An ideal op amp is given (with infinity gain), what is the current flowing through all the resistance for the given circuit?
It is unclear from those diagrams how current flows from the op amp output pin back to ground. Current must flow in a complete loop, which involves the +DC supply, and the -DC supply going to the op amp.

So let's take your example 10 ohm circuit and see where current flows. There will be one amp of current flowing in this circuit. Your ideal op amp will maintain its output voltage at zero volts (because its two input pins will be at 0V).







simulate this circuit &ndash; Schematic created using CircuitLab

One amp flows through the 10V supply (V1), through R1 and into the op amp output pin. From there, it continues through the op amp to the -DC supply (which is grounded). That's a complete loop. No current flows through R2, and no current flows through R3. No current would flow through the +ve supply in this ideal case. In a real op amp, internal circuits draw a little extra current from its DC supplies.