Current readings of Ammeter

Question

I was trying to solve this problem (number 27) and as per the KCL equations I am getting that an infinite number of Ammeter readings are possible.

I used KCL after taking the outer loop as the ground (ideal ammeter means voltage is the same everywhere in the outer loop). I found unique values for the currents in the inner loop but I need one more equation to uniquely determine the outer loop current?

I was unable to simulate this, an error (check circuit topology appeared in EveryCircuit). None of the options are among the infinite solutions I found. Can you help me find the answer?

Answer 1

Given that two voltage sources have the same voltage (4 volts) and series impedance (1 ohm), it is clear that A1 and A3 must have the same current and that both the currents (A1 and A3) cannot be zero amps. That leaves (1) as the only feasible answer.

If you combined the two identical sources in parallel (which of course they are because perfect ammeters have zero impedance), you reduce the problem to two voltage sources; a 3 volt source in series with 1 ohm and a 4 volt source in series with 0.5 ohms; a net impedance of 1.5 ohms with 1 volt net across it.

This then leads to a current flow of 0.66667 amps into the 3 volt source. In other words 1/3 amp each from the two 4 volt sources via their respective 1 ohm resistors.