Here’s a project that let’s you measure the internal resistance of Lithium Polymer batteries. It measures the total current as the battery discharges through a 1 Ohm resistor. From the known voltage and the discharge current the internal resistance can calculated.
This device can be used to measure the internal resistance of Lithium Polymer batteries used in electric RC models. The power consumption of these models is quite high, and the batteries wear out in 100-200 recharge cycle. The internal resistance is a good measurement of the age of the batteries. New cells are below 5mohm, and the ones at the end of their life are above 20mohms. It also depends on the original quality.