Current Electricity Overview

This world is as strong as it can be to endure the injustice. It is a habit of speaking the truth in the noise of the taunts. I am deeper than the ocean. I am deeper than the ocean. How many thorns will you throw? I am deeper than the ocean. How many thorns will you throw? I will choose and move forward. How long will you stop me? How long will you stop me? My dear children, you are all very welcome. on your beloved platform, Physicswala. I am Shailendra Pandey, your physics educator. So in today's class, we will start today's class with these lines. And in today's class, we are going to study Current Electricity. Chapter 1 and Chapter 2, you all have given a lot of love. Thank you all for that. Now let me quickly revise your Chapter 3. Look, my dear children, what is the work of this Mind Map series? The work is to quickly revise the chapter. and after that, practicing Jitod numericals. Because numericals are very important in clearing the concepts of physics. So many times, students just run after the concept, do not practice the numericals. But my dear students, by practicing the numericals, you can clear your concepts more. So let's start our lecture today. In today's session, we are going to first study about electric current, then about drift velocity and mobility, Ohm's Law, Electric Cell, Kirchhoff's Laws, and also Wheatstone Bridge. So the first thing is, what is electric current? So the rate of flow of electric charge is simply known as electric current. Electric current always flows from high potential to low potential. is flowing towards the middle. This is what Om Sahib had told us that if across the conductor If there is a potential difference, then electric current will flow there. So rate of flow of electric charges through a conductor is known as electric current. Current can be simply called rate of flow of electric charge. Whenever you write current as delta Q by delta T, then this is average current. And if you want to write instantaneous current, then that is simply dQ by dt. If there is a current that is continuously varying, that is, the value of the current is constantly changing, So, you can also calculate this average current from the concept of integration. That is, integration IDT upon integration DT. So, this is also a formula to calculate the average current. So, close this in the box. The best thing about this session is that we summarize all the formulas and concepts in this session. That too in a very short time interval. So, conventionally, direction of the current is taken along the direction of the positive charge. conventional sign If someone asks you what is the convention, you will say that the direction in which the positive charge goes, we will assume the current in that direction. But later it was known that the positive charge is not moving, the move is only doing electron. So later it was said that the direction of the current is the opposite of the direction of the electron. That is, the direction of the current is opposite to the flow of the negative charge, that is basically electron. Current is your scalar quantity. SI unit is the ampere of current. And let me tell you, current is your fundamental quantity. Many times, children think that charge is fundamental because charge is upon time. But it is not like that. Basically, what happens is that charge is current multiplied by time. So, my dear children, current is your fundamental quantity. Keep this in mind. Fundamental quantities are those which we do not require any other quantity to define. It's not a trend. The next term we have is current density. What is current density? See, current is a quantity which had a direction as well, that it flows opposite to the electron. Despite that, we consider it scalar. Because if we see originally, then current is a tensor quantity. But tensor is not in our syllabus. That's why we say that electric current is a scalar quantity. But we will take the direction of that current somewhere. So to bring its direction here, we have made a new vector quantity. whose name is current density. So, what is current density? That is simply defined as current flowing per unit cross-sectional area of any conductor. So, if this is a conductor whose cross-sectional area is equal to A, then here I upon A, that is defined as current density. So, you can see, this current density is a vector quantity. Its unit is ampere per meter square. And if I write here in the form of dot product, form me liku to hum aisa bhi likh sakte hai ki electric current is defined as the dot product of current density and cross-sectional area. Dot product, whenever it moves, then here JA cos theta will come. So you can use it in this way. That means, if you ever have to assume the direction of current, then dear children, introduce current density there. And current density is your current upon area. Or you can write current density into area into cos theta. Theta is the angle between these two. That is current density and cross-sectional. Now today I will tell you about the flow of electric charges in any metallic conductor. See, in any conductor, the electric field is normally zero. But if we connect any cell or battery, we will be able to create electric field inside it. If electric field is created inside, only then the positive or negative charge, i.e. electron can move us. Otherwise, it is not going to move. So metallic conductor contains free electrons as a charge carriers. careers While positive ions are fixed in the lattice. So in the lattice, the positive charge is fixed in the nucleus. Who is moving only and only? Electrons. When no potential difference is applied. If you do not apply potential difference, motion of the free electrons is random and there is no net current in any direction. And if I tell you the initial average thermal velocity, then that initial average thermal velocity is also zero. You will say, sir, from where did the thermal velocity come? If there is any conductor, then the conductor will have some temperature. Due to which all the electrons have thermal velocity and that is called initial thermal velocity. But when you take out that average velocity, then that average velocity will come to zero. Because if one electron is going here, then another electron is going here, someone is going down, someone is going up. It means that if you look at the overall velocity of all the electrons, then you will cancel it and your average velocity will come to zero. Now when the potential difference is applied across the conductor, that means now you have connected a cell or battery across that conductor. If you connect the cell and battery, then what will happen? Free electrons drift along the direction of the positive potential. So current begins to flow in the conductor and the direction of the current is opposite to the direction of the net electron flow. It means, if I assume a conductor here, let's assume this is a conductor. And this conductor, my dear children, what we did is we connected a cell or battery to it. So let's assume I connected a battery, we are making a simple circuit. Here we have created positive potential and here we have created negative potential. So what will happen is that all the electrons in it will start moving towards positive. Because when an electron is in an electric field, the force applied to those electrons is applied in the opposite direction of the field. So the force applied to all the electrons will be applied to the left side. Or you can say that all the electrons are moving towards positive potential. When all the electrons will move in the same direction, then in the opposite direction, my dear children, there will be a generation of current here. So the current will be flowing from positive to negative terminal here. Drift velocity, the next concept is very important. You are asked, what is drift velocity? So drift velocity is the average velocity of all those electrons, my dear children. So drift velocity is defined as the average velocity with which the free electrons get drifted towards the positive end of the conductor under the influence of the external electric field applied by the cell or battery. So, by connecting the cell or battery, the electric field you applied from positive to negative, there is force applied in its opposite direction, and all the electrons are moving in one direction. And the average speed of all those electrons, my dear children, is called drift speed. So, the formula for drift speed is minus E E vector. Vector upon m into tau. Drift speed, if you want to write the magnitude, then its magnitude is E E by m into tau. Where E is the charge of electron, capital E is the electric field, m is the mass of the electron, and tau is the average relaxation time, or it is also called mean relaxation time. Mean relaxation time means the average time interval between two successive collisions. Right? So, here it is written, M, mass of electron, E, charge of electron, E, electric field, tau, relaxation