 Let's solve circuits with series and parallel resistors. Here's the first one We have two resistors 2 ohm and 3 ohm connected across 10 volt battery Our goal is to find the equivalent resistance and the voltage across this resistance How do we do that? Well, first let's identify what kind of combination this is Well, I see that these two resistors are in series How do I know that? One way to check for it is to see if they're connected end to end But a better way to think about it is to see if the current through them is the same Series resistors have the same current through them Paddle resistors have the same voltage across them. How do I check whether they have the same current? Well, what I do is I imagine throwing some charges moving some charges from here Imagine some charges flowing from here to here Now if all it not all have to check for is whether all these charges flow through this resistor as well If they do then I know the current from here should be the same as the current over here and Turns out that's exactly what's happening the charges whatever charges flow from here to here All of them have to flow over here because there's no way nowhere else for them to go So the current here and here is exactly the same therefore these two are in series and I know the formula for my series combination What is that when resistors are in series the equivalent resistance is just adding them up So that example it is going to be two plus three. So that's going to be five homes done Okay, next up. What is the voltage across this resistor? Well, isn't it ten volt? Why don't you pause and think about it? Is it ten volt? If yes, why and if not why not? Here's I like to think about it. I like to always Name some points over here. Now. I know that the voltage across a and b that is ten volt Okay, now as I move from here to here, there will be no loss of voltage There will be no loss of energy because we're assuming there are no resistors That means whatever is the energy here same is the energy here So this point is a and same as the case over here So this point is B and therefore what we now see is that since the voltage across point a and b is ten volt The voltage across these two points is ten volts Means the voltage across both of these resistors together That is ten volt. But what we are asked now is to find the voltage across our One that will be less than ten volt. So how do I find that? My go-to method is to always draw a reduced circuit. So let me redraw the circuit with the equivalent resistance Here we go. Look, I have replaced these two resistors with one equivalent resistance five ohms And I know that the voltage across that that is ten volt Since I know the voltage across that and I know the resistance I can use ohms law to find the current the current is not asked, but I can find the current So I'll first do that. That's my method. So I'll find the current. So for that, I'm going to use v equals IR So I know v is 10 is Equal to I which I don't know Times are I'm you applying it for this circuit? Okay? And so from this we get I as To ten divided by five two amps So I have now find out found out what the current in this circuit is To ampere How does that help me? Well once I have found out the current in this circuit I will go back and I will now say well if the current in this circuit is to ampere the current in this circuit Must also be two amperes right because the current through the battery must be the same So it's two amperes here as well That means the current flowing through this resistor is also two amperes and the current flowing through this resistor is also two amperes Now I know the current And I know the resistance. Can I find the voltage again? Good idea to pause and see if you can find it All right, so I'm going to use again ohms law v equals IR current is two Resistance is also two. So the voltage here now is going to be I two times R and that's going to be four volt So this is four volt Now it's not asked, but what would the voltage across this resistor? Same thing v is equal to IR is two R is three so two times three is six volt so voltage across this one is six volt and look Look the add up to give you 10. That's exactly what we wanted from here to here The total voltage must be 10 volt so it makes perfect sense So what's really happening is that as charges move from here to here? They're gaining 10 joules of energy per coulomb remember voltage means Joules per coulomb So charges gain 10 joules of energy per coulomb as they go from here to here They lose four of it and then as they go from here to here. They lose the remaining six They go to zero they come back they gain 10 and that continues. Let's come to the second one We have three resistors connected across 14 volt battery Again, our goal is to find the equivalent resistance and the current through the seven ohm resistor Pause and try first Okay, so to find the equivalent resistance our first question is how are these three connected are they in series Well to check if they're in series. We have to check whether the current through them is the same if I send some charges over here Will all of it go here? No because some of it will get divided. So clearly these two are in not in series Neither are these two. Okay, are they in parallel to check for parallel? We have to see if the voltage across them is the same and to check for that. I'm gonna do the same thing that I did over here I'm gonna draw my A and B. So this is a this is B if this is a This is a because there is no energy loss. No resistors in between Similarly, this is also a this is also a And if this is B, this is B because there are no energy losses in between no energy losses in between This is B no energy losses in between. This is B what you find is that hey They're all connected across A and B. So the voltage across all of them must be exactly the same 14 volts 14 volts 14 volts 14 volts So they are in parallel so How do I find what is the formula for parallel? Well, I know that 1 over RP the equivalent parallel resistance is 1 over R1 plus 1 over R2 and How much ever you have plus 1 over R3 and so on So in our example, it would be 1 over 14 plus 1 over 7 by 2 which becomes 2 by 7 plus 1 over 7 and If we take the common denominator of 14, I get 1 plus Multiply by 2 on both numerator and denominator and multiply by 2 here. So I get 4 plus 6 7 7 by 14 This goes one times this goes two times. So the answer is half, right? No Remember, this is 1 over RP 1 over RP is 1 over 2. So RP Right over here RP is going to be reciprocal of this. So that is 2 ohms So you found the equivalent resistance of all of these three together is 2 ohms Okay, next step, we need to find the current through the 7 ohm resistor Why don't you pause and try again one last time? Okay, to find the current I first asked myself Well, do I know the voltage and the answer is yes I do know the voltage because the voltage across this is the same as the voltage across this is the same as The voltage across this and this so I know the voltage is 14 volt. That's directly given to me So this is 14. I know the voltage. I know the resistance. So what's current? Well, I can use V equals IR So I will be V divided by R. So let's just write that down. I will be V divided by R ohms law So V is 14 divided by R is 7 and so that gives me 2 amperes So there you go it The current through the 7 ohm resistor is 2 amperes similarly you can find the current through this and this yourself