Two power sources

Question

Please consider a circuit with two loops where the two loops have a common part with a single resistor. There are two power supplies (or of it matters say these are voltage sources, like batteries, say the 9v and or 1.5v ones that can be acquired in every supermarket) - the latter two objects are located in separate loops, in a way that the positive terminales are faced towards the same junction point.

See the drawing for visuals.

What is happening here? Is the drawing wrong or is it forbidden to draw such a thing?

Could you please comment the followings, if these are true, false, undicidable, or evil in itself: (my intuition is definitely wrong about electricity. Please help!)

1. Kirchhoff s law, applying it to the two smaller loops, immediately says that the two power supplies have equal voltage. Now, this is not necessarily true, so the law can not be used.
2. The two power sources are together provide a bigger voltage and these push more charge through the circuit. (Like if these were water sources with pressure.)
3. If one power supply have more voltage then the other, then there is a short circuit type situation, because there is less preassure in one of the terminals then the other, and hence, electrons flow towards lower potential without resistance - avoiding the resistance that is present in the circuit.
4. There is no third loop - that avoids the resistance, because electricity can not flow from positive to positive terminal.
5. There is only one loop.

Is my question related to power supplies connected in series vs parallel?

What should I look up? Could you point me to some reference?

Its hard for me to say but I have a phd in math, and now I feel stupid - all this because I would like to build a synth.

My question is motivated by a current source wireing of a transistor: I can not guess what to do with the two separate power supplies.

Answer 1

Kirchhoff s law, applying it to the two smaller loops, immediately says that the two power supplies have equal voltage. Now, this is not necessarily true, so the law can not be used.

This is incorrect. KVL says the voltages will be equal, and they will be equal.

The two power sources are together provide a bigger voltage and these push more charge through the circuit. (Like if these were water sources with pressure.)

No. Two voltage sources in parallel will not create a higher voltage.

If one power supply have more voltage then the other, then there is a short circuit type situation, because there is less preassure in one of the terminals then the other, and hence, electrons flow towards lower potential without resistance - avoiding the resistance that is present in the circuit.

Close. If the the two voltage sources have different open circuit voltages, then when they are connected, current will flow from the higher voltage source into the lower. But some current will also flow through the resistor. By Ohm's Law, since there is a voltage across the resistor, current will flow through it.

There is no third loop - that avoids the resistance, because electricity can not flow from positive to positive terminal.

Not sure what this means, but what will happen has been described above.

There is only one loop.

That is just silly.

Answer 2

This will lead to infinity amount of current if V1!=V2 because there is no resistance between those two. In real life, the source impedance of the voltage source will prevent that, but using ohms law, this is an impossible circuit.