The voltage divider technique was derived from a circuit where the resistors and battery were in series. I want to focus on the the variable V in the following formula. And I only want to focus only on circuits whose elements are all in series with one another (No current division) (V_{Rn} = R_{n}/R_{eq}*V, where V is the sum of the the constant voltage sources in series. in the problem they used that voltage divider technique to solve for V_{0}, however they have a multiple of V_{1} which is the voltage source not in series with V_{0}. My question is regaurding circuits with only battereis and resistors: It is obvious that the voltage divider works with elements that are not in series. How will I know when I can use volt divider tech.? Because the only way I understand how to use it is if all elements are in series.
The circuit doesn't have a voltage source. It has a current source. And what you claim is obvious isn't actually true. Instead of blindly applying a formula, you'll probably find it useful to derive the voltage divider rule. If you understand how and why it works, you'll better understand to what situations it applies.
Miike012 - They didn't explain the first steps in the solution, perhaps that confused you? Follow these steps drawing circuits as you go.. First they calculated the equivalent resistance of all the resistors to be 40K. Then refer to diagram (c)... The current source forces 0.9mA through that 40K equivalent resistance so you can calculate V1.... V1 = 0.9mA * 40K = 24V Then back to the original circuit in (a).... Then they mentally "removed" the current source in the original circuit and replaced it with a voltage source equal to V1. The 60K resistor is in parallel with V1 so easy to work out the current through that if needed. The 40 and 80k form a potential divider from V1 so you can use that to calculate Vo. Note: The 60K in parallel with the 40 & 80K doesn't effect how the voltage divider works because V1 is a voltage source. The 60k doesn't effect the current flowing in the 40 & 80K branch.