I want to perform water electrolysis to produce hydrogen and oxygen gas. I am confused which will be more efficient for hydrogen and oxygen production. Higher voltage or higher current. and what will be more cost efficient.
The voltage and current are correlated through the Ohm's Law. However, in water electrolysis, the voltage is important that current as it drives the ions through the electrolyte.
Ideally you want low voltage, high current - the industrial dream would be 20 A/cm2 at 2V. Anything above 1.23V is overpotential. Cost efficiency is a tricky question - the lower your overpotential, the greater your energy efficiency, but to get a set output (e.g. 1 slpm/s), you'd need to increase your cell area a lot, and that can massively increase the capital cost of the device. Further complicating matters, the stack has a given lifetime that potentially may be more about total operation time than total current passed, adding to the cost per litre for high-efficiency operation.
For instance, in PEM electrolysis, where Pt loadings are gigantic and going larger can massively increase costs, and breakdown rate from what I've seen isn't massively affected by overpotential, industry is all about high-as-possible currents.
There may have another sweet spot in your cost/L H2 because you're using less expensive materials, but for a first crack at a model, assume you're operating at the very far end of your ohmic region, e.g. right on the edge of large mass-transport losses kicking in.