When jumpstarting a car, you connect those big alligator clamps to the terminals of the batteries. The cables themselves can handle the current just fine, but the contact points between the alligator clamps and the battery is extremely small. I'd imagine a maximum of 4 teeth are touching each terminal. How do those contact points not simply explode under the hundreds of amps?
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The beefy cables only handle the load because the clamps are severely limiting the current flow (and thermal mass) – Bryan Boettcher Jan 29 '18 at 21:13
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5i have cables that did 100s of jumps and the teeth now look like a jack-o-lantern... – dandavis Jan 30 '18 at 05:52
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Imagine the contact area between a trolley and a pantograph of a train. – Crowley Jan 31 '18 at 07:22
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They don't explode but they wear off. Also the clamping force reduces the impedance. – Lorenzo Marcantonio Mar 29 '21 at 09:15
6 Answers
Hint: resistance is not just a matter of cross section, but also of length.
Would you expect the jumper cables to work if they were say, 10 meters long? What about 100 meters? You got my point.
Even if the contact surface is very small, the effective length of the contact is very short. One could argue that having flat, rounded surfaces would lead to a better contact anyway, but this is not true. The battery contacts are dirty and oxidized, the pointy alligator clips, together with the strong spring, help the stranded driver to perforate said oxide and guarantee a good enough contact.

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9Yes. Stronger pressure on a small surface (here aligator tooth) offer a better contact than a larger surface with loosy pressure on it. Assuming that the small cross section at the contact area is rapidly enlarged (hence the thoot shape). – Fredled Jan 29 '18 at 21:53
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2If by "working" you mean "not blowing up", I bet a 100 m jump start cable will work perfectly. – Dmitry Grigoryev Jan 30 '18 at 08:22
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7Also, a small ugly tooth that is part of a big ugly piece of metal has a big ugly heatsink. – rackandboneman Jan 30 '18 at 12:08
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@DmitryGrigoryev, at 100m (vs 10 m), the cable resistance is 10 times higher, the battery voltage may not be enough at that point to drive hundreds of amps through the cable, so it **may** still work, but not "perfectly" (assuming same gauge, only length is different) – nurchi Jan 30 '18 at 16:12
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@nurchi I know that. I believe the question is about current-carrying capacity, not about resistance. Current capacity doesn't normally change with length. – Dmitry Grigoryev Jan 31 '18 at 07:31
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@DmitryGrigoryev, I agree, the capacity would not be affected, I was writing more of a general info (for a future reader maybe), while the capacity is not affected by length, the ability is (of a car battery). – nurchi Feb 01 '18 at 16:47
Have you noticed how the clamps get hot after a jump-start?
That means power is lost, it ends up in those clamps. You're right the connection isn't ideal so power is lost but not so much that anything melts or explode. What is there to explode anyway? Nothing :-)
You wouldn't want to make that huge starting current flow for more than a minute as the clamps will heat up severely and the plastic insulation would melt.
But since we just want to start the other car, which usually takes much less than a minute, it is OK. The clamps can handle that huge current for a short time.

