Is 12/2 UF wire suitable for a 500 foot circuit with four 400 watt heaters for watering troughs in various locations - 120 volt system?
At 400W, each trough is about 36 ohms (with a 120V supply).
Assuming equidistant placement, they'd be 125' apart, and the 1st is 125' from the source.



simulate this circuit &ndash; Schematic created using CircuitLab
12ga copper has a resistance of around 0.1985 ohms/125', and that's for each wire.
So including the wire resistance in the circuit gives:



simulate this circuit
The 1st 125' of wire sees all of the current flowing through all 4 loads, so it therefore has the highest voltage drop - about 2.5V on each wire, resulting in 'R1' seeing approximately 115V and dissipating about 368W (assuming that there's 120V measured at the source).
The 2nd 125' of wire sees the current for the next 3 loads, resulting in about 1.8V voltage drop per wire, or about 111.5V at 'R2' - which dissipates about 345W.
The 3rd 125' of wire sees the current for the last 2 loads, resulting in about 1.2V drop per wire, and about 109V at 'R3' - dissipating about 331W.
The last 125' of wire only sees the current for 'R4', which causes a voltage drop of about 0.6V per wire, so R4 sees about 108V and dissipates about 323W.
108V is 90% of 120V, so you've lost 12V across the 12ga copper wire, and due to this 10% voltage drop you'll only get 323W at the last load instead of the 400W it's rated for.
If you bumped the wire up to 10ga copper (0.1249 ohms/125'), the losses would all decrease proportionally and give you:
R1: 116.8V, 379W
R2: 114.5V, 364W
R3: 112.9V, 354W
R4: 112.1V, 349W
112V is 93.4% of 120V, so for 10ga wire you only lose 6.6% across the wire.
If your target is to be NEC compliant, then afaik you're only allowed up to 5% drop, so even 10ga wouldn't be good enough.
If you increase the wire gauge of just the 1st 125' segment to 8ga then you'll only lose 0.63V on each wire, giving 118.7V at 'R1'. The remaining segments at 10ga would drop the same voltage as before, resulting in about 114V at the end - which is a 5% drop.
Of course increasing all 4 segments to 8ga would improve this even more.
These calculations assume that the load is 'resistive' like a heater (to defrost the troughs I guess). Non-resistive loads would behave differently and could potentially draw more current at lower voltages, resulting in higher voltage drops across the wires.