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In Horowitz The Art of Electronics on page 72 there is a schematic that provides an "ohmmeters view" of a transistor (see below.) In the description it says:

The base–emitter and base–collector circuits behave like diodes in which a small current applied to the base controls a much larger current flowing between the collector and emitter. Normally the base–emitter diode is conducting, whereas the base–collector diode is reverse-biased, i.e., the applied voltage is in the opposite direction to easy current flow.

The picture provided in the book.

Shouldn't the two diodes be switched? That is, shouldn't the B-C diode be the Zener one and the B-E diode the normal one? It says that the base-emitter diode is conducting and the base-collector diode is reverse-biased. Zener diodes are mostly used in reverse bias, right?

Sorry if this is obvious or something. I'm not studying electrical engineering, I am doing a physics lab and trying to understand transistors.

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The diagram is correct; the use of the Zener diode as the base-emitter connection is to remind the reader that the reverse breakdown voltage of the base-emitter region is much smaller than the reverse breakdown voltage of base-collector.

And, in relation to an explanation of how you might test a BJT using an ohmmeter, you have to be conscious that a fairly low voltage (usually less than 10 volts) can cause Zener breakdown when positive is applied to emitter and negative to base (NPN BJT).

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