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That depends on the zener voltage rating:

  • "low voltage" zeners are just a simple single diode, the zener diode
  • "high voltage" zeners contain 2 back to back diodes in one package, the zener diode and an ordinary diode that is reverse biased when the zener diode is forward biased to block forward conduction of the zener and protect it from overcurrent damage if installed backwards by mistake

Thus in "low voltage" zeners when forward biased they will have a normal diode drop (e.g. 0.7V), but "high voltage" zeners when "forward biased" they will act open due to the reverse biased blocking/protection diode in series with the zener.

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