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I initially had this question because I was playing around with brine electrolysis and I found that the resistance is 0 one way (positive in negative cell) and infinite the other way (positive in positive cell).

I tested it again using a normal AA battery, and I had the same effect. When I measured the resistance negative-negative and positive-positive on the battery, it was infinite. But when I measure it through opposites, there is no resistance.

Why is there infinite resistance one way, and none when the polarities are flipped? Since it behaved somewhat like a battery, I assume the reason for the battery is the same for the electrolysis cells.

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    \$\begingroup\$ How did you measure the resistance? \$\endgroup\$ – The Photon Jun 3 '17 at 16:53
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    \$\begingroup\$ An ohmmeter works by (1) by placing a known voltage across the terminal leads and then measuring the resulting current or (2) forcing a known current through and measuring the resulting voltage across; the resistance is the ratio of the voltage to current. Can you see why this won't work with a battery? \$\endgroup\$ – Alfred Centauri Jun 3 '17 at 18:44
  • \$\begingroup\$ This was done using a DMM. \$\endgroup\$ – popdog Jun 4 '17 at 0:04
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    \$\begingroup\$ The ohmmeter in a DMM measures resistance exactly the same way as @AlfredCentauri's link. The only difference is the digital display instead of an analog meter. \$\endgroup\$ – alephzero Jun 4 '17 at 0:59
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    \$\begingroup\$ You cant use an ohmmeter across a live source. You wont ever get accurate results - I mean you will get grossly inaccurate results. Thats assuming you dont damage the ohmmeter. Simply dont do it. Always deactivate the power sources before applying an ohmmeter. Clearly you cannot deactivate a battery. \$\endgroup\$ – CogitoErgoCogitoSum Jun 12 '17 at 20:08
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Why do batteries only have resistance one way?

They don't.

To a first approximation, a battery is a voltage source in series with a resistor.

Your wrong impression is probably due to invalid measuring. You can't just connect an ohmmeter across a battery. Most ohmmeters aren't designed to measure resistance with a voltage source in series. That will seriously confuse most ohmmeters.

To measure the internal resistance of a battery, you take two measurements at different voltage and current combinations. For example, you might measure a AA battery when it is putting out 0 mA (open circuit) and 50 mA. You make the assumption that the voltage source in the battery is putting out the same voltage in both cases, and the difference in output voltage is due to the voltage drop across the internal resistance. Then use Ohm's law to find the resistance, but use the change in voltage and current instead of the absolute values:

  R = (V1 - V2)/(A1 - A2)

In this case V1,A1 is the voltage and current measured at one point, and V2,A2 at the other point.

You can do the same thing for charging if the battery can take reverse current.

After some time, especially at high current, the chemical reaction in the battery "wears out", and the voltage of the voltage source goes down (or up if charging).

Batteries are complicated, but they don't have resistance "one way", whatever that even means.

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The error was in your measurement method using a DMM. You should only measure voltage drop with an external current sink or source to measure ESR or use a series current shunt and voltage source or sink.

The ESR will be a loose indicator of mAH storage capacity left and rises sharply below 10% SoC.

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