 Okay, good afternoon guys give your attendance in the chat box There was some issue from my side. So that's why the class was delayed for 50 minutes. I'm waiting for others to join I'll start in next two three minutes Because I know a lot of people will join this So I'm waiting for next two three minutes then we'll start Okay, anyway, uh, okay Let's wait for two two moments Two more minutes. Let's wait. I don't want people to to come at 140 and and then Ask me what I'm doing because this is a revision class. So I Don't know why people are not joining Okay, let me start. Let me start with definition of charge So I have told you charge is presence of or let me start with Atomic level. So suppose I have Suppose I have small Atom and in or let me make a bigger one for you so that you can understand and atom will have positive protons and Same number and then few neutrons would be there and same number of electrons would be moving around it So what happens is? that if these electrons get some energy which is Capable enough of getting them out of their orbit in which they are revolving around the proton the electrons will come out Conventionally electrons are denoted as negative charge So I will tell you from here that conventionally we have two types of charge one is positive So generally nucleus Which contains protons is Denoted as positive charge So when I'm and negative charge is electrons so this is just convention that this is positive and this is negative and I have to also told you in the class that Positive charge it it denotes that not deficiency of protons Protons in the nucleus remains same. So what do I mean by positive charge then so positive charges just deficiency of Electrons it means that out of the neutral atoms few electrons have jumped out of their orbits and they are no more revolving around the protons Or the nucleus which makes the atom neutral and they are not in their orbit They have got some energy from some other source and they are Wandering somewhere else. So free wandering of the electron is known as presence of Charge at In at any particular place now from charge I Started teaching you after charge. I started teaching you that this was the charge now. There are few characteristics of charge like We have few characteristics of Any particular element like mass charge these are intrinsic characteristics one is mass second one is Charge so when I have electron and if it is free electron So I have charge on it And the charge is supposed to be 1.6 into 10 to the power minus 19 coulomb now There are a few more things which is like First one is Charge is Conjunct So what do I mean by charge is conjunct so try to understand if I have atoms So suppose I take any particular Object it will make it will be made of billions of atoms and when I say atoms atom is is Combination of proton and neutrons in its nucleus and number of protons would be equal to number of electrons in an in a neutral atom and There would be billions of such atoms Now what happens if I give some energy to these electron electrons and even if they come out We are not creating any new electron or proton the electrons from its orbits are jumping out of it and They start moving freely around that particular object whatever space that is present over there You can understand the size of electron is very very small. So they don't I mean they can sneak through the object because of their very very small size and Due to this There is a property which is like charge is conserved by which I mean to say that In an atom number of protons are equal to number of electrons Even if electrons are jumping out of their orbit, we are not creating any new electron So suppose I have any particular atom z and If z has n number of protons So new neutral Z will have n number of electrons also And now what happens if two electrons comes out of here? So z becomes too positive z becomes too positive means two electrons have left The orbits of z now these two electrons are moving freely somewhere else But if we add the number of protons total number of protons and total number of electrons they remain same Inside that object Sorry So it means that the charge is conserved in that manner the second thing is charge is quantized And what do I mean by charge is quantized? So What are the charged particles charged particles are electrons and protons and Try to understand Any time charge would be an integral multiple of charge of one electron Now this particular sentence may look like a very heavy sentence or very difficult to understand But I would like to explain it in this manner. So try to understand when one electron comes out of The Atom the atom becomes one positive and the charge is Charge equivalent to charge available on one electron Now the number of electrons coming off the out of the orbit would always be integers I am saying the number of electrons it will never be the case that two and a half electrons come out of the orbit It will always be either one electron or two electron or three electron or four electron or five electron likewise So the number of electrons which are coming out of their orbits and moving freely are in integers and that is why the charge and that is why the charge Is written like n into e now. What do I mean by n into e? So e is generally denoted as charge on one electron. So this e is 1.6 into 10 to the power minus 19 coulomb now if 150 electrons are moving freely inside a particular um piece of object So then the total charge would be 150 e that is why I am saying that the charge is quantized So charge quantized means The charge of any object would always be an integral multiple of e. That's what I mean Why it will be an integral multiple of e? Because the number of electrons which will be moving freely inside a particular object Will always be in integers and That is why charge quantized means n e So I hope you understood this now. I'm moving to another concept which is coulomb's law So by coulomb's law, I have taught you this so this this is written as coulombs, but it is called as coulomb's law now You all might have because this is a revision class so I can discuss a few things which I have discussed in the class time and again, I tell you that uh, suppose I have to Shift my almyra from one place to another place I have to apply some physical force on the almyra so that that almyra can be shifted from one place to another But what happens is when two charges are kept in near vicinity Or if two charges are separated by a distance r Then we see some kind of force being applied on those two charges My question is those two charges are not touching each other So from here two questions arise. What are those two questions? First from where does that force eliminate? From where does that force comes into picture? So, um Like if I have two charges if I denote it here And this is my charge positive charge q1 And this is my positive charge q2 And there is another case where I have a positive charge q3 And a negative charge q4 and I have another force where I have a negative charge q5 And another negative charge q6 Now my Question is there are two things Once when the charges are not touching each other when they are separated by certain distance how force is originating And if force is there and if The charges experience certain force What is the magnitude of it? So first one is I'm answering the second question and then I'll go to the first question So, uh The magnitude of force is given by f is equal to k q1 q2 divided by r square So it means that force is proportional to The charges on them And force is antiproportional to the square of the distance between them And what is this k k is called constant the value the k is written