Soz for the lengthy quote but I think this is a good post to fall back to.
Perhaps the interested parties could just fill in appropriate values for voltage, resistance, current, etc., instead of rambling off about everyone else not understanding stuff. I've had a go.
Isn't the circuit on the left essentially two separate circuits, each burning 1W? The circuit on the right is a single circuit burning 2W overall. But the currents and voltages across the resistors are the same in each.
Suppose on the left you have just one circuit - let's delete the bottom battery, wires, resistor. So it is now a single circuit burning 1W. That top wire is passing 1A. On the right it is still passing 1A but the circuit is burning 2W, so how is that extra 1W getting around if the top wire is passing no more current (with no difference in voltage drop)?
I see that is not just hamster_nz that is confused. You seems to have the same confusion.
The two circuits due to symmetry are not different in any way. From an electrical point of view they are identical as that wire in the middle has no electrical role (no current meaning no electrons flow through that wire).
But I guess same as hamster_nz you agree with the above fact is just that you do not understand what power and energy is.
Both power and energy are calculated and not measured.
What you measure is just voltage (pressure will be the analog for fluids) even the current is not measured but calculated as the voltage drop on a length of wire with known resistance.
Also just to be clear there is no current flow through that piece of wire connecting the GND symbol.
One electron has a charge of about 1.6 * 10
-19C
So 1A for one second 1As a number of 1/1.6*10
-19 = 6.25 * 10
18 electrons flow each second trough that wire.
That is a huge number of electrons that flow through the wire each second.
So that number of electrons leave the negative of the bottom battery every second and travel all the way around the wires/resistors (wires and resistors are the same thing) and enters the positive of the top battery.
At the same time same number of electrons leave the negative of the top battery and enter the positive of the bottom battery.
The above is valid for both diagrams thus there is no difference between the two.