What is ground and what does it do?

The first time I tried to do the current calculation for a circuit similar to the previous circuit on a simulator, the program complained about not having a ground and "floating voltage sources".

Your simulator wants to be able to do its calculations and report out the voltages of each node relative to some reference, rather than have to report the difference between every possible pair of nodes. It needs you to tell it which node is the reference node.

Other than that, for a well-designed circuit, the "ground" has no significance in the simulation. If you design a circuit where there is no dc path between two nodes, though, the circuit will be unsolvable. Typical SPICE-like simulators resolve this by connecting extra resistors, typically 1 GOhm, between every node and ground, so it is conceivable that the choice of ground node could artificially affect the results of a simulation of a very high-impedance circuit.

I picked ground at the bottom, but would it be okay to pick ground between the 7 ohm and 2 ohm resistor - or any other place? And what would be the difference when analyzing the circuit?

You can pick any node as your reference ground. Often we think ahead and pick a node that will eliminate terms for the equations (by setting them equal to 0), or simplify the schematic (by allowing us to indicate connections through a ground symbol instead of by a bunch of lines connecting together).

I've read that there are 3 typical ground symbols with different meanings - chassis ground, earth ground, and signal ground. A lot of circuits I've seen used in exercises use earth ground or signal ground. What purpose is there in using earth ground? What is the signal ground connected to?

Earth ground is used to indicate a connection to something that is physically connected to the ground beneath our feet. A wire leading through the building down to a copper rod driven into the ground, in a typical case. This ground is used for safety purposes. We assume that someone who handles our equipment will be connected to something like earth ground by their feet. So earth ground is the safest circuit node for them to touch, because it won't drive currents through their body.

Chassis ground is just the potential of the case or enclosure of your circuit. For safety purposes it's often best for this to be connected to earth ground. But calling it "chassis" instead of "earth" means you haven't assumed that it is connected.

Signal ground is often distinguished from earth ground (and partially isolated from it) to minimize the possibility that currents flowing through the earth ground wires will disturb measurements of the important signals.

Another question: since the ground is at unknown potential, wouldn't there be current flowing to or from ground to the circuit?

Remember, a complete circuit is required for current to flow. You would need connections to earth ground in two places for current to flow in and out of your circuit from earth ground. Realistically, you'd also need some kind of voltage source (a battery, or an antenna, or something) in one of those connection paths to have any sustained flow back and forth between your circuit and the earth.

However, when there are multiple voltage sources, some of them are "floating". What meaning does the voltage of a floating voltage source have?

If I have voltage source with value V between nodes a and b, it means that the voltage difference between a and b will be V volts. A perfect voltage source will generate whatever current is required to make this happen. If one of the nodes happens to be ground, that gives you immediately the value at the other node in your reference system. If neither of those nodes happens to be "ground" then you will need some other connections to establish the value of the voltages at a and b relative to ground.

Sometimes people get confused just by the many definitions of the word.

ground
noun

1. the solid surface of the earth; firm or dry land: to fall to the ground
2. Often, grounds. the foundation or basis on which a belief or action rests; reason or cause: grounds for dismissal.

In the context of electronics, sometimes ground means sense 1 above. Earth is, after all, approximately a \$6\cdot10^{24} kg\$ ball of iron. Like everything else, it exists at some electric potential, and if you stick a long conductive rod in Earth, you can make other things connected to that rod at approximately the same potential:

Of course, Earth is really big. Not all of it is at the same potential. In fact, not even close. Earth's huge magnetic field is constantly changing, and induces currents all over Earth. Other people have their own rods stuck in Earth and put currents in Earth. Lightning moves tremendous current in Earth. Since Earth is not a perfect conductor, and by Ohm's law any current through any resistance much be accompanied by a voltage, the potential between two points on Earth is not the same, unless you are lucky, or the points are very near each other.

And, if you've ever operated a battery powered device, you know that electronic devices can function perfectly well without a connection to Earth. Yet, these devices do have a ground. So, this is probably not the sense of ground you should use for your basis of electrical understanding. The other sense, the basis on which a belief rests, is probably a better start.

It's a very astute observation that your confusion involves voltage, as well. Ground is, simply put, \$0V\$. But to understand what this really means, one must really understand voltage. Many people fall into the trap of thinking that since ground is \$0V\$, then ground is where there is no voltage. Thus, there must be voltage everywhere else. But, once you understand voltage, you see this can't be true.

So what is voltage? The more rigorous term for it is electric potential difference. All three words are part of the understanding of voltage. Electric is obvious.

What about potential? Potential has specific meaning in physics. Potential energy is the capacity for some arrangement of things to do work. For example, a compressed spring, a stretched bow, or a high-pressure tank of gas have the potential to do work, if released.

Imagine a ball at the top of a ramp. If the ball is allowed to roll down the ramp, at the bottom, it will be moving quite fast. It acquired this kinetic energy from the potential energy it had at the top of the ramp. If there were no other losses (friction, for example), then the kinetic energy gained by the ball is equal to the potential energy it lost, by the law of conservation of energy.

That's potential energy. Just potential by itself has a different definition: it is potential energy per unit of stuff at some point in a system. Obviously, a massive ball at the top of the ramp has more potential energy than a small ball at the top of the same ramp. So, the two balls have different potential energies at the top of the ramp, but they are at the same potential.

The relevant kind of stuff it is depends on the kind of potential. For gravity fields, the stuff is mass. For electric fields, the stuff is charge. Potential energy is measured in joules. Gravitational potential is measured in \$J/kg\$. Electric potential would then be measured in joules per coulomb (\$J/C\$), which actually, is exactly the definition of the volt.

So earlier we said voltage is electric potential difference. What's the difference? Imagine again our ramp. If you assume that gravity is equally strong anywhere on Earth (this is only approximately true, but is a valid simplifying assumption for much practical engineering), then does the location of the ramp matter? It could be in Death Valley or on Mount Everest: the ball, after rolling down the ramp, will have at the end the same kinetic energy. The potential at the top and bottom of the ramp is irrelevant; the important thing is the difference in potential between the top and the bottom. If we are assuming that Earth's gravity field is the same wherever we might take this ramp, than just the height of the ramp is relevant.

So, since voltage is a difference, we need two points to have a voltage. If we say some node in a circuit is \$5V\$, then we are saying it's \$5V\$ more than some other point. Ground is that other point, unless context says otherwise.

A similar convention exists with height. If I say the height of Mt. Everest is \$8848 m\$, you will assume I mean its height is \$8848m\$ more than sea level. I can also override this reference with explicit context. For example, I can say Mt. Everest is \$237m\$ higher than K2. The default reference can change, also. For example, if I say that Olympus Mons is \$21229 m\$, you probably don't assume this is above sea level, but instead some equivalent datum on Mars. There is no universal reference for elevation.

This is why ground is \$0V\$, just as sea level is \$0m\$. It's not that ground has no voltage, or sea level has no elevation: it's that these things are differences, and the difference between a thing and itself is \$0\$. Thus, there is no magic about ground. It doesn't do anything. It's just a node in the circuit, just like any other. It's only by definition that it is also \$0V\$, and this definition exists just as a convention to simplify our discussion of a circuit. There is no universal ground or \$0V\$ until we define something as such. Usually, it's just whatever we decide to stick the ground symbol on. We can put it anywhere we like, but we usually put it where it makes calculations easiest and discussion simplest.

Related questions:

• Is voltage a delta? Can it always be treated as a potential difference from a reference point?
• Difference between negative terminal and copper ground?

See my answer here about what ground is and how the term "ground" is used in electronics. Significant parts of that answer are also relevant to the question here.