batterieslithium ionresistance
I'm coming from a computer science background, and will be writing some software to automate battery testing. I have background in math, but little to none in physics or electronics. Please consider this in your answers.
That said, how would I go about testing the internal resistance of a small lithium polymer cell by hand?
The motor runs faster b/c you're applying a higher voltage to it; the motor has to turn faster to generate the back emf to balance the battery voltage. Now, if you limit current, and the motor runs more slowly, it will again be generating less than the battery voltage, so the remainder of the voltage will be the drop across the current limiting device or circuit. The voltage drop across the current limiter, times the current through it, represents power that is wasted.
I assume your idea is that you still want the motor to run faster than the original device, but slower than the direct lithium-to-motor configuration. But you see, the concept of limiting the current here is kind of counter productive: You added a higher voltage battery, and inserted an extra element, and then burn off power to bring the motor speed down from what it would be w/o the current limiter. The more direct solution would be to choose a battery that's not so much higher than what the motor was intended to see. I.e., instead of jumping from 1.5V to 3V, maybe try to hit something like 1.8 or 2V. Of course, batteries don't come in arbitrary voltages like that, but the point is, don't overkill it with 3V, then try to kludge it back to where a lower battery voltage would get you to directly.
Probably the best solution would be to modify the motor itself. If you rotate the brush assembly relative to the magnets, the motor's speed/torque characteristics can be changed. It requires mechanical finesse, but you might be able to mod the motor to work well at 3V. Or you might be able to outright replace the motor.
The nature of the Kelvin measurement is that you have a separate current path and measurement path so that no current (except leakage and bias currents) flow through the measurement conductors.
Thus, the PCB layout (unless the design itself is faulty) is remarkably easy, and I don't expect you'll have any troubles, since series resistance hardly matters.
simulate this circuit – Schematic created using CircuitLab
In the above schematic, the exact value of the resistors R1, R2, R3, and R4 hardly matter, provided they are reasonably low. R4 affects the common-mode voltage the instrumentation amp sees, R1 and R2 affect errors due to input offset current (and noise) a bit, but really the PCB layout is not very important until currents and voltage drops start to become significant wrt the common mode range of U1. So you want to keep the voltage drop across R4 reasonably low (not a problem typically unless you use very thin traces and/or very high currents).
Best Answer
Measure open-circuit voltage \$V_{oc}\$, then load the battery with resistor \$R_{load}\$ and measure voltage \$V_{loaded}\$.
$$ R_{in} = R_{load} \cdot \frac{V_{oc}-V_{loaded}}{V_{loaded}} $$
This is the internal resistance at DC and at your specified load. Internal resistance varies with load and temperature and battery charge and age, etc. And you'll need more advanced equipment to measure at higher frequencies.