Ok, so maybe I can squeeze in my 2 cents to this topic.
At work, we do some some battery tests on some Lithium-Iron-Phosphate batteries, 1Ah capacity and of course, the internal resistance of the battery is important, because we can know it it is healthy or not.
To do this, the voltage of the battery is measured (VNO_LOAD) Then, a 1A load is connected to the battery. After about a second, when everything is settled down, the voltage is measured across the load (VLOAD). The calculation of the resistance will be: (VNO_LOAD - VLOAD ) * RLOAD / VLOAD
Of course, the resistance , as some have said, will vary according to the temperature and the state of charge of the battery, so the calculated value is useless without knowing the characteristic of the battery, either from a datasheet from the manufacturer, or from doing real measurements across a range of temperatures and states of charge. For us, it's the latter.
The switching of the load is done by a MOSFET. 1A isn't that much, but paralleling some big ass power MOSFETs can make possible the switching of some really large currents, of 10's of amps up to about 100 Amps or so.
We've never done any AC measurements, because, for our purposes that isn't useful at all.