Operational amplifier circuit, but one of Kirchoff laws doesn't work
There is a 'hidden' ground connection within each ideal op-amp for output current to return.  The output terminal of the ideal op-amp is connected 'internally' to an ideal controlled voltage source.  The other terminal of this source is grounded.

For example:



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If you redraw the op-amp with this hidden connection, you should find that KCL at the 0 node holds.



I'll demonstrate the problem as I see it and the solution.  Consider this simple ideal op-amp non-inverting amplifier circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

Clearly, KCL does not hold at the 0 node.  There is no current through the battery since there is no current into either input. Since the output terminal is at 9V, there is 9mA of current 'down' through the load resistor RL.  There is no other ground symbol shown and so there is no current through the ground symbol.  Summing currents at the 0 node gives

$$9 \mathrm{mA} - 0 - 0 \ne 0$$

in contradiction of KCL.

However, if we explicitly show the assumed grounded terminal of the controlled voltage source in the ideal op-amp model, it's clear that there is 9mA leaving the 0 node and entering 'the bottom' of the controlled voltage source, exiting through the output terminal.  Summing the currents now yields

$$9 \mathrm{mA} - 0 - 9 \mathrm{mA} = 0$$

satisfying KCL.