Voltage Meter and Voltage Tester?

In response to Almond's answer: I am a professional installer, and my digital multimeter is the most-used tool in my box. If you are going to be working with car audio, as a profession or a hobby, then you need to own a multimeter. A test light does not cut it. You do not have to spend a lot; you can get a $20-$40 meter at Sears or Radio Shack that will work perfectly well. A test light wo not show you the difference between 9 volts and 12 volts at the radio power supply, but that can be the difference between a working radio and a dead one.

1. Why do you have to use the nominal voltage of the transformer for the no-load or open-circuit test?

I think I understand your question so first here's a representation of the equivalent circuit of a transformer: -Under no load conditions the only current flowing into the primary is the current taken by the "parallel components" Xm and Rc. For a normal power transformer that current will be small compared to the current normally taken by the primary when the secondary is driving a load. For that reason you can ignore (short circuit) Xp and Rp and of course the secondary is only producing an open circuit voltage so Rs and Xs are of no consequence.The "thing" in the middle that looks like a transformer is a perfect power transformer and because no current is being delivered to the secondary that perfect transformer takes no current.So, it boils down to Rc and Xm being connected to the incoming power and no further components need to be analysed.I was wondering why exactly you have to use the nominal voltage of the transformer for the open-circuit or no-load test.There is one very important reason for this and that is core saturation - if you do not use the normal applied voltage you will either have too much saturation or too little and you wo not have a representive measurement. Saturation of the core is non-linear with voltage so it's important to use the right applied voltage. Look at the BH curve to see why: -You can see that it is very non-linear once you start approaching saturation and, most transformers will be designed to run at a magnetic field strength (H) in the early to mid areas of saturation. This of course means a smaller transformer size and less iron. Commercial reasons prevail.So, to do the test justice you need to run at nominal levels.If you were doing a test to find out the values of the series components then you would run the primary from a variac and short circuit the output. The sort of voltage that is now applied is a fraction of the nominal voltage so core losses are low (very linear BH curve) and eddy current losses (Rc) are also quite small.

2. Measuring floating gate potential with minimal leakage current

If this is for professional use, use an Electrometer such as this. This type of meter has an input impedance of 10^14 which is adequate to measure voltage in the leakage environment you have. There are a huge range of devices spanning low cost to high cost. You could build an electrometer if you were willing, and here might give you a starting point using an LMC662.If you are simply DIY experimenting then you can build/buy an electroscope. These are not easily calibrated, but can provide good comparative measurements of charge on a point. You could get something like this for $50 or less

3. Extension Cord for 20 amp load and other heavy loads?

Every 30' is about 2% voltage drop. Voltage is indirectly proportional to Amperes thus as Voltage goes down Amperes goes up. Extension cords are for temporary applications agreed but over time your motors will wear out faster. If I were in the carpet cleaning business I would only use 10AWG for all my needs regardless.

4. Bad voltage regulator?

There would be no way to tell for sure if something was frying them, but would suggest to you this would be highly unlikely. It is completely within reason for the rebuilt alternator to have gone bad ... that's why they have a warranty. Yes, it's a PITB to take on and off, but at least it did not cost you anymore than an extra trip to the store.