formula-derivationinternal-resistancemosfetohms
This question is related to MOSFET.
NMOSFET's resistance was till now defined in many different ways, for example as:
or 
which value varies from 1-50k Ohm.
And there is also drain-source on-state resistance 
which is usually lesser than 1 Ohm.
Which one can I actually use in an equation like this one which applies for common source configuration?
I can't answer questio 2n since my computer got a problem and I can't see your schematic but I can answer question 1:
Q1. Am I measuring the Rdson correctly? (it does not need to be accurate, good approx is enough)
Answer: No you don't. A multimeter is not meant to measure a resistance if there is current flowing through it. The resistance measurement need to be done without power on the board.
If you want to measure Rdson you can do the same operation but putting your multimeter in voltage mode. You measure the voltage between the drain and the source. With another multimeter you measure the current flowing through the transistor. then You do R = U/I and you have your Rdson.
The key to choosing a MOSFET as a switch is - ignore the current rating!
First decide how much voltage drop you can accept, and choose a FET with RDSON to match. For example if you want <= 0.1V drop at 1A then you need RDSON of 100mΩ or less. From this you can also calculate the FET's power dissipation, eg. 0.1V *1A = 100mW.
Next, make sure the Gate drive voltage is sufficient to turn the FET fully on. If you only have 3V available then look for a FET that is specified for 2.5V Gate drive.
Finally, ensure that the VGS and VDS ratings are at least 20% higher than the maximum voltages they may receive in your circuit.
The other thing to ignore is Gate threshold voltage. This is the voltage required to just start turning the FET on, and is poorly controlled so it may not turn your FET on at all!
To get an idea of required Gate voltage and expected voltage drop, look at the graph of ID vs VDS in the datasheet. Here's an example:-
You can see that at 3V (4th curve from bottom) it should drop 0.1V at ~2A. Note that as temperature increases so does resistance, so if the FET gets hot it will drop more voltage (and get hotter, and...). Therefore it pays to use a FET which is rated well above the actual current it is expected to pass.
Best Answer
@Keno Let's put it this way. When you operate your MOSFET in the saturation regime, as an amplifier, you use r0 in the small-signal analysis of the circuit. If you operate MOSFET as a switch (as in digital circuitry), and the switch is turned ON, you can use Ron, as long as the transistor is in the triode region. For detailes on MOS regimes of operation, i suggest looking up one of great books from Baker, Sedra & Smith, Gray & Meyer etc., because you can't really cut corners with these stuff if you want to build proper circuits.