Ground connection or referencing is used when it is used because long experience has shown it to be the best choice in practice. "Reinventing the grounding "wheel"" may have its place in some cases, but usually not. In many cases there are competing aspects, but the overall best result is gained by using ground. Power distribution systems are one such example.
Mains or grid voltage systems would be safer if the system was entirely NON ground referenced, and this is the principle that safety "isolation transformers" use BUT the moment that a fault fully or partially grounds one leg of the system anywhere on a circuit then the whole system becomes lethally dangerous to users.
Note that ONLY ONE tool should be used with an isolation transformer, and the transformer should be located near the tool. Using long cable runs after the transformer and two or more tools risks a fault to ground in one tool or wiring leaving the other unprotected.
The difficulty in keeping a system isolated is in practice (which is what counts) far harder than the issues caused by grounding. Some shipboard power systems do have both conductors floating relative to ship ground (= seawater potential when you are floating in salt water) BUT and fault to ground is dangerous, as above, ad great effort is made to track down and remove any ground faults. In a land based system that was not ground referenced, any fault to ground on the same phase would affect all users on the same phase. So a whole street of houses may be affected by a fault on one circuit in one house.
Once you have a ground referenced system the safety aspects of detection and management for individual circuits are easily handled. Earthed housings provide both protection and detection, fault currents flow to ground and can be either "encouraged" to allow easy fault termination (fuses) or detected at very low level (ELCB / GFI). Ground referencing is an overall positive in domestic power systems.
Few modern systems use ground as an actual conductor.
SWER (Single Wire Earth Return) power systems were much used at one time and are still used in some rural systems. I saw one here (NZ)some months ago but they are rare. They are in fact very useful and cost effective but are generally eliminated for reasons which often do not make technical sense. The cost of providing a good enough ground connection at each end is in most cases low compared to he cost of many km of adding an extra conductor.
19 kV SWER line:
Wikipedia SWER
SWER slidehow - good
SWER video - NZ
Superb SWER slideshow / tutorial
SWER - Australian experience with application to developing country use
SWER - Wikipedia
RF signals are often "launched" as imbalanced signals against a phantom image reflected in the ground. A typical quarter wave vertical radiator has an implicit image reflected in the ground plane. The tall towers of AM brodcast stations almost all use this system. There are economies in materials used compared with dipole or other antennas, radiation pattern is omnidirectional and radiation angles are suited to direct wave communications - most audiences are near the transmitter for AM broadcast stations.
- TV receiver antennas 9the traditional Yagi designs) and long distance broadcast stations used for intercontinental news etc often use beam or similar aerials instead. The HRH delta Loop non ground referenced antenna was developed specially for and from such applications.
In systems that need grounding, techniques have been developed to provide grounds which are adequately good to adequately minimise the effects of local conditions. Ground proper is of essentially zero resistance as it is of sensibly infinite size. Connecting the local ground to the actual ground is the challenge and methods and needs are well understood for each relevant application.
Short answer is Yes.
The differences in geology (chemical, water content, magnetic (Earth's magnetic field), electrical disturbances (including lightning), physical stresses) mean they are different.
Remember the Earth is a rubbish conductor (mixture of insulators, semiconductors, conductors and liquids in random proportions from place to place) so if you tried to harness this I believe you won't get much consistent power.
You might get a huge magnetic input of power during a solar storm due to the changing magnetic field of the Earth as it interacts, but until we can store such unpredictable power, it is of limited use.
Best Answer
It doesn't know nor care. Opamp's internal circuitry works like this:
Uout is near 0V when U1 < U2 and Uout is near the full supply voltage Us when U1 > U2. Just around the case U1=U2 there's a transition zone A. Its width in practical opamps is well below one millivolt. Nobody guarantees that the zone is linear or symmetrically around the zero, but normally opamps are used with a feedback circuitry which forces the opamp to output such Uout that U1-U2 is inside the transition zone.
People often divide Us to two parts in series. The upper part is said to be the positive supply and the lower part is said to be the negative supply. The midpoint is said to be the ground and all voltages in application designs are referenced to it. But internally the opamp references all to one of the poles of the supply voltage Us.
In low cost IC designs the internal circuitry cannot accept U1 and U2 to be whatever, they must be between 0 and +Us and there's some margin needed. The margin is needed at least in one end of the range 0...+Us to leave some operating room for the internal circuitry.
Many buyers want no margin at 0V, they want that U1 and U2 can be 0V. If the internal circuitry is designed properly (=PNP input transistors), the usable range for U1 and U2 is from zero to 1...1,5V less than Us. One old and well known IC design LM124 is like that. Analyzing its internal schematic reveals that it actually uses the plus pole of the Us as its internal reference point, but that makes no difference to my drawings and equations.