# Trying to find Vo in this circuit diagram

I am pretty lost working this textbook example (not homework).

Will someone verify if I did this correctly?

1) simplify the circuit

1a) 20k + 40k = 60 k

1b) 60k || 30k = 60k*30k / 90k = 20k

1c) 20k + 20k = 40k

Resulting in a collapsed circuit with just the 12V source and a 40k ohm resistor.

Is this even the right start? It appears that with this simplified circuit Vo would just be 12V. What did I do wrong? The answer is 2V.

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You were moving in the right direction but deviated away.Compute the potential difference across the equivalent resistance (20 k ohm) using the voltage divider law, that potential difference will be equal to the potential difference across the 30k ohm resistor.After getting that information, use the voltage divider law again to get the value of Vo. –  KillaKem Jun 12 at 1:09
I referenced vdiv in my text and I see it now. Thanks! –  eestack Jun 12 at 1:39

Try re-drawing the circuit like so:

simulate this circuit – Schematic created using CircuitLab

(It is much easier to discuss a circuit when you use reference designators (R1, R2...) on the components.)

You correctly determined that R3 and R4 are in series, and are equivalent to a 60K resistor. You also found that R3 and R4 in series, are in parallel with R2, to make an equivalent 20K resistor. You then added that combination to R1, and got lost.

R1 in series with the combination of the other three resistors make a voltage divider, giving a voltage (to be determined by the student) at V1.

R3 and R4 make another voltage divider, multiplying the voltage at V1 by 1/3, giving the desired voltage at Vo.

You can easily solve this problem by looking at the resistor values - there's no need to calculate currents (although doing such calculations may be useful practice...)

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I understand now, thank you! –  eestack Jun 12 at 1:43
The "mistake" is that the terminal Vo didn't collapse to the top of the equivalent resistance, it is buried inside that 20 kOhm resistance. The final part of the solution is "unraveling" the lumped resistor now that you can identify all of the parameters of that one resistance (voltage, current, resistance).