So I'm trying to understand a basic, fundamental concept. I'm guessing this will be extremely basic to most of the pro's here, but I'm begging for a detailed, simplified, plain-language explanation if possible. Please In a simple voltage divider circuit, you have Vin, then a resistor, then Vout, then another resistor, and then ground. What purpose does the second resistor serve? If Vout comes after the 1st resistor, isn't the voltage already dropped? How does the second resistor come into play? I'm asking because my understanding of electrical flow through circuits is still very water-pipe based...I think it's throwing me off. Thank you!!!
What I'm still not understanding is, fundamentally, in an electric circuit, how does the second resistor impact the Vout, when the second resistor is past the Vout in the circuit (so to speak)?
OK, trying to put it into the water pipe analogy...
The resistors are restrictors. Your basic garden hose spraying out onto the lawn can have a restrictor nozzle at the end that varies the flow rate by varying the restriction (upstream water pressure is basically fixed.) But we aren't spraying it out onto the lawn - it must stay inside the pipework. So think about a pipe system with two restrictors in it, in series. Think of these restrictors reducing the flow to a slow trickle.
What is the pressure "after" the two restrictors? We can call that zero, just to give us some reference point to measure from. What is the pressure "before" the two restrictors? It should be the same as the upstream pressure.
So what is the pressure in the pipe in between the two restrictors? It should depend on the restrictions: if the first restrictor has a high resistance then the water loses more pressure pushing through that one. So the pressure difference measured "across" the second restrictor (between zero and the middle pipe) will be less than half of the initial pressure.
But it gets more complex... In order to measure the pressure at that middle point, we actually send a little bit of the water to our measuring device. So the flow of water through the top restrictor is slightly more than what goes through the second one. So the second one is not resisting the same flow - the pressure across that restrictor will be less. The act of measuring has changed the pressure that we are trying to measure.
First, you need to know that the same current flows through both resistors. ...Just like water in a pipe would have to be the same in a closed pipe where there's nowhere else for the water to go. Note that this is NOT true if there is a "load" connected to the voltage divider and some of the current is diverted to the load. That's why you can't use a voltage divider to power a 5V circuit from 12V.
The next thing you need to know is that resistors in series sum. i.e. Two 1K resistors in series is 2k total. ...If you put two restrictors in your water pipes, you'll get twice the restriction.
Finally, you need to know [u]Ohm's Law[/u] which describes the relationship between voltage, resistance, and current.
First, knowing total voltage and total resistance we can use Ohm's Law to calculate the current (Current - Votage/Resistance).
Since the current is the same in both resistors, we can apply Ohm's Law again to calculate the voltage drop across each resistor (Voltage = Current x Resistance).
Think of a long wire - it has constant cross-section and thus the same resistance-per-unit-length
everywhere. Connect it to a voltage source and you'd rightly expect a linear relationship between
voltage and position along the wire - the same current flows everywhere so the same voltage
gradient everywhere along the wire is constant.
Now think of a resistor as a piece of wire, with length proportional to resistance, and its clear how
voltage divides up according to resistance ratio.
Put another way the power dissipated per unit length is also constant (the wire could be a heater
element in your toaster). This is intuitively correct, and since power depends on current and
voltage difference, clearly voltage varies linearly with position along the wire, and thus with
total resistance to the end of the wire you are callnig zero volts.
