27. Resistors & DC Circuits

Kirchhoff's Loop Rule

# Combining Voltage Sources in Series

Patrick Ford

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Hey, guys. So this short video, we're gonna talk about how we can merge. Voltage is in a circuit to make that circuit simpler. Let's check it out. All right. So you can combine voltage sources if the sources are connected in Siris. This only works if they're connected in Siris. You could do this to simplify a circuit. So, for example, I have a 10 volt battery here in a five volt battery. Here they are in serious Because there's a direct path between all these four guys here. The white doesn't split so their own Siri's so I can combine these two. So instead of having to batteries, I could just have one. And generally what you do, you just add up. The voltage is something like view on plus V two. Now, if the voltage sources are in opposite directions there, voltages are actually not going to add. They're going to subtract, Okay. And we're gonna do these two quick examples, and I think this is gonna make a ton of sense. Totally obvious. So look at this battle here. The positive terminals. This way. So it's pushing current this way, right? Like current police leaving the charge is leaving the battery through this side. This battery is here. So the positive sign is here. Let's put positive and positive. So this guy is also pushing this side. So you might imagine think of this as forces. Almost right. This thing is pushing clockwise. And then this thing is also pushing clockwise. They're helping each other. They're both pushing this in direction so I can redraw this and just say that these to act as a single battery of voltage. 15. It doesn't matter that there's a resistor in between them. Got it. Similarly, by the way, if you remember, we can also merge these two resistors there in Siris. So they're also just going to add up. So an equivalent circuit here would be one with a 15 volts battery. I'm actually just gonna draw in this direction here. That 10 instead of gonna put a 15 volts here, and the resistance is will add two plus three is five. It would be this five owns, okay. And by the way, this example here is asking us to find the magnitude and the direction of the current because they're both currents are going the same direction three direction of the current will simply be Let's right here. Direction is going to be clockwise now, what about the magnitude of that current? The current goes this way. Well, to find a magnitude of a current in a circuit like this, you can just right V equals I R. So I is going to be V over r the voltages the current. The resistance is five. So it's just three amps. Very simple. Now, here it's a little bit different because this guy over here is pushing current. Or at least it's trying to push current this way. Something that be really cool. If you could pause this video and try to do in your own, I think a lot of you are gonna get this right, because it's very straightforward. Um, but I'm gonna keep going here, So this guy is pushing this way. This guy is pushing this way. The clashing Well, who do you think is pushing current harder, Right. So the 10 volts is putting more of a pressure or providing more influence for the current to move, so that one is going to win, which means that despite the fact that they're pushing against each other. The currents will overall move in this direction. Okay, so the five is actually fighting against the 10 volts in making it weaker. Therefore, we can just subtract. The two were going to say 10 minus five is just five, which means the effective the equivalent voltage here is going to be five in this direction. Five volts this way again going up against a five ohm resistor. The direction is still clockwise, but the current will be different. Currents is going to be V equals ir We're gonna solve for I and this is gonna be the over our. The voltage is a five. The R is a five. So the answer is one amp coat. That's it for this one. Super simple. Let's keep going.

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