Mark you are correct it is basic ohms law lets take a look.
Lets say the circuit is 300 watts at 12 volts
300 watts / 12 volts = 25 amps
12 volts / 25 amps = 0.48 ohms
Now we know that the collection of lamps has a total resistance of 0.48 ohms
Now drop the voltage to 10 volts
10 volts / 0.48 ohms = 20.8 amps
Drop the voltage to 3 volts
3 volts / 0.48 ohms = 6.25 amps.
Drop the voltage all the way down to 1 volt
1 volt / 0.48 ohms = 2.08 amps
As far as the dimmers, I understand how a modern dimmer works, it does not matter the effect is the same.
Bob