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I had the same doubts and ran a similar simulation to convince myself I hadn't gone mad.
Yes, the voltage does change. So does the current at the same rate. There is a gradual sloped/sloping increase to the voltage, and then a gradual drop off of the voltage in a sine wave. We do not have an instant on/off as in a digital square wave. That's why Nigel's explanation of printing out the sine wave on grid paper, and then counting the squares, or square area, within the half cycles, above and below the center "0" reference line works to explain the power in the circuit. Does your simulation schematic drawing, not show both R1 (w/diode) & R2 circuits wired parallel across the input voltage source??? I am confused by that. Do Nigel's simple bench test to see what you get.
That test disproved Nigel's theory.
With your logic, a fully rectified AC current/Voltage is also 1/2 the peak to peak voltage. So is a full wave rectified voltage also 1/4 of the power?
Here is where I think the problem, or confusion lies, that they can not understand in the point we are trying to make. Nigel is comparing the input 240v "peak to peak" "value" of the AC FULL sine wave input voltage, as referenced to the neutral wire, (which the input voltage "value" IS 2x compared to the output), to the pulsating half wave rectified DC output. Which no longer actually can be referred to as a "peak to peak" value; only as either a peak and/or RMS voltage value, because the resulting sine wave still has an AC component, and is not pure DC.
No. The full AC sine wave, and the full wave bridge rectified pulsating DC output are the same. But please note, that with the bridge rectified pulsating DC wave, we are no longer referencing the output voltage to the neutral wire; because of the extra diodes. Only the single diode, half wave rectified, pulsating DC wave, (for which the output voltage is referenced to the neutral wire), is different, because the peak output voltage is 1/2 the "peak to peak" input voltage. Minus the obvious voltage drop in the diode. I also would like to point out or mention, that the difference that Nigel may have experienced with his simple "bench test", (not getting less than 1/2 the voltage), may be due to the fact that most VOMs I do believe, display "RMS" voltage and not peak or P-P; and he did not make it clear whether he was reading AC or DC voltage on the output of the circuit. Or whether he was using a VOM or scope? Some VOMs & DMMs may not give an accurate AC voltage reading, if it is not a pure sine wave. But I'm sure he knows that!
Your 240v value here is stated wrong! 240v "peak" times(x) 0.707 equals(=) 170v RMS. 240v RMS half wave rectified, would be 240v RMS? NO? "Peak to Peak " in this case now would be 480v. Hi, Hi.
Now I am getting a headache and need a FEW beers!
Definitely NO. 240v RMS full-wave rectified would be 240v RMS.
Would not R 1 be loading the circuit 100% of the time (100% duty cycle), and R2 (with the diode in series), only be loading the circuit 50% of the time (50% duty cycle) if they are in parallel with the AC voltage source???
YES, maybe you've finally got it. It will load the circuit 50% of the time and consume 50% of the energy.
But would they not ONLY be in parallel, 50% of the time, when the diode is forward biased; as the circuit is drawn? The circuit we have been discussing all along, or started out with; only involves 1 diode which is added to the circuit by a switch, and 1 resistive heating element!
Think about the voltage of the half cycle, it's no different to the voltage when both cycles are present. Therefore the current during that half cycle will be the same. The only thing that has changed is it's only on for 50% of the time. Another way to think about it is, HOW does the on cycle know to reduce power because the other half cycle is off?
