Let us assume a Zener of 10V having a power rating of 1W. For that Zener the maximum current carrying capability is I = P/V = 1/10 = 0.1A. It is always preferred to use this Zener diode at less than or equal to 0.7 times of the maximum current rating. So, in this example, it is not preferred to use a diode beyond 0.1*0.7 = 0.07A. Also, for a zener diode it is not preferable to use the diode at a current less than 0.1 times of the maximum current. Any current below 0.1 times of the maximum current causes regulation of the Zener not to function properly. So, in the case of above example, minimum current where Zener can be used is 0.1*0.1 = 0.01A.
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