by 1 by 4 1 by 4 pi epsilon naught where epsilon epsilon Not is permittivity of free space or permittivity of I'll explain this permittivity constant k is the value of k when you put the value out here Uh, I'm writing the value of epsilon naught here. It is 8.85 Into 10 to the power minus 12 And when you put put these values here you get k is equal to 8.99 into 10 to the power 9 Which I also call 9 into 10 to the power 9 so you can use any of these values Doesn't matter now try to understand why I have made these three cases So if if you if you put these values here Of q1 and q2 if both of them are positive anyway distance is positive and k is a positive constant So force would come out to be a positive If one of them is positive and one of them is negative So force will come out to be negative if both of them are negative then again negative negative will get multiplied here And it will be positive it means that try to understand it It shows me that if force is positive and what do I mean by force is positive and force is negative So force as we all know is a vector quantity and if force is a vector quantity it it In for any vector there are two properties one one is its magnitude and second one is its direction Now I'm not bothered about direct magnitude here magnitude anyway is given by k q1 q2 divided by r square But what do I mean by this positive and negative? force it means that direction of Two there are two kinds of diamond two directions for these forces One is positive direction and one is negative direction It means and and and we can also see that when the charges are of same type same type means Magnitude of the charge may be different But when I when I say that the charges are of same type I mean to say that the charges have same sign And if charges have same sign Then the force is coming out to be positive when both of them are positive the force is positive When both of them are negative then also the force is positive But when the charges are of different sign when the one charges are one charge has positive sign and then another charge has negative sign So then in that particular case The force becomes negative it means that the direction of the force changes So this tells me that the force applied between the different kind of charges Are of different nature and from here we come to a conclusion by experimenting this That two like charges Repel each other and two unlike charges attract each other So this concept of force being positive and negative Tells me that the direction of the force between two charges When they are same is away from each other So this particular charge q1 when will when it will apply force on q2 So suppose it applies force f1 f1 would be away from this If I draw a line from here f1 would be away from charge q1 And if this applies force f2 f2 would be away from charge q2 So this is a force of repulsion Similarly here, but in case of q3 and q4 which are of different signs or One positive and one negative if I draw a line joining them q3 would be a force of f3 would be a force of attraction And similarly f4 would be a force of attraction So two like charges repel each other and two unlike charges attract each other This is what ulems law is all about. I hope you understood it Okay, so somebody asked me why charge is quantized. I am saying that let me go to the first Thing charge is quantized because what I'm trying to say is a charge is when the atom does not remain new Neutral it means that few of the electrons jump out of their orbit and start wandering freely around the space available Now number of electrons jumping out of the orbit will always be in integers So it will never be the case that three and a half electrons jump out of the orbit It will always be two electrons Coming out of the orbit three electrons 150 electrons are in roaming inside some space So that is why the charge Would inside an object will always be written as n into e it means that charge on one electron Multiplied by number of electrons roaming around freely inside a space And that is why I'm saying it saying that charge is always quantized It can be quantified in terms of or the total charge can be quantified in terms of number of electrons roaming around In an object I hope you understood it. Did you understand suti? Tell me I'll move ahead I hope she understood it Now let me move to electric field So the first question was when Two charges are separated by Certain distance how they are able to exert force on each other So my question was that if I have an almira at my house And I want to put it from a place a to b What I will do is I will have to exert a force Physical force on it and then if the force is able to come able to overcome the friction that it is already having and and the inertia so in that particular case the Then I'll be able to move this almira from place a to b But what happens is if two charges q1 and q2 are separated by a distance r And there is no physical contact in between them still they are exerting force on each other how this is possible Explain this particular phenomenon there Is a concept of electric field and I have discussed this in the class also That whenever the we have to explain a force where physical contact is not happening We try to explain it with presence of field. So what we say that is This particular or any charge what is electric field Electric field is a mathematical definition. I'll give give you I'm giving you now electric field is defined as force applied per unit charge But this does not explain the concept very well. So let me explain the concept what happens is what happens is Any particular charge if I have We assume that the charge creates electric field around it now. What kind of electric field it creates So electric field is generally denoted by electric field lines So try to understand if I have a positive charge q1 It is assumed that electric field is created with the help of electric field lines and if charge Is positive electric field lines are Conceived to be coming out of the electron something like this then If a charge is negative charge electric field lines are conceived to be Going towards that particular charge So then if electric field lines are defining me the creation of electric field and hence The application of force. How does that phenomenon happens? So try to understand all of you That due to this charge wherever there would be a presence of these electric field lines The charge will be able to create it create its own electric field and due to its own electric field if any other charge comes into the uh If any other charge comes in contact with the electric field lines of Charge q1 then that other charge will feel certain force In the electric field of charge q1 what I say that if charge q1 is here And it is sending back it is sending outward electric field lines something like this Now what happens there there comes a positive charge q2 Now what happens this charge will also be sending electric field lines outside Now what happens how the interaction of field lines will happen here? So let me explain you interaction of field lines There is one possibility that this field line goes and and touches this charge q2 But what happens if there is another if if there is a field line from charge q1 which is going and And merging with q2 then you see here if charge q2 is positive all lines are going out But this line is going and merging with q2 which is against our convention So in that particular scenario what it is assumed that when two positive charges are interacting with each other Then there would be a place where These field lines will never interact And these field lines will move away from each other Because moving