I have a silly question relating to ground. If i have a circuit that has a ground symbol on it, can i always substitute this for a negative power source terminal? If it must be ground then how can i properly test that i have a ground connection? Is it possible to see a potential difference between a power source terminal and an earthed ground terminal (using a DMM)?
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I do not think so. Because ground is a common place (which may have some relative potencial but we assume that it is our 0) and in regarding to this potencial we calculate the voltege(U=V1-V2) in our circuit. However you cannoct substitute it by minus potencial. eg. in OAMP (http://upload.wikimedia.org/wikipedia/commons/9/97/Op-amp_symbol.svg) sometimes you have to supply it with +/- voltage
You can not substitute for a negative power source, but can mark as negative(potential, not power source) just to represent the current flow direction for your convenience.
Remember that ground acts as a source/sink for current, always remaining at zero potential. Moreover, we are always concerned with the relative potential difference. For example, if two terminals are at -2V and -4V respectively, then current will flow from -2V to -4V (relatively +ve to -ve).
Yes, you can measure potential between a -ve terminal and GND with DMM,
GND -> -ve terminal = +V (potential difference)
-ve terminal -> GND = -V
What matters in a circuit is potential difference. A potential difference across a resistor results in current flow, a changing potential difference across a capacitor results in charge accumulation on the plates, a changing magnetic flux through a coil induces a potential difference across the coil (inductor) terminals, a battery creates a potential difference between its + and - terminals. Nowhere does the behaviour of a circuit rely on the "absolute" potential of any point in the circuit.
The concept of "absolute" potential does not even make any sense from a physics point of view because potential is defined as the work per unit charge in moving from some point A to another point B so by definition potential is measured between two points. Quite often we decide a point at infinity has 0 potential and then measure all voltages in space with respect to that. That's probably as close as you can get to a definition of absolute potential.
What is the point of all that? You can decide that one node in your circuit has any "absolute" potential you want for purposes of calculations. This is the ground node that you arbitrarily decide is 0 volts. You could decide it is -5 volts, -a million, + a million. It does not matter since the circuit operates on potential differences but 0 is a very convenient number for purposes of calculations. A ground symbol does not necessarily mean that point of the circuit is Earthed (I should be careful because there are different kinds of ground symbols and one of them used by electricians *does* mean it is earthed). There are several types of ground symbols -- signal ground (a point where circuit signals are measured against), chassis ground (the physical body of a device), analogue ground, digital ground, etc.
So to answer the question, yes you can decide the negative terminal of the battery is at ground. But keep in mind there can only be one electrical node in the circuit that can be called 'ground'. Is it possible to see a potential difference between earth and a circuit ground? Yes it is unless the circuit ground also has a connection to earth. In your home's electrical outlet you have three prongs : one is the 'hot' which comes from the utility and carries 120V ac, another is the neutral which is the home's electrical ground and the other is earth. Both the neutral and earth wires are physically grounded at the point electricity enters the house but the neutral wire carries current under normal operation and its finite resistance means there is a voltage drop. So the neutral and the earth wires are not at the same potential at the electrical outlet.
Another example is an isolation transformer. On the primary you have power provided by the utility and one side of the primary winding is earthed. On the secondary, a potential difference related to the windings ratio is created but if that secondary has no connections to earth, it can "float", ie a potential can exist between the secondary's circuit "ground" and earth. This is called an isolation transformer.