Are you breaking down, zener? This is the first question you should ask when you see a zener circuit as such:
Zener is usually used under reverse bias, so hopefull everyone can see that the zener in the circuit is reverse biased.
What is VZ? VZ is the zener breakdown voltage, that is, if the supply voltage is greater than VZ, the zener will be conducting, ie, under breakdown or avalanche. If the VZ is 13 volts which is just at the point that the zener starting to conduct, so what is happening?
Well, imagine that you are increasing the source voltage from 0 to 13 volts, to the point that the zener is starting to conduct, there is no current, so there is no voltage drop across the resistance R and the zener should be the same as the source because KVL says, VS=VR+VZ and here VS=VZ because VR=0 (I=0).
It’s that simple!!! At Vs=13V for VZ=13V, I=0 and VR=0 and VZ or VD=13V. As Vout=VD, so Vout=13V (=Vs). IZ=I=0. Power=0. What else can be said?