I realize connecting two different voltage sources in parallel is a contradiction (in an ideal circuit). But if I were to connect this in practice and measure the voltage across points A and B, what value of voltage would it show? And how much current would be sunk by the 5V battery? (Non ideal conditions)
Answer
That totaly depends on the internal resistors of the voltage sources.
simulate this circuit – Schematic created using CircuitLab
Then you can use the superposition principle and calculate the voltage level on the top of the circuit.
So, if both internal resistors have the same value the voltage V_out would be 7.5V. With other resistor values the voltage can vary between 5V and 10V.
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