time. If you want to get relaxation time, then you can get it from this formula. That means, mean free path, that means, between two collisions, the free path, which the electron is moving between two successive collisions, we call it mean free path, divided by RMS velocity of the electrons. So, if I talk about RMS velocity, then you can understand here, If I talk about the root mean square speed of the electrons, then speed means distance upon time, right? So that will be mean free path. We call this lambda RMS. Remember, this is not wavelength. We call this mean free path. And T here is time, right? What time is it? That is mean free time or we call it average relaxation time. So from here, we can get average relaxation time. That is mean free path divided by the RMS. velocity of the electrons, right? The next very important concept is what we call mobility. Mobility is defined as the ratio of drift speed to the electric field applied, right? So the drift speed that you have put up, if I divide the electric field in that, then this is called mobility. As soon as you divide the electric field here, E will be cut off, then it will become E tau by m. So you guys are seeing that mobility is... directly proportional to relaxation time. If relaxation time is increasing, then the value of mobility is also increasing. Mobility represents how smoothly the electrons in the conductor are moving. Right? One more thing, the direction in which we applied the electric field, like we applied electric field as positive and negative, this was the electric field, in the opposite direction of this, electrons are moving, that means the direction of the drift velocity is opposite to the electric field. That is why we have also applied a minus sign here. If you want to see the unit of mobility, then the unit of mobility is meter square per volt second. Now, In terms of drift velocity, current is equal to I is equal to NEA VD. This is a very important derivation, it is asked a lot. That is the relation between current and drift velocity. So current I is equal to NEA VD. Where N is the number of electrons per unit volume. Remember, this N is the total number of electrons divided by the volume of the conductor. So this is small n. E means the charge of electrons, A means the cross-sectional area of the conductor and Vd means the drift velocity. That was the average velocity of all the electrons. Now in terms of the mobility, if we take it in terms of mobility, then mobility is mu is equal to drift velocity divided by electric field. So you can write mobility multiplied by electric field instead of drift velocity. As soon as you write mobility into electric field, then it comes under the terms of mobility. So I is equal to NEA mu E. Here N is the number of electrons per unit volume, that is per meter cube. And A is the cross-sectional area of the conductor. Right. Here, many times, you are asked about the relation between current density and drift velocity. So, if you bring this area in the denominator, then it will become current divided by area is equal to NEVD. So, this is drift. This is your current density. So, that will become NEVD. So, current density is equal to NEVD. So, these three relations are very important to you. You can ask numerical on this. Now, we have read two relations. The first relation we read was about drift velocity. We read the value of drift velocity as E E by M into tau. And the next relation we read was between current and drift velocity, that is, N E A V D. If you put the value of drift velocity in the lower one, then this will be our current expression, from where we derive Ohm's law. physical properties of the conductor are constant. Physical properties are its temperature and its pressure. If temperature is kept constant, then the current flowing in the conductor is directly proportional to the potential difference across that conductor. So current I is proportional to V. V means potential difference. Or we can also say that potential difference is directly proportional to current. Both are directly proportional. The quantity increases automatically when one increases. And if we remove the sign of proportionality here, then a constant will come, that constant R is there. We call R the resistance of the conductor. So, remember, whenever we talk about Ohm's law, then there the resistance is our constant. Now, resistance is also defined as rho L by A. We all know that resistance is directly proportional to length of conductor and inversely proportional to cross-sectional area of the conductor. If we remove the sign of proportionality, If we remove it, we get a constant, rho. This rho is called specific resistance. Or it is also called resistivity. And the formula of this resistance, which is obtained by combining these two, that is ML upon NE square tau into AM. What is M? Mass of electron. What is L? Length of the conductor. N, number of electrons per unit volume. E square, electron's charge square. tau relaxation time is there and A cross sectional area of the conductor is there. You can see that this resistance is dependent on length, this is dependent on area, that is, it is dependent on its shape, geometry of the conductor. Along with that, this resistance is dependent on average relaxation time too. That is, it is dependent on temperature too. It is dependent on material too. So, my dear children, resistance is dependent on material of conductor. It is dependent on geometry. Geometry means length and area. And at the same time, it is dependent on temperature. So resistance depends on three things. But if we talk about resistivity, then this is dependent only on temperature and material. Resistivity or specific resistance that depends upon temperature and material of that conductor only. And this does not depend on anything else. That means resistivity does not depend on geometry. I will tell you that if you double the length of the conductor, half it, increase or decrease the area, there is no difference in its resistivity because the material is the same. If you change the material, the resistivity will change. If we talk about the unit, the unit of resistance is on volt. meter, that is known as ohm. In fact, if I see, V is equal to IR, so R is equal to V upon I. So this is not volt per meter, this is volt per ampere. It is volt per ampere. Volt per ampere is what we call ohm. So ohm's law is not applicable to all conductors. My dear friends, ohm's law is not applicable to all. It is applicable only for those conducting materials for which VI graph is linear. That means if we make a graph of voltage and current, and that graph becomes a linear graph, straight line passing through origin, then only we will say that ohms law is being followed, otherwise ohms law is not being followed. We will talk about it in more detail, don't worry. Let's talk about variation of resistance. It is a very important topic. This slide is very important for you from a numerical point of view. Here you are being told, my dear children, if we cut any wire, or if we increase its length, increase, decrease, alter, if we have changed the length, then resistance is directly proportional to length. But if any wire is increased by pulling the length, or we have folded it and decreased the length, then increase the length by pulling the wire, or if you fold it, then its length will decrease. In such cases, resistance is directly proportional to square of the length. Why is that? Because if you have pulled any... wire, then length will increase, but cross sectional area will decrease in that ratio. Right. If length doubles, then area will be half. So, my dear children, in such a case, if you take out resistance, which is rho L by A, then length doubled, area was half. So, you can see, this 2, this 2, what will happen? 2 square. Right. So, you can see here, this will become 4 times rho L by A. So, we can say that length is proportional to square. If you double the length, then the resistance will be 4 times. In the same way, if you have increased or decreased the area, but kept the length the same, then in this way, resistance is inversely proportional to area. And area is equal to pi r square. So, we can also say that resistance is inversely proportional to r square. Radius will increase, resistance will decrease or area will increase, resistance will decrease. But if it is said that wire is pulled, right? You are pulling and increasing the length, you are halving the area. If it is done like this, that is, if its volume is constant, then my dear children, what will be the concept here? That resistance is inversely proportional to square of the cross-sectional area. If you have pulled and halved its area, Hey. So length will be doubled, that is, resistance will be 1 by 4. Right? And if I write pi r square instead of this area, then this resistance will be inversely proportional to r to the power 4. My dear children, this slide is very important. Think carefully once, you all. Now let's come to the omega and non-omba conductor. conductors. Omic conductors are those in which Ohm's law is followed and non-omic conductors are those in which Ohm's law is not being followed. Now, when will the So I upon V is its slope which is equal to 1 by R. If this graph is straight line, then slope is constant. Slope is constant means 1 by R is constant. 