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.