Hello, electronics newbie here. I have some questions that might sound noobish to you guys, but they are somewhat hard for me to
comprehend.

I have a circuit on my breadboard that is powered by two separate channels from power supply, each providing different voltages (see the picture below):
figure 0:

And my question is I don't really know how I should ground/earth the circuit or just leave the circuit as it is in figure 0.
The following two options are what I have in mind, but I'm not so sure which is the correct one.

figure 1 - connect the negative terminals together:

figure 2 - connect both negative terminals to the earth terminal on power supply:

 

First, answer the questions about how does the added connections change the operation of the circuits. Is there a needed signal or current path in common between them? What would a common Earth connection to the circuits provide to the circuits under normal operation?

 

If your PS is derived from a PC supply, the common is usually referenced to earth ground anyway.
Max.

 

Is there a needed signal or current path in common between them?

Not when I'm using the bench power supply to power the circuit. However, I'm planning to use a 12v 5.5mm barrel connector to power the LED along with a regulator to step down 12v to 5v to supply the load and in this case I guess they do have a current path in common, maybe?

What would a common Earth connection to the circuits provide to the circuits under normal operation?

I'm not sure about this question.

If your PS is derived from a PC supply, the common is usually referenced to earth ground anyway.
Max.

My power supply is just a regular bench top power supply.
If the common is usually referenced to ground, wouldn't that be the same in figure 2?

 

If the common is usually referenced to ground, wouldn't that be the same in figure 2?

I generally use Common instead of ground, In N.A. P.S. Common is usually referred to as Ground and so is Earth ground. where I come from (UK) you run a Earth wire, not a Ground wire.
I generally like to distinguish between the two and call it PS Common and earth ground.
Max.

 

I generally use Common instead of ground, In N.A. P.S. Common is usually referred to as Ground and so is Earth ground. where I come from (UK) you run a Earth wire, not a Ground wire.
I generally like to distinguish between the two and call it PS Common and earth ground.
Max.

Thanks MaxHeadRoom for clarify the usage on common/ground/earth.

But I'm still confused about the circuit.
I mean, the whole thing works fine when I connect the circuit like in figure 0.
So, does it mean that negative terminals are acting like common in figure 0?

 

Due to the fact opto isolation is used you have the option of keeping each circuit isolated, this is required in some cases such as where for example, one side may referenced to earth ground and it is desirous to isolate the other side common from earth ground where it could cause circuit or safety problems, if this risk does not exist, then it is optional.
And the opto isolator just acts as a voltage level transition.
In Industrial electronics, some prefer to keep all ancillary circuitry separate, I generally use the alternate method where possible and connect all commons to a central star point that is also connected to the service earth ground .
I found this method tends to eliminate electrical noise causing circuit malfunction.
Max.