Electronic – The effect of grounding a simple circuit

For your answer, you have to go back to basic op-amp theory.

When you provide negative feedback to an op-amp, you make the negative input track the positive input as closely as possible.

Now tie the positive input to ground. The op-amp feedback is going to try to keep the negative input at that same potential: ground. Thus the name: Virtual Ground.

Note that when you inject current into that (-) node, the op-amp's output drives the feedback resistor to keep the (-) input at ground. This property is used to create a summing amplifier, where multiple currents can be summed into that node to create a voltage output that represents the sum of those currents. This configuration is called a "Virtual Earth Summing Amplifier".

Most analog audio mixing consoles use virtual-earth summing amplifiers for their mix busses.

Finally, note that it DOESN'T have to be the the (+) input grounded and (-) input as the virtual ground. If your op-amp has an inverting stage after its output, you could quite easily take your feedback from the output of that inverting stage rather than from the output of the op-amp. In this case, the (+) & (-) inputs swap: the (-) input is grounded and the (+) input is the virtual ground.

Do note that you have to take into account the phase margins of both stages when you cascade stages in that manner.

The reason this is confusing is because the ideas are confused, mixed up in the word "ground".

Sometimes “earth(ing)” is used to refer to the concept of electrically connecting to the earth, allowing “ground” to be used for the concept of “a part of the circuit we consider to be 0 volts”.

Some say Ground is just a reference point for measuring voltages

That's one of the meanings. You have some device, some circuit, and say that this conductor is 0 V and measure everything else relative to it.

If the device is isolated (battery powered and not hooked up to anything else), then it's truly arbitrary, but if you have connections, signal or power cables, to something else — power supply, digital signal, analog audio signal, whatever — then the expected electrical characteristics are generally such that the two devices share the a common 0 V reference — a common ground.

(If there's a problem so that one of the devices is causing current to flow along different parts of the system that should be the same “ground”, that's called a ground loop.)

some say ground is a safety device for appliances

The safety device here is the presence of a connection between the chassis of the device (generally, any exposed metallic parts) and the “ground” conductor of the electric circuit, which is also joined to earth. The safety comes from the idea that if somehow the chassis gets joined to line voltage (“hot”) and current will flow to the “ground” (and perhaps trip a breaker or GFCI/RCD device) instead of through you when you touch it (as you are a higher-resistance connection to earth).

some say ground is just a bare piece of metal regardless if its even connected to the actual earth

A bare pice of metal is never “a ground” by itself. It's just common, for safety reasons and for electrical design convenience, to design things so that all exposed metal is joined to, or a part of, the circuit's “ground”.

Can you not be safe just by touching a hot wire alone, granted you don't touch neutral?

If you jump in the air and poke the hot wire, you're certainly safe. If you're touching anything else, like what you're standing on, you might be able to make a circuit.

What if you touch a hot wire then, stick you other finger in the dirt (soil)?

So its telling me that the current flow from a hot wire, to the grounding wire-> (connect to some rocks and dirt/poop) is so high, it can trip a breaker?

Depends on the kind of dirt, and how wet it is. If it's sufficiently conductive, the circuit consists of the incoming electric service (hot branch) → house wiring → you → dirt → service ground connection at the breaker panel → service neutral. (That is if your wiring is like USA wiring, at least.)

But safety grounding isn't just about “dirt” — think about the kitchen. You've got electric appliances, salty (conductive) water involved in cooking, possible spills and/or damaged wiring —

In a DC situation there is no hot wire, and

This is true but misleading. The reason we use the term “hot” with AC only is because AC voltages reverse all the time and so we can't just say “the positive wire” or “the -5V wire” or such. A way to describe either case would be to say “not at 0 V”. (Nominally in that resistance in wiring means that almost nothing is at exactly 0 V.)

(correct me if i'm wrong) but if I have a 350v Capacitor fully charged, there is absolutely no way for me to get electrocuted unless I touch both terminals.

If you had a 350 V AC power source that was isolated, then you could touch one terminal and be just as fine as in the capacitor case.

(Well, mostly fine. Because AC can pass through capacitors, and lots of things are a little bit like capacitors, there could be some current flow, though not much if the other terminal isn't connected to anything and therefore has no opportunity for capacitive coupling of its own.)

But your household AC line supply is not isolated — the neutral side is joined to earth — so it is not safe in this way.

people say step 4 is to ground that wire, How? The car is insulated from the earth All I see is an open circuit.

What they're not showing in the picture is that the “Yours” car is assumed to have the negative battery terminal connected to the car's metal frame, thus completing the circuit in the picture.

The reason for that hookup scheme is not anything about the electric circuit itself — it's because the final connection when current starts to flow may make an arc for a moment, and you want that arc to be away from the battery so it doesn't ignite any hydrogen gas that may be in the vicinity. (Mistreated lead-acid batteries electrolyse their water and thus produce hydrogen gas.)