So I'm trying to teach myself basic electronics without a real textbook or teacher. I've got several resources at my disposal: Articles and video lectures I find on the net, circuit modeling software, and a book on guitar amp construction with an intro chapter on basic electronics theory.
This is where I'm stuck, since the book claims to be for the beginner, but seems to offer examples with lots of gaps in the reasoning. When introducing new ideas, the author just spits out formulas for certain example circuits without proving it component by component, or sometimes even without sufficiently defining some of the terms being used. I'm the kind of person who wants to verify that what I'm reading is true, so I end up making little examples for myself to make sure I understand what's going on... and it's been working - I can fill in some of the gaps. But I've hit a wall at what I feel is a pretty basic concept (don't laugh).
The voltage divider. I understand how this simple example works:
The author of my book uses the terms "input voltage" and "output voltage," with input coming from the 10V battery and output being the voltage across R2. He spits out the formula: Vout = R2/(R1+R2) * Vin (which I verify component by component to make sure I get it), and all is well.
But then later in the intro chapter, the author brings up this next situation, and simply regurgitates the same formula without any further explanation:
When I try to verify component-by-component, I get stuck. My calculations do not measure what my software simulator seems to indicate. The values for Voltage and Current in R1 and R2 have changed in my software (understandably, since they are now part of a larger network), but I cannot account for this change. How do I approach analyzing this circuit component-by-component?
Any web searches for this situation have returned only the simple case of the original voltage divider I posted above. Can anyone suggest an approach to this?