1 by R is constant means R is constant. Right? But if this graph is curved, then this time the slope which is I upon V which is 1 by R, that slope is not constant. If slope is not constant, then resistance is also not constant. And if the resistance is not constant, it means that Ohm's law is not being followed. Right? Now, when does Ohm's law follow? Any metallic conductor, Ohm's law is being followed there. But if we talk about any junction diode or transistor, then Ohm's law is not being followed there. We will say, sir, what is this diode? When we will read the semiconductor chapter, we will read PN junction diode. Where P type and N type semiconductor are the same. ek hi samal lo It is inside the semiconductor. When we will teach, we will talk about it. So this is PN junction diode and transistor is PNP or NPN transistor. Although now it is not in your syllabus, transistors. But earlier it used to happen. So as an example, just remember it now. PNP or NPN transistors or PN junction diode. So we are going to study this in the semiconductor chapter. That means some places are also in your syllabus where Ohm's law will not be followed. Otherwise, generally, Ohm's law follows. Right? Now, let's come to Joule's law of heating. So, from class 10th, you are reading this formula that the heat, if there is current flow in any conductor, then there will be collision of electrons between each other and with the atoms of the conductor, due to which heat is generated there. And that heat is directly proportional to I square RT. So, if we remove the proportionality sign from here, a constant will come. So, that constant here is equal to 1 by J. Right? So, we got the value of heat. I square RT by J. Or indirectly, you can also say that the formula of heat is I square RT. In more than 95% case, we use this formula. But the heat that will come out of here will be in joules. But we all know that generally, the unit of heat is calorie. So here many times we feel like changing the calorie into joule or joule into calorie. We feel like that too and many times it happens in numerical. So we have to change that calorie into joule. So for that you should know a formula that 1 calorie is equal to 4.18 or 4.2 joules. This is the reason my dear children because this value came in joule. And when the value in joule is converted into calorie, then you will divide it by 4.18. So, the J written below, you see carefully, that is 4.18. Is it clear? I hope you are understanding the thing. So, if you divide 4.18, my dear children, then these values will come out in your calorie. Otherwise, if you have applied this formula, then the answer will come in joule. And if you have applied the formula I square RT divided by 4.18. 4.18, so this is the value that you have got in calories. 4.18 into 10 to the power 3, if you have divided it, then it will come in kilocalories. So, all that is the same. You all know that. There is no need to get too confused. If you are a little scared to see this formula, that what is this J, then understand from here. If you have applied this formula, then the heat will come in joules. If we have applied this formula, then this heat will come in calories. Now I hope you understood the point. There is no big deal here. If there is current flow in any conductor, then heat will definitely generate there. Now let's talk about power. What is power? Power is the rate of doing work or rate of consumption of energy. Rate of generation of energy is known as power. So what is power? Work done upon time taken. P is equal to Vi. P is equal to I square R. P is equal to V square upon Rb. These are all formulas. Power unit is Watt. Power unit can be big. 1 kW is equal to 1000W. This is also known by all of you. Apart from this, 1 MW is equal to 6W. Horse power is also equal to 746W. So these all are units of the power. Now let's talk a little more about resistivity. We all saw that resistance R was equal to Rho L by A. My dear children, if any conductor If the length is 1 unit and its cross sectional area is also 1 unit, if both of these are equal to 1, that means if length is 1 unit, area is also of 1 unit, so resistance will be equal to rho. From here, the definition comes out. What is resistivity? Resistivity is equal to resistance. If length conductor is 1 unit, area is also 1 unit square, then my dear children, resistance and resistivity are the same. So read the definition. Resistivity of a substance is defined as the resistance. offered by the wire of that substance of 1 meter length and 1 square meter cross-sectional area. Length 1 meter, cross-sectional area 1 meter square, so in this way, resistance and resistivity both become the same. Right? Now, here, resistivity is dependent only on material, it is dependent on temperature, but it does not depend on the dimension of the conductor. Dimension means, it is dependent on its length and area. So resistivity is independent of length and cross-sectional area of the conductor. Resistivity's value can be seen. That is m upon n e square tau. Where m is mass of the electron, e charge of electron, n number of electrons per unit volume. Or this is also called number density of electrons. Tau means average relaxation time. Clear? Next is conductance and conductivity. Look, the reciprocal of resistance is conductance. Conductance is denoted by G, that is 1 by R. Its unit is Ohm inverse, we can write MHO, we can write Simon. Or the reciprocal of resistivity, which is denoted by sigma, is called conductivity. Its unit is Ohm inverse, meter inverse, or MHO per meter, or Simon per meter. So, all these are its units. Some people read Maho, you can write MHO too. It is just the opposite of Ohm, MHO. Right? So this is how its units are defined. Now let's show you the dependence of temperature for any conductor or semiconductor. See, in the case of any conductor, if you keep increasing the temperature, then resistance and resistivity are increasing. And here the formula is resistance RT is equal to R0, 1 plus alpha delta T. Where RT is resistance at T degree Celsius, R0 is resistance at 0 degree Celsius or resistance at reference temperature. Alpha is our temperature coefficient of resistivity and delta T means change in temperature. So that is equal to T minus T naught. So what is R naught, what is RT, you should know a little about what alpha is. If I talk about any conductor, then alpha is positive for conductor. This is the reason that if you increase the temperature of the conductor, then its resistance will also increase. And my dear children, its resistivity... The formula for resistance is the same as for resistivity. Rho T is equal to Rho naught 1 plus alpha delta T. This is the same formula. The formula is the same as for resistivity. Actually, the reason for resistance to increase with temperature is that resistivity increases with temperature. The resistivity is increasing, so the resistance is also increasing automatically. So if you increase the temperature of the conductor, the resistance and resistivity will increase, the conductance and conductivity will decrease. But if I talk about the semiconductor, then the matter is opposite in the semiconductor. In the case of semiconductor, if you have increased the temperature, then the resistivity will decrease. The resistance will decrease when the temperature increases. The resistance will also decrease. Whereas the conductance and conductivity will increase. You will say, sir, now tell me why this behavior is happening? After all, sir, why is it happening that it is different in this and in that? So, my dear children, the conductor has a lot of free electrons. When you increase the temperature, they start colliding with each other. Collision increases. Due to increasing collision, the resistivity and resistance increases. But if I talk about the semiconductor, then it does not have free electrons. So now when you heat, their bonds break. And when bonds break, free electrons are generated. And when free electrons are being generated, then we will say that now free electrons have grown. Now they are born, so now they will flow. Now they will generate current. That means now its resistance and resistivity will decrease. Right? So see the graph, it is very important, it is asked. Now let's talk about electric cell. Till now we were talking about passive element, that is, resistance. ke baare mein baat kar rahe the. Ab hum log... element of any circuit, i.e. cell or battery. So, what is a cell? The principle of a cell is that it converts chemical energy into electrical energy. What is an EMF of any cell? If a cell is not giving current, then its total potential difference is called EMF. So, EMF of a cell is