simulate this circuit – Schematic created using CircuitLab
Figure 1. Original circuit redrawn using the built-in CircuitLab editor.
simulate this circuit
Figure 2. Redrawn with mains wiring removed for clarity.
Figure 3. Electrical equivelant circuit for even more clarity.
- If the two transformers' polarity matches as shown in Figure 2 and 3, and the output voltages are the same then no current will flow through the bells as there is no voltage (potential) difference across them.
- When SW2 is pressed both bells will have a return path to their respective transformers.
- If the transformers are wired in anti-phase (either on the mains side or on the low-voltage side) both bells will ring continuously.
The circuit is safe but very unusual.
From the comments:
- Given that two transformers never have perfectly the same output voltage, does this mean that probably some (little) current flows permanently in the bells (perhaps ~0.5 V), even if the button is not pressed? Is this a problem?
Yes, a little current will flow.
It could be a problem if it's enough to heat the coil given that it would be on continuously. You could tell by touch.
- How can we know that each bell's return path is its own respective transformer, and that the current doesn't flow to the other transformer?
Since current flows in a loop what leaves the top terminal on each transformer must return on the bottom terminal. Technically the mobile charge carriers (electrons in the case of metallic conductors) could cross over but the quantity in each branch would remain correct.