Do current limits apply just the same on lower voltage?
Yes, the fuse only reacts to current.
The fuse does not &quot;see&quot; what voltage is applied, the fuse reacts only to the current flow. If you connect a lower voltage to your circuit, then the load impedance can also be lower before the maximum current is reached, but the value of the maximum current stays constant.
Fuses do have voltage ratings, but they mean something different: The voltage rating of a fuse tells you, up to which voltage the fuse guarantees to work. If the fuse has a rating of 500 V, then it might fail for an applied voltage of 750 V by arcing over.