0:03

The topic of this problem is series and parallel resistors and what we're trying

Â to do in this problem is we want to find the equivalent resistance for

Â the resistor network that is shown.

Â So we have a network of resistors that are connected in series and parallel.

Â And we want to be able to ultimately find the equivalent resistance that if we were

Â to place a home meter across the leads it would give us that resistance measurement.

Â So, it's RAB across the leads on the leftmost side of the circuit.

Â To solve these type of problems, usually the best way to start is

Â to look at the far side of the circuit opposite to where RAB is.

Â What the equivalent resistance you're looking for is and if that's not the place

Â to start, then what you want to do is you want to look for something that looks easy

Â to combine in terms of either series or a parallel combinations of resisters.

Â So in our circuit, it's pretty easy to decide what we want to do first.

Â The first thing we want to do is we want to combine the two resistors on

Â the right most side of the circuit that are in series with one

Â another that is the 1k and the 2k resistor.

Â So if we combine the 1k and 2k resistors together,

Â they're in series with one another and

Â that gives us a 3k resistor.

Â Now, we see that that 3k resistor that

Â we have is in parallel with a 6K resistor.

Â And so the combination of this 3k resistance on the right most

Â side of the circuit, and the 6k resistor which is running diagonal down the socket

Â from the top to the bottom gives us a parallel combination of the 3k and the 6k.

Â So the combination of these six kilo ohm resistor,

Â and its equivalent of three kilo ohm resistor

Â is a 6k in parallel with 3k amp resistors.

Â And that gives us a 2 kilo ohm resister, so

Â they're 2k in combination.

Â So if we redraw this circuit,

Â we can redraw it with that equivalent resistance in it.

Â 2:43

Top to bottom in two places.

Â And then across here we have the equivalent resistance switch which was 2K.

Â The top one is a 10k.

Â This leg is a 6k ohm resistor,

Â another 6k ohm resistor, a 4k ohm,

Â and a 2k ohm, and again RAB is measured,

Â 3:13

On the leftmost side of the circuit.

Â So, now we see that we have more to we can do on the rightmost side of the circuit.

Â We can combine the 10k and the 2k together because they're in series

Â with one another and we get a 12k resistors from that.

Â We then can see that that 12k resistance is in parallel with a 6k.

Â So the combination of these resistors that circle is drawn around in blue,

Â is a 12k resistor in parallel with a 6k resistor.

Â And that parallel

Â combination of the 12k and

Â 6k resistor will give us

Â a 4 kilo ohm resistor.

Â So, if take the circuit and we draw it.

Â Again, we have the 2 kilo ohm resistor at the top.

Â We have another 2 kilo ohm that I forgot to mark,

Â another 2 kilo ohm resistor at the top and

Â then we have a combination of the 12 and 6k in parallel which gives us 4k.

Â 4:38

Like this, we still have our 4 kilo ohm from the top

Â to the bottom of the circuit and we also have the 6 kilo

Â ohm From the top to the bottom of the circuit.

Â So, our RAB remains the same.

Â On the left hand side of the circuit we have a 4 kilo ohm resistor,

Â a 6 kilo ohm resistor like this.

Â So, while we slowly whittling the circuit down to an equivalent resistance.

Â So again, as we have before, we can see that this series combination

Â of 2 kilo ohm and 4 kilo ohm will give us an equivalent 6 kilo ohm resistance.

Â We then can take that equivalent 6 kilo ohm and

Â we will see it's in parallel with the existing 6 kilo ohm

Â resistor that's already in the circuit, and so we have a 6 kilo ohm.

Â And parallel with a six kilo ohm and

Â that gives us a three kilo ohm equivalent resistance.

Â And so once again, we're going to redraw the circuit so

Â we're going to go down here and

Â redraw it with our two kilo ohm in there, we haven't really modified that yet.

Â And we have the 4 kilo ohm, we haven't use that,

Â it combined that into our problem yet.

Â But we have the rest of the circuit combined and

Â I guess there's a three kilo ohm on the right-most side of the circuit.

Â So if we redraw it and we put it in our vise the 2 kilo ohms, 4 kilo ohms,

Â and 3 kilo ohms for our resistors, and ultimately we want to find RAB.

Â So, now it's becoming an easier and easier problem to work.

Â Okay, so in our resistor network,

Â we also have this 9k resistor at the bottom of the network and

Â we're going to add that into our network.

Â On the right most circuit like this and

Â we're also going to add it to our bottom circuit like this.

Â So, we have this 9k resistor that needs to be added in to each one of those circuits.

Â And so if we do that, we can then rewrite our circuit one more time

Â with the two kilo ohm resistor at the top.

Â A three kilo ohms resistor at the rightmost side,

Â combine with a 9k, and we still have the 4k here.

Â So we have a 2 kilo ohm resistor at the top, 4 kilo ohm top to bottom,

Â and then a 12 kilo ohm resistor on the right hand side of our circuit.

Â