defined as the maximum potential difference when no current is being drawn from the cell. If the cell current is not giving, then its total potential difference is called EMF. What is the terminal potential difference? If the cell is giving current, then the potential difference across it is called terminal potential difference. So terminal potential difference is defined as the potential difference when current is being delivered to the external load resistance. That means if the cell has given current, then across it is the potential difference, the terminal potential difference, which is slightly less than EMF. And when it is not giving current, then the potential difference across it will be maximum. That is called EMF. Now, when it is giving current, then why is the value decreasing? The reason is that in any cell, there is some internal resistance which is due to its electrolyte. That electrolyte is offering internal resistance there. So, its voltage. The total EMF of the cell, the total potential difference, some of that voltage it consumes on its own. This is exactly the same thing that when you bring a 256 GB mobile, whose ROM is 256 GB, so when you buy it, it is written on the box 256 GB, but when you buy it at home, you find out that 20-30 GB is filled with Android. Now if we want to use it, if we want to fill movies, songs, if we want to fill anything, then how much space do we have to fill that? So you never get 256GB, you can check it in your mobile. If you are bringing a 128GB mobile, then 15-20GB is filled with Android. You will get only 110GB, 112GB maximum usable. Right? So the same thing is that if any cell is of 10V, then 1V, 2V, whatever is there from 10V, that consumes internal resistance. So we will get only 8V from 10V for external circuit. So that 8V is called terminal potential difference and 10V is called EMF of any cell. Right? So what is internal resistance? Internal resistance of the cell is the hindrance offered by the electrolyte of the cell. That means any cell's electrolyte, which we generally call Tejaab, the battery of the inverter, in which generally people say Tejaab is filled. So that is not Tejaab, that is electrolyte. The electrolyte which offers resistance is called internal resistance. Internal resistance depends on many things. It is very important, you can ask. Note these things very carefully in your copy. man. If the distance between the electrodes increases, then the internal resistance will also increase. If the area of the electrode increases, then the internal resistance will decrease. So everyone knows that resistance is proportional to length and inversely proportional to area. If the concentration of electrode increases, then also resistance will increase. If the temperature increases, then the internal resistance will decrease. So if you are talking about electrolyte, then internal resistance will increase when concentration increases. and increasing the temperature of the internal resistance will reduce our Now let's talk about any cell. If any cell is being discharged, discharge means that this cell is giving current. If this cell is giving current, then dear children, here EMF is more and the terminal potential difference is less, that is, V is equal to E minus IR. That is, if we reduce IR from EMF, then we will get the terminal potential difference. So the example I gave, if our EMF is 10 volts, If the EMF is 10V and the internal resistance voltage is 2V, then the terminal potential difference will be equal to 8V. So, my dear children, it is simple here that the value of EMF is high. If it is being discharged, then EMF is high and the terminal potential difference is low. But if the cell is being charged, we are charging the cell with an external battery, we are using a charger, So now what will happen here is that the external battery... The terminal potential difference should be more. So, my dear children, this time V will be equal to E plus IR. And here it is clear that the terminal potential difference is more than the EMF of the cell. Now think for yourself, if there is a 10V battery whose total EMF is 10V, then will we charge it with a 10V battery? No, we will charge it with a bigger battery than that. Say, if there is a 10V cell, then we will charge it with a 20V battery. We will charge it with a 50V battery. charging from the battery, so simple to say means This is the case here, right? That here the terminal potential difference is more and the value of EMF is less. Now let's talk about the combination of cells. First of all, think about what is the work of the cell. The work of the cell is to provide current or to maintain the potential difference. If that cell is not able to give us the desired current, then we will do the combination of cells. There are two or three combinations of cells in your syllabus right now. First of all, the series combination of the cells. In series, you will keep connecting the cells in a line. So, in this case, the current that we are going to get here, the value of current is NE upon R plus NR. Where N is the total number of the cells which are connected in series. And E is the EMF of all these cells. That is, if I assume that E1, E2, E3, E4, all are equal to each other. And all of these are equal to E. Means we have considered such cells whose EMF is equal to each other. And I am taking all internal resistance equally. So in this case, NE upon R plus NR will be. So what is this R? What is capital R? This capital R, my dear children, is external resistance. Right? This is external resistance. Any bulb you have connected, any fan you have connected, motor you have connected, all that is called external resistance. So NE upon R plus NR. You will say, sir, where did this formula come from? Son, look, all these cells are giving current on the left side, that is, all these cells are supporting each other. So all of them will add EMF, E plus E plus E plus E plus E. And if there are N cells like this, then NE will be formed. So NE divided by total resistance. Total resistance, look, this one is capital R, all these small R are in series. So, Nr plus capital R will be done. The thing is, sir, when will we do series grouping of cells? When the external resistance of the circuit and the internal resistance are more. If the external resistance is very high and the internal resistance is very low, then in this way, we are doing series grouping. Now, let's talk about our parallel grouping. In parallel grouping, we have combined cells in parallel as shown in this figure. and here the current is E upon R plus small r by n. You will say, sir, how did the formula come? Son, look, if you talk about parallel, then all EMFs are the same. So net EMF is also equal to our capital E. Understand, it's done. Right? Divided by, now these small r, small r, small r, small r, such n cells are there. All of them are in parallel. So we can say, 1 upon r dash is equal to, all of them are in parallel. So 1 by r plus 1 by r plus 1 by r such n terms are there. So son, this will become n by r. 1 by r dash is equal to n by r. So from here, you can take out r dash. which is R by N. This is the net internal resistance of all the cells. So, my dear children, the net internal resistance of all the cells is corrected in this series with R. So, R plus R by N. This is our internal resistance, this is external resistance, this is total resistance and above is EMF. So, E upon this value. When will this be used? When the value of internal resistance is very high in comparison to external resistance. Remember this, when it is used, you should remember the conditions. In parallel combination, the numerical chance of coming this year, remember this, this slide can be your numerical. The thing which is important, understand that it is really very important, it can be asked in the exam. And there are many chances of being asked this time. So, assume this is your one cell, which has EMF E1, internal resistance R1, this is E2, this is R2. Look carefully, this is also giving current on the left, this is also giving current on the left. There are two cells which we have connected in parallel. in the world. So, the formula of net EMF is something like this. E1 by R1 plus E2 by R2 upon 1 by R1 plus 1 by R2. And the formula of internal resistance, you must have understood. It is very simple. That is 1 by R1 plus 1 by R2. All the cells, if you combine them in parallel, then you will get net internal resistance from here. And from this formula, you will also get net EMF. But if one cell is giving current here and the other cell is giving current here, there, sir. then what will happen? So, my dear children, then minus will be applied here. E1 by R1 minus E2 by R2. But plus will remain below because the formula of parallel combination is the same. It never applies minus in this. Okay? So, you must try these types of numericals. I have also asked you such questions in the curriculum batch. And for the children, when they will bring the marathon class, then I will bring