towards each other would mean that this field line and is going and merging with charge q2 And field line emerges emerging from q2 and is going and Merging with charge q1 it means that there would be one common line Which is going going towards positive charge as by convention We know that there is no line which goes towards positive charge all the field lines comes out of the positive charge hence The field lines are represented like this And that is why there is a force of repulsion between two positive charges So the field lines interact in such a way that the field lines from two positive charges will never cross each other And will always move away from each other. That's why between two light charges. We have Force of repulsion If I have a positive charge and I have a negative charge then the case is simple Because a charge with our field line will come from here and can go and merge over here Because all the field lines come and Converge on the negative charge the field lines diverge from the positive charge So a charge which is coming out like this will go and converge on negative charge Similarly a field line coming out like this will go and merge here So there is a force all the field lines from positive and negative charge Do cross each other and they they diverge from positive charge converge on negative charge That is why there is a force of interaction over there Now what is the magnitude of electric field? Let me come to that part So magnitude of electric field is given like this. So if this is the charge q and at this distance r Suppose this is point p at distance r How much How much electric field it will produce so we keep a one coulomb charge over there So I told you that electric field is force applied per unit charge per unit charge means if I keep A one coulomb charge or a unit charge a one coulomb charge is also known as a unit charge So if I keep a unit charge here, so force applied would be equal to k q into one coulomb divided by r square So if I divide this charge by one coulomb divide this force by one coulomb So force divided this one coulomb goes here Is equal to k q divided by r square So force per unit charge is known as electric field. So electric field is k q by r square Now Before I explain it with It with non unit charge. Let me tell you that what is this q this q is charged because of which I want to I want to know the magnitude of electric field So electric field is property of the charge which is creating it Not the Property of the charge on which it is exerting the force try to understand. I'm trying to tell you electric field is property of Charge Which is creating it And not The charge on which the force is Getting applied So suppose what what I have is Instead of this one coulomb. I have a charge q1 here or or a charge q here And and suppose I take this as q1 So force applied on q would be f k q q1 divided by r square Now force applied per unit charge I mean what is the force applied if q1 Becomes one unit so that would become f by q1 is equal to k q by r square So try to understand look at here if I keep one coulomb charge here Or if I keep q1 coulomb charge here the electric field remains k q by r square at distance r So that is why I have been telling you this that electric field is property of charge which is creating it Not the charge on which it is applying the force So try to understand now electric field is proportional to amount of charge and electric field is antiproportional to square of The distance from which I am trying to calculate it So try to understand that if the distance from the charge is increasing Then the amount of electric field will go down or the sorry the magnitude of the electric field will go down so if Understand here if this is charge q So the amount of the magnitude of electric field here at point p and there is one Point here. I can say that e p is greater than e q just by looking at it. Why because distance from the charge suppose this is r1 and This is r2 so r1 is lesser than r2 so magnitude of the electric field from any particular charge will keep on reducing Depending on the distance. I mean depending on as the distance is reducing Going away from the charge So this is the concept of electric field lines. Now. Let me move to electric potential Do you understand electric field? Yes. No now Uh, give me a moment guys I'll be just back in one moment Okay, so before I teach you, uh electric field, uh, sorry electric potential Uh, let me discuss potential energy with you So in grade nine, you all might have studied gravitational potential energy So, uh in that particular concept you might have studied that if this is the ground level And here if I assume this is ground level So here if I assume ground level means I am assuming h to be zero So if here I assume potential energy to be zero If here I assume potential energy to be zero So at any particular height h My potential energy or or or the or not my potential energy the objects potential energy was mg h where m was mass of the object z is gravitational acceleration And h is height Now why this potential energy? So look at here. There is I'm not getting into much details Uh work done is always defined as change in energy As kinetic energy One second change in energy as kinetic energy remains same What is kinetic energy kinetic energy is half mv square So mass is there, but velocity is not or speed is not there So I'm assuming that my object is at rest at both the points So there is no change in kinetic energy hence work done would be equal to change in potential energy So which is nothing but work done is equal to mg h minus zero Because I'm assuming potential energy to be equal to zero and work done is coming out to be mg h Now why am I doing all these things? Try to understand a lot of uh, uh, when you When uh, you were learning potential energy concept of potential energy Uh, there might be a line which which was written in the book or which might you which you might have studied While doing this concept that potential energy is dependent on position of the object now generally if you see Potential energy is is a notional concept. So what do I mean by notional concept? So try to understand here Uh Kinetic energy is actual energy like which comes due to its speed But potential energy is considered to be energy which is stored inside a body because of its position in the in in in the space or in the universe or in in in a plane or in a three dimensional plane Likewise, whichever term you want to use you can use it here So why potential energy is is stored in a body because of its position because it is assumed that at infinite The potential energy is considered to be zero and if at infinite the potential energy is considered to be zero What happens over here is that If if an object is kept at is at its place p and forget about this put Forget about this Ground level thing now if at infinite The potential energy is zero and from At infinite I am bringing that object to any particular point p I'll have to do some work To bring this particular object from infinite to this particular point p And due to which as the work is done on this object Some amount of energy would be stored in that particular object Now, I know that work done is equal to force into displacement So if work is getting done certain amount of force is applied on that body And if force is applied on that body some amount of stress would be there in that body And due to that some amount of potential energy would be stored out there This is why this concept I apply in electric field also. So what It is done is so try to understand look at here if I have a positive charge over here Now what does this positive charge do the