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As input voltage increases, input current decreases. Conversely, as the input voltage approaches zero, the input current approaches infinity. These high input currents at low voltage can damage components. Usually at highest risk are the semiconductor switches in switching-mode power supplies, which may be driven well outside their safe-operating region.
The problem often occurs at turn-on, when the source voltage starts at zero and then increases to the desired operating voltage. Failure can also occur at turnoff but is not found until an attempt is made to turn the supply on again. Then the failure is usually classified as a turn-on failure - masking the real cause of the failure and complicating trouble-shooting.
A common mistake in lab checkout of prototype designs, before protection is added, is to start with zero voltage and slowly bring the voltage up. Rather than minimizing stress, this can apply maximum current stress to the design causing failure.
Do not use this information for design without independent verification of the information.