these types of numericals for you. Right? So, now let's talk about combination of cells, a little bit out of syllabus, i.e. I am talking about mixed grouping of cells as well. Where there are some cells which are connected in series and we have some rows like this. In such cases, the current value is total EMF upon total resistance, i.e. MNE upon MR plus NR. Where M and N are, look at this carefully. We have M rows and every row has N cells. So, how many cells are there in every row? N cells. In one row. And how many such rows are there? M. We have total M rows. Right? So if someone asks the total number of cells, it is equal to Mn. Okay? So, Mne divided by Mr plus Nr. If someone asks the total internal resistance of the circuit, the total internal resistance is equal to Nr by M. You will say, sir, how did you come up with this? Tell me a little. So, in one row, Small r, small r, small r, small r. How many cells are there? N cells are there. So how much is the resistance of every row? Nr. R plus R plus R plus R plus R, how much will be N R? And N R, N R, N R, N R, N R, there are such M rows, my dear children. So 1 by R dash is 1 by N R plus 1 by N R plus 1 by N R. How many M terms will there be? Such M terms will be there. So 1 by R dash will be M upon N R. So from here, the value of R' will be N R by M. This is net internal resistance. You will say, sir, when do we use mixed looping? So my dear friends, you will use mixed looping when the external resistance and internal resistance of the circuit will be equal. And if these two are equal, then let me tell you, here the current will be maximum. And in that condition, the power loss that was happening in the circuit will be maximum. This is called maximum power transfer theorem. which is also called B-Tech. For now, let's talk about Kirchhoff's laws. So, Kirchhoff had made two laws to analyze the circuits of direct current. The first law is based on the conservation of charge, which we call Kirchhoff's current law, Kirchhoff's junction rule. Nodal law is also called this, which simply means on any joint, any junction, any node. What is a joint junction or node? Where some wires are getting. So, the current coming at this point is equal to the current going from this point. Right? So, the coming moment is going to go. It is a simple thing. The current that is coming here, it will go from here. So, I current has come. I1, I2 is going. So, I is equal to I1 plus I2. That means, if I write it here in short form, then I can also say that summation of the total current passing through this junction is always equal to 0. Right? Then, come on, there is the second law, which we also call loop law, which is based on conservation of energy. And this says that across any loop, The more active elements provide the potential, the more voltage they provide, the more passive elements will consume the voltage. If it has given a potential of 10 volts, then this 10 volts will be consumed completely. So my dear children, try to understand the method of applying the loop law carefully because children have a lot of problems in this. The big line in any cell is plus, the small line is minus and the current always goes from high voltage to low voltage. So when current is going from here, then this is high voltage and this is low voltage. Current goes from high to low. High is shown as plus and low as minus. So the first thing, no matter how big the loop is, you have to do this first. Make plus minus in all the cells and make plus minus in all the resistances. Now consider any loop. Loop means any closed path of the current. So my dear children, this is our loop which is a closed and continuous path. Now start running from one side to one corner. Start running from here, here, here, anywhere. Okay. If I am starting to run from here, then see, I am reaching minus. Right. So, what will be the voltage in resistance? Minus IR. Say, V is equal to IR. We all know that. Right. So, what does it mean? Because we reached minus, we took the sign of minus. Minus VR. Okay. IR. Then move forward, move forward, move forward. We have reached plus. So, plus V is equal to zero. Right. Total voltage, sum of all the voltages across all elements is always equal to zero. That means the amount of voltage supplied by the active element, the passive element will consume that much voltage. So delta, sorry, sigma V, summation of V is always equal to zero across any closed loop. So you can apply it this way. Start running from one side, take the sign wherever you reach. If I reach negative, I have taken minus IR. If I reach plus, I have taken plus V, which is equal to zero. So this is Kirchhoff's second law. It is important, my dear children. Practice these two laws a little. You can be asked. On the last topic, let's come to Wheat-Stones Bridge. Sir, what is Wheat-Stones Bridge? It is a formula to calculate the value of resistance. Wheat-Stones Bridge is used to measure any unknown resistance. In Wheat-Stones Bridge, this method is... There are quadrilaterals on each side of the quadrilateral. There are resistances on each side of the quadrilateral. That means we have four resistances. There are two diagonals in any quadrilateral. One diagonal has a cell on it. On the other diagonal, we have a galvanometer. Galvanometer is a device that tells us that the current is... or not? It means it takes the attendance of current. It represents whether current is present or not. So, my dear children, what will be happening here? It will be happening that from here, I current will be coming out of the cell. As soon as I current will reach here, that I current will be divided. I1 went here, I2 went here. As soon as I1 reached here, now it became known that we consider Wheatstone Bridge to be balanced when there is a current in the galvanometer. If no current goes in this galvanometer, then my dear children, where will all the current go? In the Q, because it does not have to go here. So all the current went to the Q. When the I2 current reached here from here, now again he remembered that the current did not go in the galvanometer, so all the current went to S. So I1 came from here, went here, I2 came from here, went here, and finally both together again became I current and went back. Remember one thing about any cell, the more current the cell gives from its positive, and takes back the rent in negative. Clear? So, it means that any wheat stone bridge will be balanced when P upon Q R upon S is equal to this resistance upon this resistance equal to this resistance upon this resistance. Or this resistance upon this resistance equal to this resistance upon this resistance. Right? So, R1 upon R2 equal to R3 upon R4. Or P upon Q equal to R upon S. Or P upon R equal to Q upon S. All the ways are the same. Write as you want to write. Write. Okay? In Charbis, it's... you will know three resistances, you will not know the fourth, you can calculate that. There is no problem in it. But remember, the wheat stone bridge will be balanced only when the current is not going in the galvanometer. That means, no deflection is showing in the galvanometer. Right? Now, sir, the null point of the galvanometer, does it depend on the resistance? No, it doesn't. Galvanometer and E, E means cell's EMF. Right? It is not dependent on the EMF and the resistance of the galvanometer of this cell. It is not even affected if positions of galvanometer and cell are interchanged. That means, if you lift this and put it here, if you lift the cell and put it here, there is no difference, brother. Right? So, let me teach you one more thing. Whenever in any circuit, in any question, in numerical, how will we recognize that, sir, that is a galvanometer? So, for that, there is a method, this one, right? Yo-Yo Singh's method. So, this is positive. If you check the positive cell, you should have two resistances connected. If two resistances are connected from the positive part of the cell, if two resistances are connected from the negative part, if there is a resistor or galvanometer connected between them, then there is a possibility that it can be our wheat stone bridge. But you have to check whether that wheat stone bridge is balanced or not. So, my dear children, This was your Wheatstone Bridge. This was your chapter number 3. I have revised the entire chapter for you. Chapter number 3 has been revised very quickly. I hope you have understood everything. Everyone, please comment and tell us how you liked this lecture. Then we will meet in our next chapter, which is Magnetic Effect of Electric Current. It is a very beautiful chapter. And we are going to revise that chapter as well. Your homework is to revise the chapter with me. Now you solve the numericals of this chapter. And per day, 10 numericals are your homework. That means when you are watching the lecture of next chapter, then I am giving you at least Sunday's leave. At least 60 numericals you have solved on your copy. Right? So brother, let's meet in our next class. Till then, goodbye and take care.

