The topic of this problem is series and parallel resistors and what we're trying to do in this problem is we want to find the equivalent resistance for the resistor network that is shown. So we have a network of resistors that are connected in series and parallel. And we want to be able to ultimately find the equivalent resistance that if we were to place a home meter across the leads it would give us that resistance measurement. So, it's RAB across the leads on the leftmost side of the circuit. To solve these type of problems, usually the best way to start is to look at the far side of the circuit opposite to where RAB is. What the equivalent resistance you're looking for is and if that's not the place to start, then what you want to do is you want to look for something that looks easy to combine in terms of either series or a parallel combinations of resisters. So in our circuit, it's pretty easy to decide what we want to do first. The first thing we want to do is we want to combine the two resistors on the right most side of the circuit that are in series with one another that is the 1k and the 2k resistor. So if we combine the 1k and 2k resistors together, they're in series with one another and that gives us a 3k resistor. Now, we see that that 3k resistor that we have is in parallel with a 6K resistor. And so the combination of this 3k resistance on the right most side of the circuit, and the 6k resistor which is running diagonal down the socket from the top to the bottom gives us a parallel combination of the 3k and the 6k. So the combination of these six kilo ohm resistor, and its equivalent of three kilo ohm resistor is a 6k in parallel with 3k amp resistors. And that gives us a 2 kilo ohm resister, so they're 2k in combination. So if we redraw this circuit, we can redraw it with that equivalent resistance in it. And so we're going to take some time, and we're going to redraw that circuit with that resistor in there. So, we have a 6k coming down. Top to bottom in two places. And then across here we have the equivalent resistance switch which was 2K. The top one is a 10k. This leg is a 6k ohm resistor, another 6k ohm resistor, a 4k ohm, and a 2k ohm, and again RAB is measured, On the leftmost side of the circuit. So, now we see that we have more to we can do on the rightmost side of the circuit. We can combine the 10k and the 2k together because they're in series with one another and we get a 12k resistors from that. We then can see that that 12k resistance is in parallel with a 6k. So the combination of these resistors that circle is drawn around in blue, is a 12k resistor in parallel with a 6k resistor. And that parallel combination of the 12k and 6k resistor will give us a 4 kilo ohm resistor. So, if take the circuit and we draw it. Again, we have the 2 kilo ohm resistor at the top. We have another 2 kilo ohm that I forgot to mark, another 2 kilo ohm resistor at the top and then we have a combination of the 12 and 6k in parallel which gives us 4k. Like this, we still have our 4 kilo ohm from the top to the bottom of the circuit and we also have the 6 kilo ohm From the top to the bottom of the circuit. So, our RAB remains the same. On the left hand side of the circuit we have a 4 kilo ohm resistor, a 6 kilo ohm resistor like this. So, while we slowly whittling the circuit down to an equivalent resistance. So again, as we have before, we can see that this series combination of 2 kilo ohm and 4 kilo ohm will give us an equivalent 6 kilo ohm resistance. We then can take that equivalent 6 kilo ohm and we will see it's in parallel with the existing 6 kilo ohm resistor that's already in the circuit, and so we have a 6 kilo ohm. And parallel with a six kilo ohm and that gives us a three kilo ohm equivalent resistance. And so once again, we're going to redraw the circuit so we're going to go down here and redraw it with our two kilo ohm in there, we haven't really modified that yet. And we have the 4 kilo ohm, we haven't use that, it combined that into our problem yet. But we have the rest of the circuit combined and I guess there's a three kilo ohm on the right-most side of the circuit. So if we redraw it and we put it in our vise the 2 kilo ohms, 4 kilo ohms, and 3 kilo ohms for our resistors, and ultimately we want to find RAB. So, now it's becoming an easier and easier problem to work. Okay, so in our resistor network, we also have this 9k resistor at the bottom of the network and we're going to add that into our network. On the right most circuit like this and we're also going to add it to our bottom circuit like this. So, we have this 9k resistor that needs to be added in to each one of those circuits. And so if we do that, we can then rewrite our circuit one more time with the two kilo ohm resistor at the top. A three kilo ohms resistor at the rightmost side, combine with a 9k, and we still have the 4k here. So we have a 2 kilo ohm resistor at the top, 4 kilo ohm top to bottom, and then a 12 kilo ohm resistor on the right hand side of our circuit. Now, we notice that the 4 kilo ohm and the 12 kilo ohm are in parallel with one another. And those two combinations are 4 in parallel with 12 kilo ohm resistor. Is equal to 3 kilo ohms. And so if we rewrite our circuit one more time, it will become obvious what RAB is. We have two kilo ohm in series with a three kilo ohm, and so we end up with an RAB equal to 5 kilo ohms.
