You need to be a bit more specific about what you want I think.
A power supply can supply a fixed voltage, or a fixed current, but it cannot be both at the same time.
If the load changes, either the voltage or the current will have to change, depending on the mode that the power supply is running.
No, a PSU can either be constant voltage (CV) or constant current (CC) but not both at the same time..
When in CC the voltage is determined by the load due to ohms law ......... V_CC = I_CC . R_Load
When in CV the current is determined by the load due to ohms law ......... I_CV = V_CV/R_Load
When in CV, as R_Load decreases and the current drawn approaches the set current limit of the PSU (by set-point or PSU limitation) the PSU will shift from CV to CC operation and the voltage will drop accordingly.
Similarly, when in CC, as R_Load increases there comes a point where the PSU output voltage can no longer increase (by set-point or PSU limitation) and so the PSU moves from CC to CV operation and the current drawn will drop accordingly.
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