Anderson Video - Circuits with Resistors

Professor Anderson
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Okay, let's try another example. Let's try this example right here. Okay, so let's let our circuit look like that. And now let's label these things R1, R2, R3, and R4. And let's see if we can simplify this to our simple circuit. So the first step is to start in the innards and then work your way out. So the innards here are going to be R1 and R2 next to each other. So the first step is going to be get rid of those. We change that to an Rs, this is still R3, and then we still have R4 down below. Rs is simply just R1 plus R2. And this is supposed to be a 3. And now we're almost back to where we were just a second ago. The next step is this. This is Rp, that is R4. Rp is 1 over Rp equals 1 over Rs plus 1 over R3. And then the final step is that. And we'll call that one R sub s 2 how about, since we already use R sub s. And R sub s 2, is just going to be Rp plus R4. Okay, so if you know all the resistances you can calculate Rs, if you calculate Rs you can then calculate Rp, if you calculate Rp you can calculate the final resistance Rs2, then Ohm's law applies. V equals I times Rs2. And so you can calculate the total current in that circuit. Obviously you can do this for any number of resistors you want in any combination you want, just remember you should always start at the innermost connections where it's deepest in the circuit and then work your way out to simplify. Okay, questions about that? Yeah. Where do we see such complicated circuits? Pretty much every circuit you're going to come across will have stuff like this in it. And the reason that you might have complicated circuits like that is because you want to be able to supply different voltages to different devices, so there might be some thing that's attached here that needs a different voltage than the thing that's attached here or the thing that's attached there. So you can do all sorts of complicated voltage divisions as you go when you're building up circuits.
Okay, let's try another example. Let's try this example right here. Okay, so let's let our circuit look like that. And now let's label these things R1, R2, R3, and R4. And let's see if we can simplify this to our simple circuit. So the first step is to start in the innards and then work your way out. So the innards here are going to be R1 and R2 next to each other. So the first step is going to be get rid of those. We change that to an Rs, this is still R3, and then we still have R4 down below. Rs is simply just R1 plus R2. And this is supposed to be a 3. And now we're almost back to where we were just a second ago. The next step is this. This is Rp, that is R4. Rp is 1 over Rp equals 1 over Rs plus 1 over R3. And then the final step is that. And we'll call that one R sub s 2 how about, since we already use R sub s. And R sub s 2, is just going to be Rp plus R4. Okay, so if you know all the resistances you can calculate Rs, if you calculate Rs you can then calculate Rp, if you calculate Rp you can calculate the final resistance Rs2, then Ohm's law applies. V equals I times Rs2. And so you can calculate the total current in that circuit. Obviously you can do this for any number of resistors you want in any combination you want, just remember you should always start at the innermost connections where it's deepest in the circuit and then work your way out to simplify. Okay, questions about that? Yeah. Where do we see such complicated circuits? Pretty much every circuit you're going to come across will have stuff like this in it. And the reason that you might have complicated circuits like that is because you want to be able to supply different voltages to different devices, so there might be some thing that's attached here that needs a different voltage than the thing that's attached here or the thing that's attached there. So you can do all sorts of complicated voltage divisions as you go when you're building up circuits.