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2+1 I'd also add. the cables themselves have to be beefy so as not to drop too much voltage. The drop across the contact point is much less significant. – Trevor_G Jan 29 '18 at 21:06
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5Often they are called "booster cables" because all they are doing is adding some amps to what the weak battery is putting out, not carrying the whole load. If the weak battery is actually dead, then the situation is more marginal, and the contact resistance matters more. As for exploding, if the cables are accidentally connected backwards, there could be bits of vaporized lead spraying around. You can also read about hydrogen exploding in batteries with too little electrolyte, but it is rare. – Jan 30 '18 at 00:05
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1An arc fault can make a very nice explosion, even though nothing but metal and air is involved. Cars don't generally have enough energy, though. – SomeoneSomewhereSupportsMonica Jan 30 '18 at 07:28
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1@SomeoneSomewhere just try putting two metal rods in contact directly across a large heavy duty truck battery.. on second thoughts don't.... – Solar Mike Jan 30 '18 at 09:25
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2"What is there to explode?" Well, if your lead-acid battery is faulty (and why else would you be jump-starting the car?) there's a chance it may have been producing [hydrogen](http://goodforgas.com/hazardous-gases-associated-lead-acid-battery-charging-stations/), which can make a nice bang :) – psmears Jan 30 '18 at 11:28
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@psmears Usually, you jump-start your car because the battery is **empty**, not overcharged. Hydrogen starts to form when you exceed nominal cell voltage. – Dmitry Grigoryev Jan 31 '18 at 07:35
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@DmitryGrigoryev: OK, someone missed the smiley! Also note I said "faulty", which can cause both hydrogen discharge and failure to start. – psmears Jan 31 '18 at 09:05
You seem to overestimate the effects of current on conductors. Let's take an AWG17 wire for example, which is a mere 1mm² of copper. Guess how much current it can take for 1 second before blowing up? Now check if you guessed right.
AWG 17 (1.04mm²) fusing current: 10s @ 99 A, 1s @ 316 A, 32ms @ 1.8 kA
Jump start clamps have a contact area of about 5mm², and the teeth are cooled by the thermal mass of the rest of the clamp, so handling a few hundreds of amps for a few seconds is not a problem.
AWG 10 (5.26mm²) fusing current: 10s @ 333 A, 1s @ 1.6 kA, 32ms @ 8.9 kA... AWG 11 (4.17mm²) fusing current: 10s @ 280 A, 1s @ 1.3 kA, 32ms @ 7.1 kA

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1Thanks, Mark, I had the idea to use the spoiler tag but forgot how to do it. – Dmitry Grigoryev Jan 30 '18 at 13:16
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I'm not sure you'd get 5mm^2 with most jumper cable clips, not even close. But moving them so they seat nicely once they're clipped on makes a big difference. – Chris H Jan 30 '18 at 13:18
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1@ChrisH Usually there are 8 teeth which can potentially make contact: two on the left side of a jaw, two on the right, and another 4 on the opposite jaw. With just half a millimeter on each tooth, you get 4mm². Of course, it's a "back of the envelope" calculation, but I don't think I'm too far off. – Dmitry Grigoryev Jan 30 '18 at 13:22
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@DmitryGrigoryev mine look more like [this](https://guideimg.alibaba.com/images/shop/2015/09/13/46/30a-crimp-terminals-polar-clamps-battery-booster-clip-jumper-cable_9579546.jpeg) but nickel(?) plated and attached to serious copper cable. So no real "teeth". The insulation has melted on the clamps at some point in the past though they've never been particularly hot when I've disconnected them. Most I've used have been similar – Chris H Jan 30 '18 at 15:21
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Be sure to wear a safety helmet, eye protection, hearing protection, and rubber gloves. Is best not to use jumper cables; call a tow truck and rely on a certified professional whose training and experience allows him (or her) to make you wait an hour for service and then get paid an unimaginable fee for the job. – richard1941 Feb 07 '18 at 11:08
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I wouldn't call 17 AWG "ordinary". I've never seen odd numbered AWG wire other than 1 and 3. – Hearth Mar 28 '21 at 19:03
After starting your car, examine the lead battery terminals. Sometimes when the contact is bad you will find a tiny pit where the lead has melted. The heat melting the lead is taken away from what is needed for the thermonuclear ignition that you fear.

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Consider that copper is an excellent heat conductor. It is so excellent that, for example, you would have really hard time trying to solder the clamps to anything with even moderately powerful soldering iron.
Also, when you connect clamps there is typically a bit of arcing. The clamp actually gets welded a bit increasing the cross section of the actual contact with the battery leads.

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Any condition of jaw connection, wire size, and other as mentioned above that causes a major reduction in voltage presented to the starting motor (series wound) causes greater current flow to produce the kW of power needed to turn the engine up to starting speed. Too much voltage reduction and the extra high current may destroy a perfectly good starter motor windings/set of brushes/commutator bars. Just a word of caution for any very low voltage starting situation.