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Today I used a 12 volt power supply to observe electrolysis of water.

I mixed table salt into the water, nothing else.

The leads coming from the power supply had clamps on their ends.

When in water bubbles started evolving on the clamps.

Does this damage the clamps in any way ?

Is there something I should put in the clamps to improve this experiment ?

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It depends on the substance you have used for your electrodes. If they are in platinum, they will not be altered. If they are in carbon (charcoal, graphite), they will not be chemically tansformed, but after a while, they will be slightly corroded, and some powder of charcoal will progressively appear under the electrode on the ground of the flask used for the electrolysis. If they are in copper, there will be oxidized and a chemical reaction will occur at the anode. The copper metal will be oxidized and transformed into $\ce{Cu^{2+}}$ ions, which will produce a precipitate if the solution is basic or contains an anion like phosphate or carbonate. If the electrodes are in iron or zinc, the anode will be quickly corroded and transformed into the corresponding ions. In the beginning, the cathode will not be altered, but in the long run, they will also be corroded, specially if the solution is acidic.

Anyway you have not described the composition of the electrolyte. Common metals like iron and zinc are altered by acids, with or without electrolysis.

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This question goes to the heart of production of H2 from water for the "hydrogen economy." An excellent question. Although the chemistry at the cathode, H2 production, for water hydrolysis seems to have been worked out, the stumbling block is the long term stability of the anode. Generally as practiced, both oxidation and reduction occur simultaneously. Looking at it another way, it is the oxygen production part of water hydrolysis that makes hydrogen production from water difficult.
See Nat Energy 4, 786–795 (2019). https://doi.org/10.1038/s41560-019-0462-7 for an interesting approach to the question. Short answer is yes, and the biggest changes seem to occur at the anode.

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