I am relatively new here and I am confused as to the difference between Vrms and Vm. I would be obliged if someone can explain. (This in relation to 3-phase circuits would be even better)
RMS: The RMS value of a waveform is the DC-eqvalent voltage. It means, that if you have a sin wave with an RMS value of 10 Volts RMS, in order to deliver the same power via DC voltage, you would need 10 volts DC. Don't confuse the average magnitude with the RMS voltage; Vav does not equal Vrms. In fact technically, the average voltage of an unshifted sin wave is 0
Vm: Vm generally refers to the peak/max voltage on your waveform.
Let's start with this: -
If you had a DC voltage of 10V and a 1 ohm resistor, the power dissipated in the resistor is 100W because: -
P = V^2 / R.
The RMS value of 10VDC is 10VDC - it's the number you use to calculate power in dc circuits.
In simple sinusoidal AC circuits, if you have a peak value of 10V, you will find that it dissipates in a 1 ohm resistor somewhat less that 100W.
It will dissipate 50W - and if you reverse the process to work out what peak sine voltage would cause it to dissipate 100W you'll find it to be 14.14V (approx).
Most engineers are so well-versed in doing this that it may seem, to the uninitiated, that there is no-theory behind it. I acquired this from the web: -
What you refer to as "Vm" I assume is an abbreviation for "Vmax" which I usually refer to as "Vpk".
Regarding 3-phase circuits, there is no fundamemtal difference except you are calculating power three times; one for each phase. If you have 3 resistors in a delta connection then, the power is the RMS Line voltage squared and divided by the delta resistor to which that line voltage is across. Repeat for the two other line voltages and sum all three.
That gives you 3-phase power.
If you have resistors in star-formation you must use the phase RMS voltage (line divided by sqrt(3)) and calculate the 3 individual powers. Add them together to get power.
If the loads are imbalanced and there is no neutral connection then there is more maths but I hope you get the picture.