This world is as strong as it can be to endure the injustice. It is a habit of speaking the truth in the noise of the taunts. I am deeper than the ocean.

I am deeper than the ocean. How many thorns will you throw? I am deeper than the ocean.

How many thorns will you throw? I will choose and move forward. How long will you stop me? How long will you stop me?

My dear children, you are all very welcome. on your beloved platform, Physicswala. I am Shailendra Pandey, your physics educator.

So in today's class, we will start today's class with these lines. And in today's class, we are going to study Current Electricity. Chapter 1 and Chapter 2, you all have given a lot of love.

Thank you all for that. Now let me quickly revise your Chapter 3. Look, my dear children, what is the work of this Mind Map series? The work is to quickly revise the chapter. and after that, practicing Jitod numericals.

Because numericals are very important in clearing the concepts of physics. So many times, students just run after the concept, do not practice the numericals. But my dear students, by practicing the numericals, you can clear your concepts more. So let's start our lecture today.

In today's session, we are going to first study about electric current, then about drift velocity and mobility, Ohm's Law, Electric Cell, Kirchhoff's Laws, and also Wheatstone Bridge. So the first thing is, what is electric current? So the rate of flow of electric charge is simply known as electric current.

Electric current always flows from high potential to low potential. is flowing towards the middle. This is what Om Sahib had told us that if across the conductor If there is a potential difference, then electric current will flow there.

So rate of flow of electric charges through a conductor is known as electric current. Current can be simply called rate of flow of electric charge. Whenever you write current as delta Q by delta T, then this is average current.

And if you want to write instantaneous current, then that is simply dQ by dt. If there is a current that is continuously varying, that is, the value of the current is constantly changing, So, you can also calculate this average current from the concept of integration. That is, integration IDT upon integration DT. So, this is also a formula to calculate the average current.

So, close this in the box. The best thing about this session is that we summarize all the formulas and concepts in this session. That too in a very short time interval. So, conventionally, direction of the current is taken along the direction of the positive charge. conventional sign If someone asks you what is the convention, you will say that the direction in which the positive charge goes, we will assume the current in that direction.

But later it was known that the positive charge is not moving, the move is only doing electron. So later it was said that the direction of the current is the opposite of the direction of the electron. That is, the direction of the current is opposite to the flow of the negative charge, that is basically electron. Current is your scalar quantity.

SI unit is the ampere of current. And let me tell you, current is your fundamental quantity. Many times, children think that charge is fundamental because charge is upon time. But it is not like that.

Basically, what happens is that charge is current multiplied by time. So, my dear children, current is your fundamental quantity. Keep this in mind.

Fundamental quantities are those which we do not require any other quantity to define. It's not a trend. The next term we have is current density.

What is current density? See, current is a quantity which had a direction as well, that it flows opposite to the electron. Despite that, we consider it scalar.

Because if we see originally, then current is a tensor quantity. But tensor is not in our syllabus. That's why we say that electric current is a scalar quantity. But we will take the direction of that current somewhere.

So to bring its direction here, we have made a new vector quantity. whose name is current density. So, what is current density?

That is simply defined as current flowing per unit cross-sectional area of any conductor. So, if this is a conductor whose cross-sectional area is equal to A, then here I upon A, that is defined as current density. So, you can see, this current density is a vector quantity.

Its unit is ampere per meter square. And if I write here in the form of dot product, form me liku to hum aisa bhi likh sakte hai ki electric current is defined as the dot product of current density and cross-sectional area. Dot product, whenever it moves, then here JA cos theta will come.

So you can use it in this way. That means, if you ever have to assume the direction of current, then dear children, introduce current density there. And current density is your current upon area. Or you can write current density into area into cos theta.

Theta is the angle between these two. That is current density and cross-sectional. Now today I will tell you about the flow of electric charges in any metallic conductor.

See, in any conductor, the electric field is normally zero. But if we connect any cell or battery, we will be able to create electric field inside it. If electric field is created inside, only then the positive or negative charge, i.e. electron can move us. Otherwise, it is not going to move. So metallic conductor contains free electrons as a charge carriers.

careers While positive ions are fixed in the lattice. So in the lattice, the positive charge is fixed in the nucleus. Who is moving only and only? Electrons.

When no potential difference is applied. If you do not apply potential difference, motion of the free electrons is random and there is no net current in any direction. And if I tell you the initial average thermal velocity, then that initial average thermal velocity is also zero.

You will say, sir, from where did the thermal velocity come? If there is any conductor, then the conductor will have some temperature. Due to which all the electrons have thermal velocity and that is called initial thermal velocity.

But when you take out that average velocity, then that average velocity will come to zero. Because if one electron is going here, then another electron is going here, someone is going down, someone is going up. It means that if you look at the overall velocity of all the electrons, then you will cancel it and your average velocity will come to zero. Now when the potential difference is applied across the conductor, that means now you have connected a cell or battery across that conductor. If you connect the cell and battery, then what will happen?

Free electrons drift along the direction of the positive potential. So current begins to flow in the conductor and the direction of the current is opposite to the direction of the net electron flow. It means, if I assume a conductor here, let's assume this is a conductor. And this conductor, my dear children, what we did is we connected a cell or battery to it.

So let's assume I connected a battery, we are making a simple circuit. Here we have created positive potential and here we have created negative potential. So what will happen is that all the electrons in it will start moving towards positive. Because when an electron is in an electric field, the force applied to those electrons is applied in the opposite direction of the field.

So the force applied to all the electrons will be applied to the left side. Or you can say that all the electrons are moving towards positive potential. When all the electrons will move in the same direction, then in the opposite direction, my dear children, there will be a generation of current here. So the current will be flowing from positive to negative terminal here. Drift velocity, the next concept is very important.

You are asked, what is drift velocity? So drift velocity is the average velocity of all those electrons, my dear children. So drift velocity is defined as the average velocity with which the free electrons get drifted towards the positive end of the conductor under the influence of the external electric field applied by the cell or battery.

