What's the potential difference across gap a and gab b

Question

My book insists that the gap across a and b is the same, i.e 33.33V. But I made the circuit in a simulator and the simulator says the difference across gap a is 66.66V and the difference across gap b is 0V.

I don't believe either to be correct. One end of gap A is connected to the positive terminal of the cell but the other end is connected to nothing. There's nothing for us to compare the potential difference with.

The only way the simulator's answer is correct is if we assume that the left end of gap C is connected to the negative terminal of the voltage source or equivalent (i.e both are grounded).

For context. This is a question on transient analysis of RLC circuits. I have attached the full question and the solution from the manual below.

Answer 1

Both are correct. Our at least, they're not wrong: if we actually model these things as gaps, their voltages are completely undefined. They might just as well be a=1099, b=-1033.

If we, however, model these gaps as actual capacitors with a time history where they were connected, then yes! They are charged to the same voltage when the switch opens and stay that way. Anything else would require charge to just disappear!

Answer 2

It would be undefined if they were just gaps.

But in the circuit they are not gaps.

They are two identical 1F capacitors, so before flipping the switch, both are fully charged to 1/3 of 100V.

Answer 3

A capacitor cannot be modeled as a gap, and a gap cannot be modeled as a capacitor.

For analysis of a steady state system the capacitors can be removed but the voltages remain. as well, the inductors can be replaced with a short, but the current must remain. This is a snapshot at one particular instance and so cannot be simulated correctly.

The textbook is correct.