positive charge because of its Interest characteristics of having a charge Will Have its own electric field and I call this Electric field lines presence of electric field lines Around a positive charge as stress zone Why it is stress zone? Try to understand because if you keep any kind of charge over here The charge will undergo and stress or a charge will Experience certain amount of force. Why charge will experience certain amount of force? Because of presence of this electric field line Created by this positive charge q and due to that force some kind of displacement will happen And hence position of the object will change now try to understand Look at this point p here the electric field is even and look at this point q here the electric field is e2 now Try to understand as even is greater than e2 the stress zone at point p or Amount of stress or amount of potential at point p would be more than amount of potential at point q Why because here the magnitude of electric field is more and here the magnitude of electric field is less Hence the ability of this point p to apply force on certain other charges more than Ability of this point q to apply force on any other charge. Are you understanding? I'm again repeating what I'm saying at this point p this point has more ability to apply force on certain charge than this point q because The magnitude of electric field that this stress zone if I draw this Circle here, which is equi distance from this charge this charge q and if I draw this Circle here, which is also equi distance from so suppose this is r1 and and and this is r2 so From as distance r1 is lesser than r2 at distance r1 more force would be applied Because the amount of electric field is more hence at this point The all the points will have more potential to apply force than any point at this particular circle So potential is generally written as 1 by 4 pi epsilon naught. I'm not getting into derivation It multiplied by q by r. What is q q is the charge which is creating the electric potential or electric field And r is the distance of point at which I am calculating the potential So v is proportional to q and v is anti proportional to r Did you understand the concept of potential? Yes or no Tell me I want answer from all of you. Whosoever is their answer? Okay, great So now try to understand All of you are sitting with the the So let me explain one formula to you. I already told you so Work done is equal to Work done is equal to change in potential energy When kinetic energy remains same, I mean So try to understand work done over here is potential energy is given by At any particular point. So if I take this point And I ask you what is the potential energy here potential energy Or electric potential energy is given by electric potential energy is given by q into v of certain point v means potential of Electric potential of certain point so This is the potential energy. So work done is equal to change in potential energy. So suppose The potential over here is v a and potential over here is v b And I am transferring a charge q from v a to v b. So work done will be equal to Potential energy here. So potential energy u b minus u a u b would be equal to q into v b minus q into v a what is q q is the charge which is getting transferred from one to another place q is not the charge which is creating potential energy Try to understand once again q over here in this formula is Not the charge which is creating potential at a and v q is the charge Which is getting transferred from a and v some other charges are creating potential at point a and v that is why I am calculating v and v b So q w would be equal to q multiplied by v b minus v a Now let me go to So this was electric potential for you After after electric potential I taught you what I taught you I went directly to After static I went directly to Current so let me explain you now current electric current so electric current is given as the definition is charge per unit time is Known as electric current So I is given by I is equal to q by t And what is q q is equal to any So I can also be written as I is equal to any by t Generally q would be given to you So I is equal to q by t Now try to understand So now let me And calculate The another concept of So suppose I have A wire like this generally The wire is taken as wire is considered to be cylindrical So how do I come to know that? So try to understand here now. How will you count that? How much charge is There in this wire so Why I want to calculate this because I want to calculate Is to calculate the current density sorry Yes, so to calculate the current density of of of a wire So what I do is try to understand suppose Look at here. How I am doing it. So suppose this is This cross sectional area is a so suppose Cross sectional area of of the wire is Why I am taking cross sectional area because I want to give you Electron density And what is electron density electron density is number of electrons per unit Volume So suppose electron density Is equal to n So try to understand what what is Current density current density is denoted by capital j And it is defined as Current per unit area. So j is defined as i divided by a So what I need to do I need to find out I I know that i is equal to try to understand I know I know that i is equal to q by t And what is q q is equal to any divided by t What is n n here is number of electron, but I am not giving you number of electron directly I am giving you electron directly Sorry electron density. I'm not giving you number of electron try to understand. I'm doing it on the other side if if number of electrons are given directly In place of I have explained this concept in the class. I think in place of if number of electrons are given directly in place of uh electron density then j can be written as j would be equal to n e divided by a that's the formula nothing else This is the formula where n is number of electrons But why I am giving you try to understand why I am giving you number of electron I'm in uh Why I'm not giving you number of electrons directly and I'm giving you uh electron density Because I want to explain you a concept of drift velocity And what is drift velocity try to understand Drift velocity means so it's something like this try to understand so uh suppose this is certain space in which Electrons are moving from one place to another place Now electrons don't move in one particular direction So their direction of speed would be something like this So it will be moving in jigsaw I mean in in in some random Motion of electrons they will not move in one particular direction So if they don't move in one particular direction So then what happens try to understand What the concept of current that is I started teaching you I started teaching you from the uh Mathematical perspective of it so to calculate what is the electron how to calculate the electron The conceptual basis on which the electron should be studied is something like this try to understand if this is my wire And if there is no external energy provided to this particular wire by external energy I means if there is no electric uh Potential across or if there is no battery connected across this wire there would be no current in it Even if number of free electrons are present in this conductor. Why? because the electrons Present in this suppose these are electrons few electrons the electrons present in this particular Uh conductor would not be moving in one certain direction They would be moving in this random fashion and that overall movement will cancel itself and the electron Uh would be Sorry, and the current would be zero Also, they collide with each other. They'll be losing their energy and