How is the output voltage calculated in clipper circuits?

I answered this SE EE question an hour ago. Here is my answer.

Looking for the idea

Perhaps we should first see what the meaning of all this is and only then determine the exact values ​​of the quantities…

The idea of ​​such a device called a "limiter" or "half-wave rectifier" is to "cut off" (do not pass through the load) one of the two half-waves (in this case the positive one) of the input AC voltage.

Implementation

This can be done in two ways - by turning off a switch in series or by turning on a switch in parallel during the positive half-wave (a diode can act as a switch).

Series limiter

In this configuration (not shown here), the diode is connected in series to the input voltage source and the load. So when the diode is on, the full voltage of the "ideal" input voltage source with zero internal resistance is applied to the load (excellent); when the diode is off, there is no any voltage applied (excellent).

Parallel limiter

In this (OP's) configuration, the diode is connected in parallel to the load. But the input voltage source cannot be directly connected to this network because, when the diode is on, the source would be shorted by the diode acting as a "piece of wire". That is why, the voltage source is connected through a resistor limiting the current (figuratively speaking, the "ideal" voltage source is intentionally worsened and converted to a real voltage source with significant internal resistance).

So when the diode is off, an undesired voltage divider is formed by the resistor and the load... and only a part of the input voltage is applied through the resistor to the load (bad); when the diode is on, the load is shorted and there is no voltage applied (excellent).

Series vs parallel

Like everything in this world, switches, including diodes, are not perfect - they have some high resistance when they are off and some small resistance when they are on.

From this point of view, the series configuration is better when the load is low resistance and vice versa, the parallel configuration is better when the load is high resistance.

Another advantage of the parallel configuration is that the switch is grounded while in the series circuit it is "floating"... but in the diode implementation this is not essential.

Philosophy

We can think of the combination of the input voltage source and the resistor in series in OP's circuit as a current source. So we can derive two more rules for controlling electrical quantities...

• voltage is controlled by connecting a switch in series
• current is controlled (diverted) by connecting a switch in parallel

... and add them to our "collection of general circuit rules". I have made such a collection of general circuit principles in my Circuit Idea wikibook.

See also my answer to a related SE question.