 Hello everyone. This is Dinkar Patnaik from Valchin Institute of Technology, Solapur. In this video, I will be explaining you some of the basic features of resonance and how it happens in a single phase AC circuit. So by the end of this course, students will be able to explain the concept of resonance in a single phase AC circuit as well as explain some of the basic behavioral model of storage elements like inductor and capacitor whenever a single phase AC supply is applied to a case study circuit like series resonance circuit which is composed of R, L and C elements. To understand the basics of resonance, let's have a deeper look at the basic definition of resonance which says that the circuit is said to be in resonance if the currents in a given circuit are in phase with the applied voltage. And this condition is possible to bring up in a given electronic circuit whenever there is an electronic circuit like RLC and any AC supply is actually applied. So as we say that the circuit is composed of elements like R, L and C. So the enablement of L and C kind of components in such kind of circuits is going to generate two basic conditions that is either in case one we have XL greater than XC which talks about the inductive reactants being more than the capacitive reactants whereas in the other kind of case that is case number two we have capacitive reactants being more than the inductive reactants. So to understand resonance we need to first have a look at how resonance plays an important role in the field of communication. Resonance really plays an important role in the field of electronics especially in the field of communication. Whenever we say that we are talking about communication it's a very good idea to discuss about the radio receiver. So the ability of a radio receiver to select a specific frequency by eliminating the rest of the unwanted frequencies which are being transmitted by the other base stations is an important mechanism which is completely dependent on the principle of resonance. So let's have a deeper look at how the resonance happens by applying a single phase AC to a case study circuit like series ILC circuit. Consider a certain length of wire which is twisted into a coil this forms the basic inductor. Now let's name it as L as we all are already familiar that an inductor is denoted by using the units called Henry. So let's say we have a coil through which I am passing some current which is indicated by I. Now whenever we say that there is some sort of current passing through this inductor it generates an electro whenever we say that there is some sort of current flowing through this coil we have some electromagnetic force that is developed across the surroundings of this inductor. So this principle is based on a Faraday's electromagnetic law of induction. Now having said that we have some sort of current flowing through this it's always better to go ahead and have a look at the relation between voltage and current. So let's say that this is an inductor called L and there is the current flowing I. So based on this we can say that there is a voltage drop of VL across the shown inductor. So if we are about to identify the relation between the voltage and current of this particular inductor let's have a look at it. So we can write V equals to L di by dt where L is the amount of inductance which is indicated in the form of Henry's then I is nothing but the amount of current flowing through this particular inductor whereas V is the amount of voltage drop that we are about to identify by identifying this particular equation. Now V equals to L di by dt also indicates that we have a change in current for a given change in time. So we can simplify this equation further by writing further we can integrate both the sides by taking integral under the limits 0 to T. So this gets simplified to okay. So here it is very important to highlight this particular part that is the current flowing through an inductor as we have shown in this particular diagram is nothing but the sum of the integral sum of the overall voltage flowing overall voltage drop across this inductor plus the initial part of the current. So this highlighted part is very important. So it's a meaning that whenever we have some storage elements like an inductor or a capacitor it is always good to identify how much amount of initial energy is stored in it before proceeding for the rest of the parts. Further now let's consider a capacitor across which we are again applying some sort of AC voltage. Now again we are about to identify the relation between current and voltage of this capacitor which is now given by I equals to C dV by dt. So as previously we have seen the total amount of current that is flowing through this particular capacitor depends on the rate of change of voltage with respect to the given time. Again this is a very important factor why we will see in a couple of minutes. Now we can again simplify this as again we can integrate this under the limits. Therefore the final equation becomes V of t equals to 1 by C integral 0 to t I dt plus V of 0. So here again the V of 0 the part which is highlighted is a very important part which actually indicates that again the overall voltage being developed across your capacitor depends somehow on the initial energy that is actually stored inside your capacitor. Now this shows that whenever there is a presence of storage elements the presence of storage elements in any given circuit generates some sort of inductive as well as capacitive reactance. Now let's have a simple look at the series circuit where L and C all three are connected in series where there is an application of AC source. Let's say this as R, L and C and when we say that there is a presence of storage elements like L and C and as we have seen its dependency on the amount of frequency. Now I am going to write this as XL and XE. Now the total impedance Z is given as the sum of resistance plus some sort of reactance. Now what is this X? This X is nothing but a combination of XE as well as XL. Now this X can be later on replaced by two things as we have seen in our previous slide that there are two possible conditions that is case number one where XL is greater than XE where we say that the overall amount of reactivity being offered by your coil dominates this particular capacitance means the reactivity offered by inductive component in the given circuit is going to be more than the amount of reactivity being offered by your capacitor that is the case one where XL is greater than XE in a similar way. We have case number two which says that the amount of reactivity being offered by your capacitive component in the circuit dominates the amount of reactivity being offered by your inductor. So this is case number two where we can write like XE is greater than XE. Now having said that we have these two conditions now we can draw a simple graph where on Y axis we have the amount of reactivity versus the frequency. Now we can make a small table to understand how the frequency dependency generates the amount of dominance in a given circuit that is we have reactivity either it is XL or XE and also we have frequency. Now as frequency starts to proceed from zero I mean I am talking about this origin and it proceeds towards the right part of my X axis that is towards infinity and I know that XL is nothing but 2 pi FL, XE is nothing but it is equals to 1 upon 2 pi FC which also indicates that this is directly proportional to FL. If I eliminate this particular part being 2 pi being constant similarly this is inversely proportional to the frequency now forget about the suffix. Therefore as frequency proceeds from zero to infinity on the X axis we have XL proceeding from zero to infinity. So let me draw the graph of XL now. So there is a straight relationship for XL as frequency proceeds from zero to infinity XL also tends from zero to infinity whereas for inductive reactants we have a straight line similarly we are going to draw the graph for capacitive reactants. There is no linear relationship between the amount of reactivity being offered by your capacitor with respect to the frequency. Now as XE is inversely proportional to the frequency when frequency proceeds from zero to infinity your XE is going to proceed from infinity to zero and usually we don't touch this to the Y axis and X axis so it matters a lot. So this curve actually shows that we have the capacitive reactants starting somewhere on the Y axis at infinity and then it is going to approach towards zero. So later on we can broadly elaborate the concept of resonance into series resonance and parallel resonance which we will be covering in the next video.