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31. Alternating Current

1

concept

3m

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Hey, guys, in this video, we're going to start talking about resistors in a sea circuits. All right, let's get to it. Just a reminder in an a C circuit, the current produced by the source is always going to look like this. Okay, it's always going to be signed the soil. All right, Now, because of that, OEMs law tells us that the voltage across the resistor at a sorry as a function of time has to be this current as a function of time, times the resistance, right? If we had a basic circuit exactly is above the voltage across the resistor as a function of time would just be equal to the current traveling through it as a function of time. Times are the resistance. This means that the voltage across the resistor is i Max times are cosine of omega T that it's simply plugging in this equation into homes law. Very basic. Let's do an example. A 10 ohm resistor is plugged into an outlet within arm's voltage of 120 volts. What is the maximum current in the circuit? What about the arms current? Okay, we know that the RMS voltage is 120 volts. Now, just like we could say that the maximum current is equal to the maximum voltage over our. It turns out that the RMS current is also equal to the RMS voltage divided by our. This is something that's really easy to show, and you guys can convince that yourselves of that on your own. So this is 120 volts, divided by 10 owns, which is 12 aunts. Now what's the maximum current? Well, the maximum current is just going to be the square root of two times the RMS current. So that's the square to to times 12 amps, which is about 17 ants. Okay, resistors and a C circuits are very, very simple problems. Alright, now for multiple resistors in an A C circuit. What if you had something like this, for instance, all we have to do is combine them into a single equivalent resistor, as we would with D C circuits. And then we can apply the same equations as we did in the previous example to thes circuits that have multiple resistors. Nothing changes from D C circuits. All right, guys, this was a little bit of a start with resistors in a sea circuits, and we'll get to more of that soon. Thanks for watching

2

Problem

The voltage across a resistor is found to be given by v _{R }(t) = (10 V) cos[(120 s^{−1})t]:

a) At what frequency does the AC course operate?

b) If the resistance is 12 Ω, what is the maximum current in this circuit?

c) What is the RMS voltage of the AC source?

A

a) 19.1 Hz;

b) 0.83 A;

c) 7.1 V

b) 0.83 A;

c) 7.1 V

B

a) 120 V;

b) 1.2 A;

c) 2.2 V

b) 1.2 A;

c) 2.2 V

C

a) 754 Hz;

b) 120 A;

c) 14 V

b) 120 A;

c) 14 V

3

example

2m

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Hey, guys, let's do an example that involves multiple resistors in an A C circuit what is occurring through the 10 ohm resistor in the following circuit. Now, your first instinct might be to just jump right in and start combining resistors like you would in the D C circuit. But hold on just a second. All of these elements air in parallel, so they all share the voltage with the source. Okay, so the maximum voltage across across each of these resistors is the same as the maximum voltage across the A C source. So we can say V 10 which I will call the maximum voltage across the tandem Resistor is just five volts, which is the maximum voltage produced by the A C source. Okay, now what does this mean about the maximum current through the 10 ohm resistor? Well, by owns law, I'll call I 10 really quickly the maximum current through that 10 ohm resistor By OEMs law, that's just gonna be the maximum voltage divided by the resistance. So that's going to be five volts, which is the maximum voltage divided by 10 owns. So this is gonna be half an amp now the question says, what is the current? It didn't ask for the maximum current or the R. M s current just said the current. So what we wanna assume it means, is the current as a function of time. Okay, because the current doesn't have one particular value. We have to list a current for all possible values of time, all of the possible values of current. Okay, so the current as a function of time we know is just gonna be the maximum currents times cosine of omega T. So what we need to know is the maximum current and omega. We know that the maximum current through the tunnel resistor is half a nap, and we know that the angular frequency is seconds. So this is just going to be 0.5 amps times cosine of inverse seconds, times time and this is the current at any point in time through that 10 ohm resistor. All right, guys, Thanks for watching

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