# Multiple voltage dividers

So I have this circuit. I've been trying to figure out Vout. I couldn't find a specific formula for this situation. Can anyone help me figure out the formula? Thank you.

In 1, below, the two 500 ohm resistors are in series, so they add to an equivalent resistance of 1000 ohms.

That 1000 ohms is in parallel with the 1000 ohm resistor, making the total resistance of the series-parallel network 500 ohms, as shown in 2.

In 2, the 500 ohm net is in series with the 1500 ohm resistor so they add to 2000 ohms. That 2000 ohms is in parallel with the 2000 ohm resistor, making the total resistance equal to 1000 ohms, as shown in 3.

In 3 we have the 1000 ohm net in series with 1000 ohms, creating a voltage divider with an output voltage equal to half of its input, or 3 volts.

In 4. we have redrawn 2, and we can use the 6 volts we got in 3 as the input to the 1500+500 ohm voltage divider, which will give us an output of 1.5 volts.

In 5 we have reconstructed 1, and with the voltage we got from 4 and, as in 4, we can find the voltage originally being sought, which is 0.75 volts.

• Can we solve this using Nodal analysis and Kirchhoff's Laws? or else you have already used above and i am unable to recognize. Commented Sep 13, 2020 at 4:40

Work backwards from the output towards the input and calculate the equivalent resistance for first the 1k resistor, then the 2k resistor.

Then calculate the voltage drop for each stage of voltage divider.

• Note that you can figure this out in your head - the numbers are extremely easy to work with. Please work it out for yourself and show your work. After you have done that, I'll show you the shortcuts that I used. It's really easy. Commented Oct 25, 2015 at 3:13
• Thank you very much. Took me some time but finally figured it out. I did it like shown in the image. Got equivalent resistance for the first resistance and the second 1k resistor. Next I just divided it up into three voltage dividers and got the answer of 750mV. !Image Commented Oct 25, 2015 at 3:29
• Oops wrong one. i.imgur.com/gJhBJkY.png Commented Oct 25, 2015 at 3:34

This isn't a direct answer, but if you are trying to figure our the formula, then you could use some kind of simulation software. Build the circuit and add the necessary voltage measurements you consider relevant. Once you add places to measure voltage, run the solver and check the values it outputs. Take note of them and use them as a reference. Work your way through the problem checking the numeric answer against the solver's.

As a side note, only Dwayne's answer is correct. You don't have three simple voltages dividers. Each step is a voltage divider with some cascading parallel resistances.

• He's already using that falstad.com/circuit in case you didn't recognize the graphics. Commented Oct 25, 2015 at 6:18
• @RespawnedFluff Sorry! I did not recognize them. I had never before heard of falstad. Thanks. Commented Oct 25, 2015 at 18:17