 We have a scary looking circuit with 5 volt battery connected to these four resistors and our goal is to find the voltage across this resistor How do we do that? Well, my go-to method when we have such complicated looking circuits is to first try and reduce the circuit by finding some Residues resistors and parallel resistors and then see if I can find voltage and current in that reduced circuit If I can't then I'll reduce it even further and even further until I can find the voltage and current in that circuit Reduce circuit once I do that, then I'll come back. So let me show you what I mean So over here, can we find a couple of resistors which are in series or in parallel? Well, I see I see that this four and one ohm are in series with each other because whatever current goes here All of that current comes here same current means series Similarly, I find these two resistors are in series. Whatever current goes here the same current comes here But look these two resistors are not in series because whatever current comes here Not all the current necessarily goes here some of the current might go here or some current might come here So there's branching so not in series these two not in series Okay, so now that I know these two are in series I'll replace them with one resistor in series current Resistances add up. So this single resistance will be four plus one five What about these two again? I can replace these two resistors with one single resistor and that Combination will be two plus three five ohms. So let me draw a new series or reduced circuit Here we go. So this is the series combo of these two and this is the series combo of these two And now that I've reduced the circuit I asked myself Can I find the voltage and the current across these two resistors if I can I will do that if I can't I will try to reduce it even further Okay, can I find the voltage and current across these two resistors? Yes, because notice these two resistors are directly connected across the battery. They are in parallel Here's what I mean if this point is a and this point is b and I know the voltage across a and b is 5 volt But if this is a this point is also a because there's nothing in between no energy loss here This point is b nothing in between this point is also be nothing in between Nothing in between here. So this point is also a so look The voltage across this is the same as the voltage across this five volt and same is the voltage across this So I have found the voltage across these two resistors. What can I do with that? If I know the voltage across the resistor, I can find the current by using Ohm's law. And that's the whole game. If you know the voltage, you can find the current. If you know the current, you can find the voltage. So what does Ohm's law say? V equals IR, so I is V divided by R. So what is the current here? V divided by R, five by five is one amp. So the current here, and let's see the direction, this is positive, current goes from positive to negative. So the current here through this resistor must be one amp. And the current here through this resistor must also be one amp. And then that basically means the current from the battery must be two amps. The two amp gets split as one amp and one amp. And look, I have solved this entire circuit. I know the resistance, voltage and the current through both the resistor, which means I don't need to reduce it further. Okay, what do I do next? Because our goal is to find the voltage here. What I do now is I come back and I see which of these values I can use over here. Well, this thing has stayed the same. So the current here must also be two amps. And look, this branch is basically this one, right? So the current here must be one amp. Remember, I replaced this with this five ohms. So the current here must be one amp. The same current flows here. And similarly, the same current flows here and the current here must be one amp. The same current that I got here, right? One amp. And so now I know the currents everywhere. And my goal now is to find the voltage here. Can I do that? Yes, because I know the current. If I know the current, I can find the voltage. If I know the voltage, I can find the current. That's the game. So again, I use Ohm's law. So what is voltage here? Well, I know I, I know R. So I R one times three, three volt. Boom, that's the answer. Can I find the voltage here even if it's not asked? Yes, I times R, two volt. And look, two plus three gives you five. That's exactly that five volt that got split as two and three. Makes sense, right? And you can do the same thing over here and here.