[Physics] Why can different batteries with the same voltage send different currents through the same object

electricity

According to an answer in this thread on Skeptics:

If you take one of the little 12V
garage door opener batteries and short
out (directly connect) the two
terminals with a piece of wire or
something else. You'll get a light
current flow through the wire or
metal. It may get a little warm. This
battery is only capable of supplying a
small amount of current.

If you take a 12V car battery and
short out the two terminals (don't do
it, it's not fun), you will be met
with a huge current arc that will
likely leave a burn mark on whatever
was used to short it. This is because
the car battery is capable of
discharging a large amount of current
in a very short period of time.

I'm not sure how this could work given Ohm's law V=IR. If we assume the resistance of toucher is constant, then we'd expect the current to be the same as well.

  1. Could it be that a car battery has
    less internal resistance than a
    garage battery?
  2. Does it have anything to do with contact area? If it does, then how would you model it? Generally resistances add in series, but if I only half touch a contact, then neither the battery nor I change, so you'd expect our resistances to stay the same, but somehow our total resistance changes. So which objects resistance would change – mine or the batteries?

Best Answer

The answers of Martin and Edward are quite right, but theý lack a componet which plays a role in the case of that "garage opener battery".

If current is not limited in the circuit outside the battery, first internal resistance can be the limiting factor. But, often in such small (the measure for "small" is the area/volume of active material at the battery poles) batteries the current is limited by the speed of chemical reaction at the electrodes. This is not a linear function of current, thus it cannot viewed as a part of internal resistance.

Does it have anything to do with contact area? If it does, then how would you model it?

Yes, contact area is important, but this is a problem at high current densities mostly. Depending on voltage in such a circuit, small contact area (= high current density) can result in contact welding, sparking, or ignition of an arc, or in some strange semiconductor effects of the contact point. (metal surfaces are nearly always coated by some oxide) Did You ever watch when an electric arc is started by a welder? This is main business when designing contacts in relays, swiches in home, or the switches in 230 kV lines.

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