all sort sort of Impact will happen and and due to that their effect as Effect would be I mean effect of the motion of the electron would be zero now when you apply certain potential across this particular Conductor what happens all the electrons start moving in one particular direction And the speed at which the move is known as drift speed So what is drift speed drift speed is? The speed of the electron in which it is moving in one particular direction under the effect of certain Potential energy applied across the conductor. So this is what the drift speed is And drift speed is proportional to so you may ask that if I change the electric potential will it change Yes, it will change drift speed is proportional to the electric field applied And I know we know that how electric field is related to the potential So if I'm saying that if the potential is increasing It means that in between these two points there is a higher potential difference This drift speed would be something else If we decrease it the drift speed will also decrease So try to understand I gave you current density here to explain you this drift speed Now how it is utilized to find out current density is that if The cross-sectional area is a So and if Drift speed is vd if I assume it to be vd So in t time how much it will go? It will travel a distance of vd into t. So what would be the? volume volume is area multiplied by length So area I have already given you a and in t time the length cover by the electron would be Vd into t So this is the volume now number of electrons in this try to understand number of electrons Would be equal to current density Sorry electron density Multiplied by volume What is electron density? It has been given to me as n and volume I have calculated as a into Vd into t. So this is number of electrons. So I'm I'm I'm negating this I'm writing it Negating this multiplication sign. I'm writing it na vd t now These are the number of electrons now. I told that the charge is quantized So charge q would be equal to number of electrons multiplied by e What is e? e is my charge on one electron multiplied by total number of electrons So I can write it as na Vd t into e So remember this if I'm asking you charge and I'm giving you current density area Drift velocity time you should understand that This na vd t is nothing but number of electrons when charge density is given Here n is not number of electrons here. N is number of electrons per unit volume That is why I'm I'm repeating it time and again. I have told you Charge is quantized and I have told you that q is equal to n e where n is number of electrons multiplied by charge on one electron Here I am telling you that charge is na Vd t into e don't get confused with this n here n is not number of electrons Here n is electrons per unit volume. So this is the difference you always have to Keep in mind Now let me go to Current current is equal to q divided by t So current would be na vd t divided by e divided by t. So t and t is gone I comes out to be equal to remember these formulas direct questions come from here And j would be equal to i by a So na vd e divided by a a and a gone It gives me n vd e. So j is nothing but n vd e this is the current density Did you all understand this? Yes or no? Tell me Tell me Only few people are watching this this video So Okay, no issues Now, let me go to ohms law And ohms law I told I didn't do the derivation. So ohms law I told you that Ohms law I told you that Current is proportional to voltage or voltage applied is proportional to the current And I told you that this proportional proportionality constant is removed by a writing of tom r where r is resistance of of the conductor And I gave you formula of r as r is equal to rho l by a so if this is the conductor And rho is resistivity Resistivity I told that it is the property of the matter It is the property of the conductor if the conductors are same Irrespective of the cross sectional area and the length resistivity will remain same So resistivity is property of the object which remains same for the same object and changes as per the As per the Change in in the conductor material now try to understand I also give you this formula where R is equal to r r naught one plus alpha t. So I told that R naught is resistance at t is equal to zero where t is temperature and alpha is constant So I told that r increases as t increases Now any particular material which follows ohm's law, there are not all conductors which follows ohm's law so for conductors which follows ohm's law the Graph is something like this. This is v and this is i v is at y axis potential difference is at y axis i is at x axis and Because this is a straight line. I can compare it with y is equal to mx. So this r will represent m. So this this slope Give r value. So v is equal to ir. So for conductors following ohm's law So as we have studied Ohm's law over here. Let me get into Resistance in series and parallel So resistance in series would look something like this. I have already explained to you that Resistance in series means same current should pass through Same current should pass through all the registers so if this is r1 r2 r3 And current which is coming out of here is i so I can write that That We now what I have told you time and again that Uh as this is revision class. I'm not getting into uh that concept once again. I'm just telling you the concept. I'm not explaining it that uh In direction of current potential Decreases or increases Write it down in the comment box. Let me check how many of you remember it In direction of current potential decreases or increases write it down in the comment box quickly Okay, good decreases So potential decreases So If I start from here v minus what how much would we decrease here ir1 minus ir2 minus ir3 Is equal to zero So v is equal to ir1 plus ir2 Plus ir3 So v by i comes out to be equal to r1 plus r2 plus r3 And what is v by i v by i is circuit resistance the the equivalent resistance So I am writing it equivalent resistance. So I saw that equivalent resistance when it is in series Is summation of all the registers in series. So r1 plus r2 plus r3 Now when they are in parallel So I've told that In parallel combination The potential difference Among them it's same but current will get distributed So if i is coming from here, this will be i1 Plus i2 plus i3 Now I have also taught you Kirchoff's law So by junction law junction law means as I have told you in the class junction law means or I told you point law Where all incoming currents and all outgoing currents Summation of all incoming currents is equal to summation of all outgoing current So if I take this point p here the incoming current is i and outgoing Currents are i1 plus i2 plus i3. So i If this is v i can be written as v by r And i1 can be written as v by r3 i2 can be written as v by r2 and i3 can be written as v by r1 vv gets cancelled out. This is r equivalent So let me write it r equivalent and I am writing here p because it is in parallel This is equivalent to 1 by r1 plus 1 by r2 plus 1 by r3 and likewise So it goes like this. So this is series in Resistance in series in parallel Now, let me teach you kirchoff's law. I'll I'll just Repeat it for you So kirchoff's laws are first law. You all know this is junction law And I just told you junction law All incoming currents one point is equal to all outgoing And second one is loop law So I have explained that loop law to you in the class. I'm writing it The algebraic sum of all the potential differences Along a closed loop In a circuit You write it down Zero. So what I do is I take a closed loop like this So it's something like this Suppose this is r1 And this is e1 This