I want to monitor the current going through each of three phases to a 415AC, 2 amp three phase motor.
This is to detect supply line loss of phase/brownout or a broken or shorted winding in the motor.
I envisaged inserting a 0.1 ohm (or less) wirewound resistor into each phase of the supply to the motor and feeding the voltage across the resistor into a rectifier and buffer before reading it on the Arduino.
My question is, how do I determine the appropriate wattage rating for the resistor. I thought that it must be different from working it out for a DC circuit.
Same thing. The entire reason behind using RMS (root mean square) voltage for AC voltage rather than peak, peak-to-peak, or average is so that power calculations work out correctly.
So 2ARMS in 0.1 ohm results in 0.2VRMS and 0.4WRMS. However, you need to know the maximum wattage the resistor might have to withstand if it has a shorted winding. You can start from the rating of the breaker, but keep in mind the breaker does not open instantly. So even if the windings go overcurrent and trip the breaker, the resistor will have to be able to withstand a short, high current and therefore high power pulse.
Normally, when someone describes an AC voltage, they mean RMS unless otherwise stated.
Perhaps three current transformers might be more suited to this. They'd inherently provide electrical isolation and be able to withstand much higher current.
Whoa there, 415V is lethal, you need to start considering alternatives to shunt resistors
on safety and complexity grounds.
3 hall-effect current sensors or current transformers could be used, they clip round
the wires without making contact and thus high voltages are avoided (although placing them at the neutral side is more sensible as there will be less noise pickup.
If a shunt-resistor setup was used you would need to site them at the neutral point,
use circuitry floating at neutral potential and isolated from the rest of the system
with linear analog opto-coupler(s). (Neutral can go live during fault conditions
and during siwtching of isolation switches). I don't recommend it unless you can
find a ready-built module offering this sort of isolated sensing