So, by connecting the cell or battery, the electric field you applied from positive to negative, there is force applied in its opposite direction, and all the electrons are moving in one direction. And the average speed of all those electrons, my dear children, is called drift speed. So, the formula for drift speed is minus E E vector. Vector upon m into tau.

Drift speed, if you want to write the magnitude, then its magnitude is E E by m into tau. Where E is the charge of electron, capital E is the electric field, m is the mass of the electron, and tau is the average relaxation time, or it is also called mean relaxation time. Mean relaxation time means the average time interval between two successive collisions.

Right? So, here it is written, M, mass of electron, E, charge of electron, E, electric field, tau, relaxation time. If you want to get relaxation time, then you can get it from this formula. That means, mean free path, that means, between two collisions, the free path, which the electron is moving between two successive collisions, we call it mean free path, divided by RMS velocity of the electrons. So, if I talk about RMS velocity, then you can understand here, If I talk about the root mean square speed of the electrons, then speed means distance upon time, right?

So that will be mean free path. We call this lambda RMS. Remember, this is not wavelength. We call this mean free path. And T here is time, right?

What time is it? That is mean free time or we call it average relaxation time. So from here, we can get average relaxation time.

That is mean free path divided by the RMS. velocity of the electrons, right? The next very important concept is what we call mobility. Mobility is defined as the ratio of drift speed to the electric field applied, right?

So the drift speed that you have put up, if I divide the electric field in that, then this is called mobility. As soon as you divide the electric field here, E will be cut off, then it will become E tau by m. So you guys are seeing that mobility is...

directly proportional to relaxation time. If relaxation time is increasing, then the value of mobility is also increasing. Mobility represents how smoothly the electrons in the conductor are moving. Right?

One more thing, the direction in which we applied the electric field, like we applied electric field as positive and negative, this was the electric field, in the opposite direction of this, electrons are moving, that means the direction of the drift velocity is opposite to the electric field. That is why we have also applied a minus sign here. If you want to see the unit of mobility, then the unit of mobility is meter square per volt second.

Now, In terms of drift velocity, current is equal to I is equal to NEA VD. This is a very important derivation, it is asked a lot. That is the relation between current and drift velocity. So current I is equal to NEA VD. Where N is the number of electrons per unit volume.

Remember, this N is the total number of electrons divided by the volume of the conductor. So this is small n. E means the charge of electrons, A means the cross-sectional area of the conductor and Vd means the drift velocity.

That was the average velocity of all the electrons. Now in terms of the mobility, if we take it in terms of mobility, then mobility is mu is equal to drift velocity divided by electric field. So you can write mobility multiplied by electric field instead of drift velocity.

As soon as you write mobility into electric field, then it comes under the terms of mobility. So I is equal to NEA mu E. Here N is the number of electrons per unit volume, that is per meter cube.

And A is the cross-sectional area of the conductor. Right. Here, many times, you are asked about the relation between current density and drift velocity.

So, if you bring this area in the denominator, then it will become current divided by area is equal to NEVD. So, this is drift. This is your current density.

So, that will become NEVD. So, current density is equal to NEVD. So, these three relations are very important to you. You can ask numerical on this. Now, we have read two relations.

The first relation we read was about drift velocity. We read the value of drift velocity as E E by M into tau. And the next relation we read was between current and drift velocity, that is, N E A V D. If you put the value of drift velocity in the lower one, then this will be our current expression, from where we derive Ohm's law.

physical properties of the conductor are constant. Physical properties are its temperature and its pressure. If temperature is kept constant, then the current flowing in the conductor is directly proportional to the potential difference across that conductor. So current I is proportional to V. V means potential difference. Or we can also say that potential difference is directly proportional to current.

Both are directly proportional. The quantity increases automatically when one increases. And if we remove the sign of proportionality here, then a constant will come, that constant R is there. We call R the resistance of the conductor. So, remember, whenever we talk about Ohm's law, then there the resistance is our constant.

Now, resistance is also defined as rho L by A. We all know that resistance is directly proportional to length of conductor and inversely proportional to cross-sectional area of the conductor. If we remove the sign of proportionality, If we remove it, we get a constant, rho.

This rho is called specific resistance. Or it is also called resistivity. And the formula of this resistance, which is obtained by combining these two, that is ML upon NE square tau into AM.

What is M? Mass of electron. What is L?

Length of the conductor. N, number of electrons per unit volume. E square, electron's charge square.

tau relaxation time is there and A cross sectional area of the conductor is there. You can see that this resistance is dependent on length, this is dependent on area, that is, it is dependent on its shape, geometry of the conductor. Along with that, this resistance is dependent on average relaxation time too. That is, it is dependent on temperature too. It is dependent on material too.

So, my dear children, resistance is dependent on material of conductor. It is dependent on geometry. Geometry means length and area.

And at the same time, it is dependent on temperature. So resistance depends on three things. But if we talk about resistivity, then this is dependent only on temperature and material. Resistivity or specific resistance that depends upon temperature and material of that conductor only. And this does not depend on anything else.

That means resistivity does not depend on geometry. I will tell you that if you double the length of the conductor, half it, increase or decrease the area, there is no difference in its resistivity because the material is the same. If you change the material, the resistivity will change.

If we talk about the unit, the unit of resistance is on volt. meter, that is known as ohm. In fact, if I see, V is equal to IR, so R is equal to V upon I. So this is not volt per meter, this is volt per ampere. It is volt per ampere.

Volt per ampere is what we call ohm. So ohm's law is not applicable to all conductors. My dear friends, ohm's law is not applicable to all.

It is applicable only for those conducting materials for which VI graph is linear. That means if we make a graph of voltage and current, and that graph becomes a linear graph, straight line passing through origin, then only we will say that ohms law is being followed, otherwise ohms law is not being followed. We will talk about it in more detail, don't worry. Let's talk about variation of resistance.

It is a very important topic. This slide is very important for you from a numerical point of view. Here you are being told, my dear children, if we cut any wire, or if we increase its length, increase, decrease, alter, if we have changed the length, then resistance is directly proportional to length.

But if any wire is increased by pulling the length, or we have folded it and decreased the length, then increase the length by pulling the wire, or if you fold it, then its length will decrease. In such cases, resistance is directly proportional to square of the length. Why is that? Because if you have pulled any...

wire, then length will increase, but cross sectional area will decrease in that ratio. Right. If length doubles, then area will be half.

So, my dear children, in such a case, if you take out resistance, which is rho L by A, then length doubled, area was half. So, you can see, this 2, this 2, what will happen? 2 square.

Right. So, you can see here, this will become 4 times rho L by A. So, we can say that length is proportional to square.

