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Anderson Video - DC Circuits Intro

Professor Anderson
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We're gonna push onward and upward and we're going to talk about circuits in a little more detail. We've introduced the idea of the basic circuit with one battery and one resistor. But, let's see if we can make them more complicated. So when we had a simple circuit, it looked like this: voltage and resistors. That led to a current I which flowed around the circuit and we know what that current is because it's governed by Ohm's law. The goal of this chapter is to simplify circuits such that they look like this. Okay? If you can simplify complicated circuits to the point where they look like this , then you can understand everything about that circuit because Ohm's law applies just like that: V equals IR. So let's take the case where we have not just one resistor, but two resistors in series. So, here's my battery. Here is resistor 1. Here is resistor two. And now, I want to get it to look back like this. All right? I want it to look like a simple circuit again. So how do I do that? Well, I just draw it again and label this thing something else. Now it looks like that. The only difference is it's called R sub S instead of R. How does R sub 1, R sub 2, relate to R sub s? Well, this is called a series circuit because I've added those resistors in series -- one after the other. And when I do that, R sub s is just R1 plus R2. No problem. Ohm's law then applies. What's the current I? It is V equals IR sub s. And now you know everything about that circuit. What about when we do this? Let's add the resistors in parallel. There's my voltage, V. Now, I have R1 and R2 in parallel. How do I think about that? Well, the way I think about it is the following; there are in fact two current paths. when the current comes it splits and goes two different ways around the circuit and then it comes back together. Okay? So, it's like my river splitting into two and going through two different paths. Okay? The end result of doing that is, you don't just add up the resistors like we did before, you have to add currents. Okay. Here, we were just adding resistors but now what we're gonna do is we're gonna add currents. And we know that current goes like 1 over resistance, right? V equals IR, so current equals V over R. And when I do that, I can rewrite this as the following: We call it R sub p -- resistors in parallel. The rule for resistors in parallel is 1 over Rp equals 1 over R1 plus 1 over R2. This one is series. This one is parallel. The way you get to this is you add up the currents. We would have V over R equals V over R1, plus V over R2. Cancel out all the V's and you get 1 over Rp, equals 1 over R1 plus 1 over R2.