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University of Michigan - Ann Arbor

University of Washington

McMaster University

03:27

Kai C.

(I) A constant friction force of 25 N acts on a 65-kg skier for 15 s on level snow.What is the skier's change in velocity?

01:40

Keshav S.

(II) According to a simplified model of a mammalian heart, at each pulse approximately 20 $g$ of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?

0:00

Muhammed S.

(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?

04:15

Kathleen T.

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welcome to our first section In alternating current in this section, we're going to be looking at three simple circuits. We're gonna look at a C sources combined with out of single resistor anay C source combined with capacitor and an A C source combined with a single in Dr. For all of these circuits, we're going to have a source that generates an E m f as a function of time that looks like the function we've already presented. Except we're going to say that our phase constant fi is equal to zero. So starting off with our resist er circuit, we find that the voltage across the resistor is going to be equal to the e m f supplied by the source. So the maximum voltage will be equal to the amplitude e the mac the maximum of the MF that we will receive. So v f t then is a will be v r cosine of Omega T, just like we see appear for our EMF now using OEMs law were able to find a relationship between I and V where i I as a function of time is equal to v of r over our times the coastline of Omega T. Remember, Visa Bar is the maximum voltage will find across the resistor. If we redefine that to tell us that this is the maximum current, then we have two equations that tell us about how current and voltage change across the resistor as a function of time. We can see that they look pretty much the same except for their amplitude. Which means if I were to attempt to plot them on the same, why axis they look something like this, they're totally in phase Now if, on the other hand, I move on to the simple capacitor circuit, what I'm going to find is that, given the same source and looking at the equation that defines the relationship between Q and V and again giving that V C, the maximum voltage across the capacity will be equal to the maximum e m f supplied. We obtain an equation for V, F T and therefore on equation for Q as a function of time. Now, this isn't quite what we want. We'd really like current, So we're going to go ahead and operate on this with a time derivative, giving us current as a function of time will be equal to negative Omega times capacitance times the maximum voltage across the capacitor times the sign of omega team To make this look more like what we had before. I'm going to use this relationship between Sine and CoSine in order to rewrite our equation as current as a function of time is equal to a maximum current, which is Omega time. See Time's VC multiplied by cosine of omega T plus pi over two. So you can see there is a phase difference here between the equation for current and the equation for voltage across the capacitor. On what this means that when we go to plot it, the current is here and the voltage is here. We see that the current is actually peaking before the voltage does by about pi over two. And what this means is that we're going to have a current that leads the voltage. Just how we say this. So current leads voltage. Okay, so they aren't exactly at the same maximum magnitude at the same time. We're gonna have a maximum and current, and then later we'll see a maximum in voltage. This is kind of an interesting interaction here later on, if we want to get a little more insight, what we can do is we can define something known as capacitive reactant capacitive reactant is equal to one divided by Omega time. See, And what this allows us to do is write a relationship between I m v similar to OEMs law. If you remember, OEMs Law said, I r equals V r over our and here we have this. So if we think about the capacitor as having sort of an impeding effect on the circuit, same way that the resistor does notice that when Omega gets really, really big, that capacitive reactant swill get very, very small, okay? Which means that it will have less and less of an impeding effect if omega is very large. So the faster we alternate back and forth with our current or applied m s, the less that capacitance capacitors are actually going to impede the flow of current through the system. On the other hand, if this alternation, this angular frequency is very, very small. What we get is that we have a much larger capacitive reaction reactant, which means that when we go over here, it's gonna look like we have a very large impediment to our current flowing in this circuit. We can do a similar analysis for induct er's where instead of C equals Q over V. What we have is V l is equal to l times D I over d t notice here that we're just interested in the measurement of potential across it, not necessarily the loss. So we've ignored the negative. Now again defining that we have a maximum potential across our induct er equal to the maximum e m f. We can write out our voltage function and then plug it into our equation relating the I. D. T and the voltage. And we will be able to find that I as a function of time again, using our trick to switch from sign to cosign is going to look like the maximum current multiplied by cosine of omega T minus pi over two. So in this case, we're going to see that current will actually be lagging behind the by an amount pi over two. So when we're talking about an induct er circuit, then current lags behind voltage, okay, and then similar to what we did with capacitance, we can define an inductive reactant. Excel is equal to Omega Times l So we can write a similar relationship to what we've had for capacitors and also for resistors and notice here that excel is going to get larger as omega gets larger. And so when we try to oscillate the current in this circuit very quickly, what we're going to get is a lot of resistance from the induct. Er the induct er doesn't want to see a lot of change, so it doesn't like a large omega. On the other hand, if we have a small omega, it will look like the induct er isn't really impeding the flow of current so much so the induct er will have a smaller inductive reactant. So the induct er prefers a small omega where the capacitor prefers a larger omega. So in the next few sample videos, we're going to continue to look at these simple circuits. But later on, we'll start combining these components to see what happens when we put them all together.

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