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I need to calculate the voltages on the 10 resistor voltage divider (V1,V2,V3...), but i don't know how to work it out. So far I found V1 by doing $$V1=Vs*(R3/(R3+R2))$$ and found V1= 0.5 Volts. Can I get some help on how to calculate the rest?

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    \$\begingroup\$ Instead of "blindly" using the voltage divider formula, think how this works. There's 1.25 V at the top of R2. You know the values of all resistors. Then you can easily determine the currents. There are only 3 different currents: I(R2) , I(R3) and the current through the string of resistors. The string's current is constant (all currents are), what does that mean for the voltage across each resistor? \$\endgroup\$ Nov 16 '17 at 10:12
  • \$\begingroup\$ I'm not looking to find the voltage across each resistor by just doing V=IR, I need to calculate the output voltages of the voltage dividers. \$\endgroup\$
    – super95
    Nov 16 '17 at 10:22
  • \$\begingroup\$ And how is that different from my approach? If you would know the voltage across each resistor then.... ? You're stuck in the "must use voltage divider formula" mode. It is possible to solve it that way. But it is easier to do the way I propose. But if you prefer to use the voltage divider formula 10 times then be my guest. I'm just an EE and very lazy so I always think to find the simplest/easiest way to an answer. \$\endgroup\$ Nov 16 '17 at 10:28
  • \$\begingroup\$ With the way you propose wouldn't the voltage be calculated the same for every resistor on on the string of resistors? \$\endgroup\$
    – super95
    Nov 16 '17 at 10:35
  • \$\begingroup\$ wouldn't the voltage be calculated the same for every resistor AHA! Yes, across each resistor the voltage will be the same. But are V1 - V10 across one or more resistors? Ergo: you can just add .... \$\endgroup\$ Nov 16 '17 at 10:46
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V1 is the resistor divider of the R2 and R3||CHAIN_RESISTANCE. That is you need to calculate the equivalent resistance of R3 with the total chain resistance in parallel with it in order to calculate V1.

\$Rp = R3||R_C = 1/((1/470)+(1/10,000)) =448.9\Omega\$

So

\$V1 = 1.25 * 448.9/(448.9+680) = 0.497V\$

After that it is easy. There are 10 resistors in the chain, all of them are the same resistance.... Once you know V1, the rest should be easy.

Consider this..

schematic

simulate this circuit – Schematic created using CircuitLab

Do you see a pattern here?

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Disclaimer: This answer doesn't contain values or formulas. It descripes the way to go:

  • You know, that there is no change of the overall resistance, so the voltage drop over R2 and R3 will always be the same
  • You can use the caculation of resistance in series and parallel one after another to get the value you need and calculate the voltage drop over R3
  • Count the resistors to GND from your searched voltage measure point to know, how high the resistance is and do it analog the step above to get your final searched Voltage value
  • You may recognize, that you don't have to do this steps for all values, as the resistors are all the same (percentage calculation)
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