is r2. This is e2 This is r3 This is r4 And this is e3 So by kirchoff's law The algebraic sum of all the potential differences along a closed loop in a circuit is zero How do we apply it? So we take a point. Suppose this point is a And we start from this point. So suppose the current is flowing in this direction And I'm moving in this direction. So I'm going the current is flowing in this direction So v a I start from here the potential difference would be what if I'm going in the direction of current here So it will be a minus i r2 Then again current is here. So I will write it here as minus i r3 Now I'm going from positive of a battery to negative of a battery So potential will decrease. So minus e3 Then again I'm going in direction of Current so minus i r4 Then I'm going from positive of a battery to negative of a battery So minus e4 Sorry minus e3 Then again, I'm going from positive of a current to to to negative of a current So something like this you if you want you can take different Currents also i i 2 i 3 i i 4 i 3 i 4 So because that there is a battery coming in between so you can write i1 i2 i3 And then you can write i4 r1 And negative to positive is plus I'm going from positive negative to positive. So this is plus e1 And then I reach this point va. So that is equal to va. So va and va is gone. You can write like this e1 minus One second. This would be e2 e1 minus e2 minus e3 Is equal to i1 r2 plus i2 r3 plus i3 r4 plus i4 r1 and likewise. So that's how the Kirchoff's mood flaw is applied in a particular circuit. Is it okay? then I have I have told you all the all those things batteries and how they are connected if they are connected in series It will be e1 plus e2 plus e3 if they are connected in parallel. So you have to find out equivalent resistance and equivalent Potential so I'm not getting into that. So Let me do Whitstone bridge for you So Whitstone bridge is something like this. I have told you It's something like this We have a galvanometer here. We have a battery And suppose this is r1 r2 r3 r4 It becomes Whitstone bridge when the current in the galvanometer Is zero So sometimes I replace this galvanometer with resistance And it is asked that for no current to pass through this particular resistance uh, what should be the I mean out of there are four resistances r1 r2 r3 r4 So out of these four three would be given to you and it will be told that for no resistance here in this Circuit, which is bifurcating r1 r3 from r2 r i4. This is separating it So what should be r1 or r2 r3 r4? So I have done that for you. So Um, do you want me to uh, okay, let me do it. Let me not ask you and let me do it for you So what I do over here is I mark these points. So this is a this is b And this is c And this is d Now try to understand Vd minus vc is equal to suppose a current i um i g flows here So it will be i g into r Now as there is no current as i g is equal to zero vd minus vc would be equal to zero It means that vd is equal to vc that I have already proved now Try to understand So let me write v a minus vc Suppose a current i1 i comes from here And the current i1 goes here and i2 goes here. So I can write is i is equal to i1 plus i2 Now v a minus vc is i1 into r1 And v a minus vd is i2 into r3 Similarly v c minus vb is i1 because no current goes here. So i1 would be here also and i2 would be here also so i1 into r2 and vd minus vb would be equal to i2 into r4. So what I write is Look at here. I want to cancel out current. So i1 i1 I will cancel out by by by dividing it vm minus vc divided by vc minus vb is i1 by r1 divided by i1 by r2 and v a minus vd divided by vd minus vb Is equal to i2 by r3 divided by i2 by r4 Now try to understand what is the difference on left hand side left hand side here it is vc and here it is vd So I can write that as vc is equal to vd. I can write this as v a minus vc divided by vc minus vb Is equal to i2 by r3 divided by i2 by r4 And this i2 i2 one here i1 i1 one so look at here left hand side at both the places are are same So here it is v a minus vc as lhs is same so r1 by r2 rhs would also be same r1 by r2 is equal to r3 by r4 Or I get r1 r4 is equal to r2 r3 So this is the condition for which stone bridge to be formed Did you understand it? Yes or no Now let me move to the capacitors So Okay, let's do one thing Let me check how many of you just let me check how many of them just came for writing their names And after writing their names, they just disappeared. So I can see that now at 243 um Harshini is there Bhunika is there Ritu is there Ruchita is there Shraddha is there Shruti Vashnavi Deo Medhan are there others are not there. Okay, no issues fine, so Let me just revise capacitors for you and then I'll Go to the questions so Capacitors I told a device which is which stores charge So capacitor is generally denoted like this. I have done in the class at very elementary level So at I told that charge stored. So I told that Generally, we have plates like this on which There is some potential difference which is applied here and So it will be something like this q is equal to CD where c is capacitance And capacitance is denoted by epsilon not A divided by D Where epsilon not we know what it is permittivity of vacuum A is equal to area Of the plates So you can see I have made plates here And D is distance between the plates so Remember these two formulas very handy. There would be questions on these formulas in your test Now try to understand that when capacitors are in series and parallel what happens If capacitors are in series So what I write over here is So this is the capacitor again I'm taking three of them and And This is connected to the battery source and this I am assuming it to be Now try to understand these are the three capacitors with capacitance c1 c2 and c3 now Please understand that suppose if this is point P and and and this is point Suppose this is point q this is point R and this is point s So look at here what happens so Point P and s are are are terminal points. Why because our battery has been connected across it And and then the charge will be supplied so suppose Uh this particular because this is the positive size this supplies charge plus q here And if charge plus q is supplied from here, we can assume that Minus q is going from the other side. So it is this is given to The last plate over here Now if this is plus q and this is minus q how will charges get transferred from from from This first. So I'm assuming it to be plate one. This is plate two. This is plate three. This is plate four This is plate five and this is plate six Now try to understand the charges are only supplied to plate one and plate six And the charges don't doesn't get supplied to any other charge from the battery. So what is the Phenomenon in which or what is uh, what are the different circumstances in which The charges are getting transferred from one plate to another plate. How does it happen? So try to understand charge plus q is supplied from the battery to to plate one and charge minus q is supplied to The battery from the battery to to to plate six Now what happens the charge plus q appears on on on the plate one Now, uh by induction I have told that are so here minus q will go here. So the facing surface of a two I mean the the plate two Will have minus charge to to to to balance it. So I told you how it happens by induction And then plate a two plate three is connected to a two. So As minus q is appearing on on on on on two. So electrons are drifted. So what happens How this becomes minus because electrons to to control this plus charge electrons are drifted From electrons. So I I can write here drift of electron From three to two. So that's why minus comes here as