What you have to always keep in mind is that volts, amps, watts, and ohms are so interlinked that you can't change one without changing at least one of the others. When you get into the realm of AC, then reactance also plays a big part, but I think you'll find it best to get a thorough understanding of the DC basics before trying to tackle that.
Can I can test the resistance through a battery?
Not directly with an ohmmeter, because the meter supplies power from its own batteries and the EMF from the battery you're trying to test would interfere with the reading (that's the best case scenario; the worst is that you'd burn out your meter!).
You can calculate the internal resistance of the battery indirectly, however. What you need to do is measure the open-circuit voltage at the battery terminals using a voltmeter of fairly high resistance.
Next, you connect a load across the battery (e.g. a lamp), and measure both the current flowing and the voltage now appearing at the battery's terminals. You can then use Ohm's Law to calculate the internal resistance of the battery.
An example:
You get an off-load voltage of 12.6V. When you connect a load which draws 2A the voltage across the battery drops to 11.8V.
The voltage being lost across the internal resistance of the battery is therefore
12.6 - 11.8 = 0.8V
You know that 2A is flowing through the battery, so the internal resistance by Ohm's Law is then
R = E / I = 0.8 / 2 = 0.4 ohm.
Is there a way to test resistance while a wire is hot, or does it always have to be dead?
Again, you can't use your ohmmeter because the circuit is energized, but you can apply Ohm's Law again if you know the current and voltage.
Measure the voltage between the ends of the wire you want to test, check the current flowing through it, then the resistance is R = E / I.
That's for DC or non-reactive AC. It gets more complex when inductance and capacitance are involved.
as safe as a GFI that won't allow me to take a lethal shock?
Just be a little careful how you take that assumption.
A GFI certainly provides a very high level of protection, but a shock at just below 6mA could still be a little risky in some situations.
The other point is that the GFI trips only if the shock you receive is from line to ground. If you get yourself across hot and neutral (and there is no appreciable current flowing to ground at the same time), then it won't help you one bit.
[This message has been edited by pauluk (edited 08-03-2003).]
