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concept

## RMS Current and Voltage

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Hey, guys, in this video, we're going to talk about these things called RMS Values. Since current and voltage are changing continuously in a sea circuits, it's helpful to know average quantities of the current and the voltage. But it turns out that it's not actually useful to know the average specifically but more useful to know a type of average called the M s. All right, let's get started. A very common question. The answer is in alternating circuit. Sorry, alternating current circuits. What is the average of the current and the average of the voltage I have above me? The two graphs of the voltage versus time and the current versus time? And you guys can see that for every peak I have above the horizontal for voltage, which represents a positive voltage or voltage with a particular polarity, I have a symmetric or identical peak below the horizontal, which represents a negative voltage or a voltage with the opposite polarity. The same thing happens when I look at the current versus time graph above me for every peak that I have, that's above the horizontal axis, which represents a positive current or a current in one direction I have a symmetric or identical peak below the horizontal, which represents a current that's negative or current in the opposite direction. Okay, and you're gonna alternate between these positive and negative peaks forever. So what do you guys think is the average value off the voltage and the current? It's going to be zero, and it's always going to be zero, because thes positive peaks are always going toe alternate with the negative peaks, and the effect is always going to cancel itself out. Okay, so a much better average quantity is called It are a mess value. Okay, RMS is an acronym, and it stands for the roots. I mean squared. So the R. M s value is the root, mean squared value. Now I space these words because there's a little bit missing here so that we really understand what in our messes, it's the roots off the mean off the squared value. That's what RMS means. That's what route means. Squared means. It's the route off the mean off the squared. So if I want to know the RMS value of X, for instance, X could be anything. It could be voltage. It could be current it could be power could be whatever to find the arms value. I first square it. So that's the first step, right? Then I average it or I take the mean of it. Then I take the square root or the route. So it is the root of the mean off the squared, right, the root of the mean of the squared. This is very important that you do it in this order because if, for instance, you were to just average X, that's not gonna be the same value as the R. M s because, for instance, what's the average of current zero? So if you then square that average, it's still zero. And if they do, then take the square root of that average squared, it's still zero. Okay, so it has to be the root of the mean of the square. Alright. Now, luckily, there are very easy relationships between the arms current and the maximum current and the RMS voltage in the maximum voltage. The RMS of either is just the maximum value divided by square to to, or you could rewrite it and say that the maximum value of either is just the square root of two times the RMS value. Okay, let's do a quick example to illustrate this. If the RMS voltage of an outlet in the U. S. Is 120 volts, what is the maximum voltage of an outlet? If you complete a simple circuit with this a c source by connecting the 12 ohm resistor, What is the R m s and the maximum current in this circuit? Okay, so three questions here, what's the maximum voltage given the RMS voltage? What's the maximum current and what's the R. M s current? So let's take these one of the time we know that v RMS equals 120 volts, and we want to figure out what the maximum is. All we need to do is use this equation right here. The maximum voltage is just gonna be the square root of two times the RMS voltage. So that's me Square to to times 120 volts, which is about 170 volts. Okay, One question down. Now we want to know what are the arms and the maximum currents. I'm gonna find the maximum current first. Okay, now imagine for a second. What this circuit. Looks like I have an alternating source and I have a resistor. Whatever voltage is across this alternating source is the voltage across the resistor by care chops. Loop rule. Right. So when the voltage is v max across the a C source, what's the voltage across the resistor? The max. So what is the maximum current? It's gonna be the current when the voltage across the resistor is V Max. Okay, so we can just say that the maximum current is going to be V Max divided by our This is just OEMs law applied to the resistor when the voltage across the resistor is V Max. Okay, so this is gonna be 120 divided by 12. Sorry, not 120. 120 is the RMS Voltage 170 divided by 12 which is about 14.2 amps. Now that I know the maximum current, I can use this equation to find the arms current very easily. The arms current is just gonna be the maximum current divided by the square root of two. That's gonna be 14 2 divided by the square did, too. And that is about 10. Okay, that wraps up this discussion on the arms values for voltages and currents. All right, guys, Thanks for watching

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Problem

An AC source operates with a 0.05 s period. 0.025 s after the current is at a maximum, the current is measured to be 1.4 A. What is the RMS current of this AC circuit?

A

0.22 A

B

0.99 A

C

1.4 A

D

2.0 A