electrons are drifting from plate three to two So this will be Plus q here again as plus q is coming here electrons would be drifting from uh from plate five And how much it will be minus q. So what comes here plus q? So you should understand that electrons are drifting from plate three and plate five to plate two and plate four respectively and that's why plate two and plate four will have minus four and plate three and plus five will have Plus five now how to calculate it. So you try to understand over here that Vp minus vq is equal to uh I have told that q is equal to cv where v is potential difference. So potential difference is equal to charge q divided by C1 similarly vq minus v r Is equal to charge q because charge remains same but the potential difference But the capacitance is different since potential difference would be Different and v r minus v s is q divided by c3 So what I can write over here is I will add all of them. So this q q will get cancelled out R r will get cancelled out. So vp minus v s Which is equal to nothing but the potential difference v is equal to q divided by c1 Plus q divided by c2 plus q divided by c3 I can write this v as q by c because uh charge q is getting transferred from this battery So q divided by c equivalent is equal to q by c1 plus q by c2 plus q by c3 And that's why the q gets uh eliminated. So I get 1 by c equivalent is equal to 1 by c1 Plus 1 by c2 plus 1 by c3. So this is in the series I'm doing it uh when they are in parallel. So in parallel Combination so in series uh when resistances where in series Is yes that is area of plate a is area of plate a is area of plate Rochita I didn't see your Chat Before in parallel C is equal to omega naught a by d this is area And this is distance between the plates And omega naught, you know already So these are if this capacitance are in parallel like this so I was explaining about Um, how it is similar and different from resistance in series and parallel. So in resistance in series The current was same here the charge is same on all the Uh capacitors. So if capacitors are in series You should know that the charge would be same on all the capacitors But how it is different in if the registers were in series are equivalent was equal equal to Some of all the resistances here. It is different here. It is uh Um We have taken 1 by c equivalent is equal to 1 by c1 plus 1 by c2 plus 1 by c3 Uh, this is c1 plus c1 c2 c3 And this is v. I know that as they are in parallel the potential difference across them is is is uh Different but uh, sorry it's same, but the charges would be different So if charge q it's transferred from here and minus q is transferred from here here It will be q1 here. It will be q2 and here it will be q3 So, uh, so what happens is q is equal to q1 plus q2 plus q3 So what I do over here is So q would be equal to um cv So I write c equivalent is into v is equal to q1 will be equal to c1 into v because potential remains same q2 would be c2 v and q3 would be c3 v d v get cancelled out c equivalent comes out to be c1 plus c2 plus c3 So here also how it is same From register's perspective that if registers or capacitors are in parallel the fundamental is the potential difference Across those capacitors will remain same But the charge would be different as the current was different in case of registers So c equivalent is equal to c1 plus c2 plus c3 So this is what from my side One more thing, uh, which is which is left out is the heating effect, which I'll tell you So that is nothing but Let's look at here So Try to understand the concept of power So first let's find out Jules law of heating and then I go to power So I have already told you these things. So don't worry that I've not taught these things or or something So jules law of heating I've just not told It jules law of heating So I know that work is equal to q into Potential difference So what is potential difference potential difference is v and what is q q q is equal to i into t So I know that v is now as resistance is there v is equal to ir So I can write it as it into ir So work done is equal to i square rt. So what is this work done this work done is nothing but The when the current passes for current to pass certain amount of work is done by the potential difference by the battery The battery source and what is that that is equal to Uh charge transferred multiplied by potential difference so that work done comes out to be i square rt And this work done this energy is vested in form of heat So we also write it as heat produced is equal to i square rt So always remember that if I'm giving you a loop something like this and uh I am telling you that this is uh, this is supposed potential difference and this is two ohm two ohm Register I am saying that find out the heat produced in two ohm registered So r here would be two ohm you I'll not give you I I'll give you all other registers Suppose this is one ohm and this is two ohm and this is 10 volts So what I'll give you is that I'll give you this kind of circuit And I'll say that in this two ohm registers in three second how much heat would be generated So what you have to find out you have you already know r you have to find out by uh loop law applying loop law and equivalent Series and parallel registers you have to find out i here Once you find i find i square multiply it with r and t has been given to you So you will find out how h can be calculated Now I know that Work done what is power? Power is equal to work done per unit time. So it is i square rt divided by t So power is equal to i square r So here only I can give that how much power is originated here or something like that. I can also write it as i into ir and ir is v So power can be written as one second power can be written as ir is v So this can be written as v into i Now, uh, if v is equal to ir i can be written as v by r So power can also be written as V into v by r. So power can also be written as v square by r So that is how Okay I'll repeat work done look at here work done. I already told you is Work done is equal to let me write here work done Is equal to charge into Potential difference So this is q into v. So that's what I have been writing here That work done is equal to charge into potential difference So q into v and q is nothing but q is equal to it. So I am writing it it If v is there. So v is equal to ir. So work done is equal to i square rt Now what is work done? So if current is passing through here So to pass to to let this current pass from this resistance some work needs to be done. There is some Hindrance in the path of current To overcome that hindrance this battery is doing certain amount of work out here, which is Potential difference into Into it. So what is potential difference i into r multiplied by i into t So this comes out to be i square rt now how this work done is is wasted So this is wasted as heat energy at the current is passed through this particular register There would be certain amount of heat generated in the register which is called i square rt. So i square rt can Be written as heat generated or heat produced in the given register heat produced in the given register Is proportional to the square of the current flowing through it. It also it is also proportional to the resistance Value and it is also proportional to the time for which the current is flow Is flowing through that particular register remember If a glass bulb is there and it is on for certain time you go and touch it don't touch it I'm saying just for the matter of Experiment just don't go and touch a white bulb your hand might burn so if if if you just feel it with with the help of certain Plot or something you will find it to be heated. Why does it