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My circuits knowledge is (mostly) limited to ideal circuit theory, where:

  • An ideal voltage source maintains a prescribed voltage regardless of current flowing though its terminals
  • An ideal current source maintains a prescribed current regardless of voltage across its terminals

The below circuits are not permissible according to ideal circuit theory, but obviously they could be connected as shown. Im trying to gain a better sense of what happens in real (physical) circuits when connected improperly.

schematic

simulate this circuit – Schematic created using CircuitLab

In reality, what happens if power sources are connected in violation of ideal circuit theory?

I expect the answer depends on specific power sources and their internal circuitry - a power source might fail, or regulate mismatched current/voltage, etc. Still, is there a predictable outcome to this type of problem and how is that outcome determined?

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    \$\begingroup\$ Add an internal resistance to your generators (series and small for voltage gen, parallel and big for current gen) and then make the resistance tend to the ideal limit (zero for the voltage gen, infinity for the current gen), a see what happens. You'll end up with the average voltage or current. In practice, all depends on the actual values of the internale resistances but if you take the limit you will see why Ltspice, for example, uses the average. \$\endgroup\$ – Sredni Vashtar Sep 10 '16 at 6:32
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The first thing you have to realize is that "real" power sources are themselves not ideal. Voltage sources have non-zero internal resistances. Current sources can only produce a limited range of voltages (called compliance). So, for instance, connecting two voltage sources in parallel will look like

schematic

simulate this circuit – Schematic created using CircuitLab

and in this case will produce a current which is equal to the voltage difference divided by the total internal resistance. Note that the circuit is now an "ideal" circuit.

There is no guaranteed way to tell how circuits will behave, unless you have a complete description of the components. Just as voltage sources have internal resistances, they will also have inductances, and in some cases will behave as if they have complex internal capacitances as well - batteries, for instance.

Plus, real power supplies will commonly only be able to source current, and are not at all good about sinking it, which requires the use (at least) of a diode when modelling the supply for real.

About the closest you'll get to your "non-ideal" connection is jumping a dead car battery. When connection is made, the strong battery will be called on to produce a lot of current, and in bad cases the current will damage the jumper cable. However, a discharged battery looks more or less like a resistor/capacitor combination, so after a while the current flow will drop to a much lower value.

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    \$\begingroup\$ Some voltage sources are very non-ideal above their rated voltage (because they have explicitly not been designed as voltage sinks) - in which case the circuit may just assume the higher voltage and no current will flow. Batteries are not examples of this type... \$\endgroup\$ – Brian Drummond Sep 10 '16 at 9:54

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