that skin effect is not part of the equation the all the current is flowing through the full cross section of each strand. Their may be a little "cross migration" but this also is way too hard to calculate and should also not be considered. Also, if you consider the idea that the hole stranded wire maybe terminated in a crimp then when a crimp is crimped all the strands are crushed together so hard they form a single conductor at that point. And another point about crimps is that they form a cold weld between the strands. If they are done properly using proper tools and not the $10 ones that come in most tool kits the termination can be just as good as a solder joint.

    <!--QuoteBegin-steveparrott
    @Feb 25 2006, 04:48 AM
    3. Resistance may be increased slightly by a single cut in some strands, but it will not be significantly higher than the resistance of the uncut stranded wire.

    [post=14344]Quoted post[/post]​
    [/quote]

    I assume you mean if one strand out of 50 strand is cut the overall resistance will hardly change. This is correct. The end to end resistance of the cut strand will be infinite.
     
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