get heated it get heated because certain current is passing through that filament of the bulb and because The because of the current passing through it. There is some i square rt um Heat is getting generated through it and that heat is making it Um Making making the temperature of the bulb rise. So that is why you feel it to be hot That's it So this is what power is. I hope shruti understood everything out here If not, let me know Let me know all of you This is the last concept. Okay. Uh, so somebody is saying, um Shruti still have not okay. You know see the flag now. Can I solve one question on heating effect? Okay, let me solve one question So Give me a moment. I have sheet number one and sheet number two. I don't have sheet number three Okay, so, um I'll solve it With sheet ruchita with sheet question number 29 Which sheet? Tell me the sheet number I'll solve it Ruchita. I'm asking which sheet number Okay sheet number three Okay, let me just Let me just find out sheet number three for you so This is This is question number 29 This is the question you are asking ruchita Tell me Okay, before she replies. I'll solve this question number 29 In question 25 Somebody bhoomika asked me to okay, ruchita. I'll solve question 29. Don't worry in in question 25 find the Heat developed in in in in three seconds So, let me write it here for you In six Register find the Heat produced in three seconds Solve it. We'll solve this question and then we'll solve Question 29 and then we'll wrap up the session done done Okay Let me check Give me the answer Make this make this diagram on on your On your notebook. I'm I'm doing it on It's something like this Okay So let me uh Solve this question for you uh This is four and a half volts This is three ohms This is six ohms This is 10 ohm and this is three volt So suppose a current i originates from here. So this goes as i here And it gets separated into two parts in two loops i1 and i2 So by junction law, I write i is equal to i1 plus i2 Now try to understand I have two loops. So I am applying loop law I'm taking this point a junction and I'm taking so suppose this is point a So va minus three i minus six i1 plus four point five Is equal to va va gone. I can write that three i Plus six i1 is equal to four and a half Now I go to this loop. Suppose this is point b So I write it vb minus 10 i2 And I'm going from positive to negative. So I write three volts And I'm going in opposite direction of current. So I write plus six i1 Is equal to vb. So this and this bomb I write six i1 minus 10 i2 is Equal to three Now here i1 i2 are there and here i is there. So I will convert it into i1 i2 So this is three i1 plus i2 plus six i1 is equal to four and a half So I write this as nine i1 Plus three i2 Is equal to four and a half. So I write here nine i1 Plus three i2 Is equal to four and a half So I multiply this with one and a half because I want to make it nine i1 So Try to understand if I multiply this with one and a half. So I get nine i1 Minus 15 i2 Is equal to four and a half So I subtract it this becomes positive and this becomes positive 18 i2 is equal to zero. It means that i2 is equal to zero If i2 is equal to zero, let me put my value here It comes out to be six i1 minus 10 i2 Is equal to three So if i2 is zero six i1 is equal to three i1 is equal to three by six which is point five Now try to understand. I am asking in six ampere. So six ampere current is not zero in 10 ampere current is zero So six ampere the heat would be equal to I1 square multiplied by six into three seconds. I have asked so this comes out to be 0.5 square Multiplied by six into three. So that comes out to be point two five into 18 Which is equal to four point five Joules so answer is four point five joules Now, let me go to question number 29 Now, let me go to question number 29. So just look at here question number 29 is This question four eight three six fifty Okay, and I have to find what? Take the potential at b to be zero find the potentials at point c and d If a capacitor is connected between c and d what will be the charge? So this is the whitstone bridge four into six is 24 three into eight is 24 So as c1 c4 is equal to c2 c3 Whatever capacitor you connect in between the charge would be zero this I have already proved So I am I am only going to solve the first part. What is the potential at? Point c and d so try to understand here Four eight three six fifty So let me Four eight three six it is something like this This is four This is four A micro farad Is eight micro farad This is three micro farad And this is six micro farad And this is connected to a battery source of 50 volts So this is 50 volts so This is in Capacitance Is in series four and eight? So let me write it. Let me not do it with this method C equivalent for series is equal to C1 c2 divided by c1 plus c2 So for four and eight for upper circuit This would be four into eight divided by four plus eight. So how much it comes 32 by 12? So it becomes eight by three. So this is nothing but eight by three now try to understand This this is eight by three And and and and similarly it would be three into six divided by three plus six So 18 by nine this comes out to be two. So this is two And so I can write this as eight by three micro farad And I can write this as two micro farad And this is connected to a 50 volt battery source Now try to understand this eight by three plus two because they are in parallel So c equivalent would be equal to eight by three plus two. So this comes out to be Eight plus two into three divided by three. So this will be nothing but 14 by three micro farad now I know that so it is something like this. Please look at here. I'm just One second it will be something like this So this is 14 by three micro farad and this is 50 volts So q is equal to cv So 14 by three into 50 This comes out to be 700 by three Because this is micro farad it will become micro coulomb Now try to understand guys from here the charge which is going is 700 by Three micro coulomb now as they are in parallel Charges will get distributed as per their capacitance So suppose charge here is q1 and charge here is q2 So q1 will be equal to c1 v and q2 is would be equal to c2 v So q1 is now q1 is c1 is eight by three and v is 50 So this is equal to 400 by three and q2 is 2 into 50 That is equal to 100. So this is micro coulomb. It can be written as 300 by three and total would be 700 by three So this is micro coulomb now try to understand guys here That this is q2 So this is this comes out to be as 100 coulomb and this comes out to be as 400 by two micro coulomb And this is 100 micro coulomb Now as these are in series So on both the capacitors, this would be 100 micro coulomb. This would be 100 micro coulomb And this is 400 by three micro coulomb. This is 400 by three micro coulomb Now this is point b. Sorry. This is point c This is point d This is point a and this is point b at I can write that vc minus vb Q is equal to cb. So v would be q by c. So q by suppose this is c1 c2 so q divided by c2 and vb is equal to zero So vc minus zero is vc and q is how much 400 by three divided by eight So vc comes out to be 50 by three volts Similarly vd minus vb would be equal to zero. Sorry. Um, sorry Not g So this is eight by three vd minus vb is q q is 100 divided by how much is this six So this is 100 by six. This is also this also comes out to be 50 by three. So this is nothing but Vd is also equal to 50 by three volts So I hope you all understood it And this is what it is So if you didn't understand it, let me know otherwise I'll wrap up the session. Okay. Thank you so much For joining the session and wish you all the best for your upcoming test. Thank you. Thank you so much