Electronic – Split Common Neutral for DC Current

Using a 120 VAC inverter and a light bulb to keep your pipes from freezing is just a dumb idea.

If you need 40W worth of heat in an enclosed space, just select a bunch of power resistors that add up to that amount, screw them to a heatsink and run them directly from your 12 V battery. For example, a 15-ohm resistor will dissipate about 10W @ 12V, use four of them.

You can also get CFL lamps that run directly from 12V.

Let's say you need a run time of 48 hours, and you have a minimum of 6 hours to recharge.

Your load is drawing a daily average of 3.33 (heater) + 5/24 × 1 (lights) = about 3.5 A. Multiply by 48 hours to get the battery capacity: 170 Ah

Batteries aren't perfectly efficient, so it'll take about 170 / 0.8 = 212.5 Ah to recharge it.

If you want to drive the load and recharge the battery in 6 hours, you need a panel capacity of about 40 A @ 12 V, or 480 W.

Short answer: Use a single common node for the whole circuit.

Long answer:

When one part of the circuit sends a signal to another part of the circuit (for example one IC sending a digital signal to another IC, or an op-amp sending an analog signal to a filter) there has to be a complete circuit for the signal to be transmitted. If the signaling scheme is notionally "single-ended" (for digital) or unbalanced (for analog), then the current associated with the signal must return by some path. Typically this is the "ground" node, or some other node that is, at least for ac analysis, shorted to the ground node.

Also, consider if two circuits have their ground isolated from each other, and one delivers a "5 V" signal to the other. If somehow their individual grounds have drifted so that there is 50 V potential between them, it's very unlikely that a signal that is "+5 V" for one circuit will be within the safe operating limits for the other.

Of course other options are available. You can use differential signalling, which tolerates small variations in ground between the parts of the circuit. This is common when the two subcircuits are several feet apart from each other.

You can also use differential signalling with galvanic isolation if you need to accommodate 10's or 100's of volts difference between the grounds of the two circuits. But this adds cost and typically limits the performance of the system (for example, transformer isolation won't pass signals that include a dc component, and opto-isolators have speed accuracy limits)

If you have no reason to do otherwise, use a common ground between all the parts of your circuit.