"Bigger" depends on how to define this.
Voltage peak, V x t ,[volt-seconds], or power = V²/R = V²(f,t) / (real{Z(f,t)})
There are a few basic rules to electronics.
- All insulators = dielectrics
- this includes the interwinding capacitance of large inductors and the dilectric medium (Water has a Dk=80, Air =1) so bigger chokes is not always better.
Here's a simple experiment.
Use a rasp file as an intermittent switch with a nail slide and a decent air coil with a spark plug and close the electrical circuit with the series loop current using a tap off the larger coil which is open to the spark plug as a step up transformer. 1:10 to 1:100 using a good low ESR battery. Avoid shocks and battery heat. The low C of Air and low L of an air coil will give a very high f resonance yet a very fast rise time and voltage . 2~3kV/mm for a 3mm spark plug = 6~9kV
- i.e. they all have capacitance and a relative value of Dk compared to air which is close to the vacuum reference. But with a low impedance 12V LED String with reverse diode protection, you can power it from a D Cell temporarily this way. Just remember polarity , you make the low side intermittent to generate a positive spike when current is released from L.
Vp = LdI/dt and dV/dt= I/C which combine give the resonant frequency and impedance ( look up)
meaning they have a Capacitance per unit area of the electrodes volume which increases with reduced gap, as does the breakdown voltage in kV/mm. Hydrogen also has a lower explosive limit of 4% with some trigger voltage.
the lower the FET RdsOn the larger the Coss during transition , although this has a geometric and packaging variation as well as Voltage rating so examining 50k different varieties of FETs with a spreadsheet from D-K can find the best for T=Ron x Coss time constant not given in datasheets.
There are many basic ways to chemically separate atoms in molecules such as electrolysis and it can can be done with DC, AC and HF pulses.
I am by no means an expert on Electrolyser design expert but you can learn what has worked for certain parameters of size and efficiency then match or try to improve it with electrode materials and methods.
With a free registration, you can read how H2 Electrolyzers work. https://www.researchgate.net/publication/341293476_Proton_Exchange_Membrane_Electrolyzer_Modeling_for_Power_Electronics_Control_A_Short_Review#fullTextFileContent
- unless you are trying something different.
You can use a MOSFET Buck regulator or DC 

There is a more than a quarter century of books and research papers on hydrogen cells yet this has not stopped Engineers and Chemists to keep improving the efficacy and safety of this next generation fuel cell.
If it was this simple, it would have been perfected long ago.
But if your goal is simpler, it's not that hard, just refine your specs. (not given) and Re-google ehhm, I mean research. ;}