David82:
We studied phase angle in my college physics 2 class. Is the phase angle what is used to measure current?No, phase angle is the relationship between voltage and current at an given instant of time and if not 0 degrees then simply multiplying voltage X current won't give you the true RMS power consumption. The phase angle must be measured so it's effect can be calculated for true power consumption as in billing rate.
When using a 1:1 transformer, I don't understand how the meter can still tell how much current is used. The wires providing power aren't actually connected to the load in any way.
Not directly connected but effectively connected by the transfer of power via constantly changing magnetic coupling from primary to secondary windings, the iron core of the transformer makes this a very efficient transfer of power. This only works for AC as DC will not pass power through a transformer as there is no changing magnetic field as in AC. AC power transfer is effectively constant (minus small transformer losses) such if the step up voltage ratio is 1:2 the current ratio transfer will be 2:1 making the actual power transferred constant.