Electronic – How to calculate the internal resistance of an alternator

Your experimental approach is valid. Your concern that the power supply internal resistance should be constant may be invalid, subject to these potential problems:

• Your power supply has an internal current-limiter.
• Contact resistance and/or wire resistance affects your measurements.
• Your power supply output voltage is affected by temperature.
• Your power supply output has "ripple" due to charging/discharging capacitors
  

Some voltage-regulated supplies have such low internal resistance that they cannot provide current to a very small-resistance load. Until current reaches a set-point, it acts as an almost ideal voltage source, with very low internal resistance. Your measurements may be affected by the first three potential problems.

The last problem arises because many unregulated supplies have non-linear elements inside (like diodes for example) that charge up an output capacitor to a DC voltage. Your experimental approach assumes that your voltage source is a linear circuit. This kind of DC supply is not linear:

^{simulate this circuit – Schematic created using CircuitLab}

What happens at the indicator terminal is that there's a trio of diodes from the winding phases that provide the current for the field coil. When the alternator starts up, some current is needed through the field winding (on the rotor) for it to generate enough magnetic field to produce an output, so that's why you needed a low resistance to replace the bulb. Once the alternator is producing an output, the trio brings that terminal up to the same voltage as the battery, since the drops across the trio and main diodes are similar, so there's no potential across the bulb, and the trio is providing the field current. With the alternator not turning, the bulb (or bias resistor) current is still being dropped across the field winding, which is a few ohms so the voltage at the terminal is not zero. You could try putting a couple of diodes, (or a zener) in series with your 4k7 and another pulldown to ensure that the input is below the low state threshold on the MCU input.

Other alternators have a regulator that switch the field internally based on the output of the windings under the residual magnetism of the rotor, these just have a transistor (usually a FET) that pull the indicator output down. These would function the same - they don't need the bulb or any other current source to aid starting up.