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I am learning how a Zener diode works.

Can anyone please explain me how to analyze this circuit (with equation if possible)?

Thanks.

enter image description here

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I don't find your circuit very helpfull in understanding / explaining what a Zener diode does.
I would suggest you try this circuit instead and see if that helps you to understand:

schematic

simulate this circuit – Schematic created using CircuitLab

And forget about equations for a moment, and before you simulate this circuit just think about: what happens if the sinewave is -10 V, 0 V, + 10 V ??? No need to be precise, just think: will there be a current flowing or not, what will be the voltage across the zener diode ?

Real engineers first think: What will happen ? Only then simulate to confirm that !

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