 Hello everyone. I am Dinkar Patnaik from Waltz in the Institute of Technology, SolarPort. Today we'll be focusing on what is serious resonance and how does it happen in a single phase AC circuit. By the end of this session students will be able to understand and explain how serious resonance happens and what are the various effects of impedance, frequency and rest of the things on a single phase AC RLG circuit. So let's have a look at how the things happen by considering practical series RLG circuit. So recall that we have talked about resonance in the last video where we said that resonance is classified basically into two things. The first is serious resonance and the second one is parallel resonance. So let's have a look at series resonance circuit today and identify what and how the things happen in a given series resonance circuit. So consider a simple series resonance circuit where we have RL and C and of course AC is applied. Now whenever we apply an AC source to a series RLG circuit the current tends to flow in a clockwise direction. For instance we are considering this clockwise it may be anticlockwise as well. But for simplicity let us go for a clockwise direction. Now when we say that there is some current flowing through this RLG circuit we need to analyze what is the effect of patches of current in a given RLG circuit. So the current flowing through this R is going to cause a drop of VR across this part and it is going to create a voltage drop of VL across this part of the section. Similarly it is going to create a drop of VC across the capacitor and we have also seen the expression for VL and VC in our last video. So just try to recall what we have identified and what is the effect of patches of current in a storage element like L and C and try to utilize that knowledge in this video. Now a circuit is said to be resonant whenever XL I mean the reactant software by an inductor is equal to the reactant software by a capacitor and as we have seen in our previous video that XL is nothing but it is given by 2 pi FL and X is nothing but it is given by 1 upon 2 pi FC. So after simplifying what we get is F equals to 1 by 2 pi under root LC. So this is nothing but FR. So what is FR? FR is nothing but resonant frequency. Now if we try to analyze the same series energy circuit with respect to a graph then it becomes very evident to understand how the frequency change is going to affect the overall impedance of a curve. So this curve would be an impedance versus frequency therefore we have frequency on our X axis and we are going to plot some reactances and altogether the impedance curve on our Y axis. So let's have a look at it. As we have seen previously we need to first of all identify the change in frequency like it is going to tend from 0 towards infinity and we need to identify its equivalent effect on the inductive reactance and similarly on capacitive reactance. So as FL tends to 0 I mean tends towards infinity from 0, XL is also going to tend from 0 towards infinity and since XC being inversely proportionate with the frequency XC is going to tend from infinity towards 0. So it's a clear indication that on your X axis here as F starts to begin from 0 and approach towards infinity we need to draw a line which is going to increase along with XL. So it is going to be a linear relationship that is the reason why we have a curve and this represents XL. In a similar way we have XC which is inversely proportional we need to draw this on a negative X axis. So this curve is representing XC. Now why are we going for the negative Y axis for representing this XC? There is a reason for that one. So for understanding this we need to first of all understand what is the overall impedance of this circuit. It is very important to understand it before understanding the graph. Now let's say that I want to identify the impedance which is nothing but R plus XL minus XC which is nothing but R plus J times omega L minus 1 by omega C. So we are not only representing this XC but we are in fact representing this complete term at this point. So that is the reason why we have this negative Y axis. Now we got XL, we got XC. Now what is the overall impedance? So let us suppose that this R is going to be some constant. We are not saying that we are connecting some sort of potentiometer or any other stuff like this. We are interested in identifying the change in L, increase or decrease. Similarly an increment or a decrement in C and we are about to identify the response of this increments and decrement in a storage element on a series resonant circuit. So for understanding the effect of variation in either L or C we need to consider that R has to be made constant. So consider that R is constant maybe like something equal to 1 kilo ohms. I am not going to represent that R anywhere here because I don't want to spoil the effect of this excellent XC on your overall curve. Now as I said that we have something known as resonant frequency. So where is the resonant frequency on this graph? Resonance frequency is going to happen or appear somewhere on your X axis whenever the resonant condition in your in your series RLC circuit happens. And when does a series resonant circuit is going to be is going to be known as a resonant form it is said to be in a resonant form whenever XL is equals to XC. So imagine that we are varying the frequency. We are trying to vary the frequency of what? We are going to vary the frequency of this AC waveform. So anyhow we are applying an AC waveform and whenever we say that it is an AC waveform we have some sort of frequency across this. So by controlling this frequency you can control the XL and by controlling the same frequency you can also control XC. So imagine that we are varying this frequency and maybe at some point in between this 0 and infinity there is going to be some point where you will say that XC is equal to XL and this is nothing but the frequency which is represented on your X axis in this graph that is impedance versus frequency and we are going to represent that point as FR. Okay now this is a very crucial and an important point in the working of a resonant circuit. So let us say that now I am trying to plot the overall Z I mean the overall impedance which is a combination of some constant resistance which I will not show on the graph and purposefully I am going to draw the waveform of the overall Z so that you can understand the equivalent effect on the overall impedance whenever XL and XC changes. Now the waveform of Z is going to be something like this. Now there is a reason for this how to read this particular graph. This is a curve which is representing the overall impedance and this curve is represent sorry this curve is representing the overall impedance it's a meaning that so this is representing the overall impedance of the curve it's a meaning that this curve is a combination of XL plus XC all together. Now what is the exact meaning of this? I can make a statement or I can conclude that the overall impedance of a series resonant circuit is nothing but it is something which decreases along with a decrement in your X okay so this is having the highest value here XC is decreasing along with Z okay so that is the reason how we actually read this. So impedance in a series resonant circuit is decreasing from F equals to 0 and when it is moving towards FR and then after FR it tends to move towards infinity again along with XL. So the effect on impedance that is provided by this reactance offered by the capacitor in a series resonant circuit is decrementing whereas the effect of reactance that is offered by this inducted in a series resonant circuit is going to increment your overall impedance. So this is a very clear indication that your circuit is completely capacitive below FR and above FR your circuit is completely inductive. So this is the overall variation and the dependency of a frequency on I mean of a series resonant circuit and we are going to work on how the voltages and currents vary in a given series resonant circuit in our upcoming video. These are the references used and that's all for this video. Thank you.