Different and opposing voltage sources?

simulate this circuit – Schematic created using CircuitLab

The diagram above, the voltage sources are equal and wired parallel, they would increase the current(2x) flow to the load(R), but what about this case:

simulate this circuit

Are the two voltage sources in series now?

• You could say they are in series in a short circuit. Output will be 0 (or smoke). – Brian Drummond Oct 14 '15 at 22:59
• The dual of your question (ideal current sources in series, instead of voltage sources in parallel) was asked before: Current and voltage sources? – The Photon Oct 14 '15 at 23:02
• The answer is the same: You have either created a contradictory circuit, or your model of your voltage sources is inadequate to predict the behavior of the circuit. – The Photon Oct 14 '15 at 23:02
• Basically a duplicate of electronics.stackexchange.com/questions/192584/… but I'm out close votes for today. – Fizz Oct 14 '15 at 23:33

1 Answer

You have drawn a circuit that expresses a logical contradiction, just as much as if you wrote down the mathematical equation

$$5 = -5$$

One way you could resolve this is not drawing contradictory circuits.

If you want to know what happens when you connect two physical power supplies in anti-parallel, then you must provide a more complete model of the power supplies. For example, if you include non-zero internal resistance in at least one of the supplies, you will not have a contradiction, just a very large current produced through the two supplies.

• I think my problem lies more with the fundamental theory, why is it in "anti-parallel" the voltages would not cancel out, while as in series they would. Given equal internal resistance. – Pupil Oct 14 '15 at 23:24
• In series, the voltages add. +5 + -5 = 0. In parallel, you assert that the voltages across the two components are equal (+5 = -5). – The Photon Oct 14 '15 at 23:26
• It's just the confusion of series/parallel voltage cancellation, in parallel opposing voltage would not cancel but would force current to one another, while in series they would :/ – Pupil Oct 14 '15 at 23:27
• When two elements are in series, there is equal current through them. (see the question I linked in comment on your question). When two elements are in parallel, there is equal voltage across them. You create a contradiction when you say that two voltages are equal (because two elements are in parallel) and that the voltage is equal to two different things (because the two elements are voltages sources with non-equal values, and an ideal voltage source forces the voltage between its terminals to be a certain value regardless of how much current it must source or sink to do so) – The Photon Oct 14 '15 at 23:30