Full-wave rectification circuit question

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In a full-wave bridge rectifier circuit, measuring input and output voltages simultaneously with an oscilloscope is discouraged due to potential grounding issues. The oscilloscope probes' ground clips, when interconnected, can create incorrect voltage readings if placed at points with different voltage levels. Specifically, the lowest point and the leftmost point in the circuit have different voltages due to the diode's voltage drop. This improper grounding can lead to misleading signals displayed on the oscilloscope. Understanding these grounding principles is crucial for accurate measurements in such circuits.
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Not sure if I'm posting this one in the right place because its not a "problem" per se. For the full-wave bridge rectifier we are warned not to measure the input and output voltages simultaneously with the oscilloscope! For example
http://www.sonoma.edu/users/m/marivani/es231/units/experiment_05_2.pdf"
on page 4 the warning is given.

Why is this? Does the problem arise through the earthing of the oscilloscope leads(my guess)? I can't quite picture what will happen in the circuit if you were to try to do this.
 
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I guess your input and output voltages are Vs and Vo, am I correct?
The ground clips of the two probes are interconnected and adjusted to have voltage = 0 simultaneously. So simply put it, you cannot choose 2 points of different voltages to be both ground! Here in the circuit, the two points are the lowest point & the leftmost point. Due to the voltage drop across the diode, voltages of those 2 points are different. You simple cannot put the ground clips to those 2 points, as that will result in wrong signals shown on the oscilloscope's screen.
 
Understand now. Thanks!
 
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