If you double the length, then the resistance will be 4 times. In the same way, if you have increased or decreased the area, but kept the length the same, then in this way, resistance is inversely proportional to area. And area is equal to pi r square. So, we can also say that resistance is inversely proportional to r square.

Radius will increase, resistance will decrease or area will increase, resistance will decrease. But if it is said that wire is pulled, right? You are pulling and increasing the length, you are halving the area.

If it is done like this, that is, if its volume is constant, then my dear children, what will be the concept here? That resistance is inversely proportional to square of the cross-sectional area. If you have pulled and halved its area, Hey. So length will be doubled, that is, resistance will be 1 by 4. Right? And if I write pi r square instead of this area, then this resistance will be inversely proportional to r to the power 4. My dear children, this slide is very important.

Think carefully once, you all. Now let's come to the omega and non-omba conductor. conductors.

Omic conductors are those in which Ohm's law is followed and non-omic conductors are those in which Ohm's law is not being followed. Now, when will the So I upon V is its slope which is equal to 1 by R. If this graph is straight line, then slope is constant.

Slope is constant means 1 by R is constant. 1 by R is constant means R is constant. Right? But if this graph is curved, then this time the slope which is I upon V which is 1 by R, that slope is not constant. If slope is not constant, then resistance is also not constant.

And if the resistance is not constant, it means that Ohm's law is not being followed. Right? Now, when does Ohm's law follow?

Any metallic conductor, Ohm's law is being followed there. But if we talk about any junction diode or transistor, then Ohm's law is not being followed there. We will say, sir, what is this diode?

When we will read the semiconductor chapter, we will read PN junction diode. Where P type and N type semiconductor are the same. ek hi samal lo It is inside the semiconductor.

When we will teach, we will talk about it. So this is PN junction diode and transistor is PNP or NPN transistor. Although now it is not in your syllabus, transistors. But earlier it used to happen. So as an example, just remember it now.

PNP or NPN transistors or PN junction diode. So we are going to study this in the semiconductor chapter. That means some places are also in your syllabus where Ohm's law will not be followed. Otherwise, generally, Ohm's law follows. Right?

Now, let's come to Joule's law of heating. So, from class 10th, you are reading this formula that the heat, if there is current flow in any conductor, then there will be collision of electrons between each other and with the atoms of the conductor, due to which heat is generated there. And that heat is directly proportional to I square RT. So, if we remove the proportionality sign from here, a constant will come. So, that constant here is equal to 1 by J.

Right? So, we got the value of heat. I square RT by J.

Or indirectly, you can also say that the formula of heat is I square RT. In more than 95% case, we use this formula. But the heat that will come out of here will be in joules.

But we all know that generally, the unit of heat is calorie. So here many times we feel like changing the calorie into joule or joule into calorie. We feel like that too and many times it happens in numerical. So we have to change that calorie into joule.

So for that you should know a formula that 1 calorie is equal to 4.18 or 4.2 joules. This is the reason my dear children because this value came in joule. And when the value in joule is converted into calorie, then you will divide it by 4.18. So, the J written below, you see carefully, that is 4.18.

Is it clear? I hope you are understanding the thing. So, if you divide 4.18, my dear children, then these values will come out in your calorie. Otherwise, if you have applied this formula, then the answer will come in joule. And if you have applied the formula I square RT divided by 4.18.

4.18, so this is the value that you have got in calories. 4.18 into 10 to the power 3, if you have divided it, then it will come in kilocalories. So, all that is the same. You all know that.

There is no need to get too confused. If you are a little scared to see this formula, that what is this J, then understand from here. If you have applied this formula, then the heat will come in joules. If we have applied this formula, then this heat will come in calories. Now I hope you understood the point.

There is no big deal here. If there is current flow in any conductor, then heat will definitely generate there. Now let's talk about power.

What is power? Power is the rate of doing work or rate of consumption of energy. Rate of generation of energy is known as power.

So what is power? Work done upon time taken. P is equal to Vi. P is equal to I square R.

P is equal to V square upon Rb. These are all formulas. Power unit is Watt. Power unit can be big. 1 kW is equal to 1000W.

This is also known by all of you. Apart from this, 1 MW is equal to 6W. Horse power is also equal to 746W. So these all are units of the power.

Now let's talk a little more about resistivity. We all saw that resistance R was equal to Rho L by A. My dear children, if any conductor If the length is 1 unit and its cross sectional area is also 1 unit, if both of these are equal to 1, that means if length is 1 unit, area is also of 1 unit, so resistance will be equal to rho. From here, the definition comes out.

What is resistivity? Resistivity is equal to resistance. If length conductor is 1 unit, area is also 1 unit square, then my dear children, resistance and resistivity are the same.

So read the definition. Resistivity of a substance is defined as the resistance. offered by the wire of that substance of 1 meter length and 1 square meter cross-sectional area.

Length 1 meter, cross-sectional area 1 meter square, so in this way, resistance and resistivity both become the same. Right? Now, here, resistivity is dependent only on material, it is dependent on temperature, but it does not depend on the dimension of the conductor.

Dimension means, it is dependent on its length and area. So resistivity is independent of length and cross-sectional area of the conductor. Resistivity's value can be seen. That is m upon n e square tau.

Where m is mass of the electron, e charge of electron, n number of electrons per unit volume. Or this is also called number density of electrons. Tau means average relaxation time.

Clear? Next is conductance and conductivity. Look, the reciprocal of resistance is conductance.

Conductance is denoted by G, that is 1 by R. Its unit is Ohm inverse, we can write MHO, we can write Simon. Or the reciprocal of resistivity, which is denoted by sigma, is called conductivity.

Its unit is Ohm inverse, meter inverse, or MHO per meter, or Simon per meter. So, all these are its units. Some people read Maho, you can write MHO too.

It is just the opposite of Ohm, MHO. Right? So this is how its units are defined.

Now let's show you the dependence of temperature for any conductor or semiconductor. See, in the case of any conductor, if you keep increasing the temperature, then resistance and resistivity are increasing. And here the formula is resistance RT is equal to R0, 1 plus alpha delta T. Where RT is resistance at T degree Celsius, R0 is resistance at 0 degree Celsius or resistance at reference temperature. Alpha is our temperature coefficient of resistivity and delta T means change in temperature.

So that is equal to T minus T naught. So what is R naught, what is RT, you should know a little about what alpha is. If I talk about any conductor, then alpha is positive for conductor.

This is the reason that if you increase the temperature of the conductor, then its resistance will also increase. And my dear children, its resistivity... The formula for resistance is the same as for resistivity. Rho T is equal to Rho naught 1 plus alpha delta T. This is the same formula.

The formula is the same as for resistivity. Actually, the reason for resistance to increase with temperature is that resistivity increases with temperature. The resistivity is increasing, so the resistance is also increasing automatically. So if you increase the temperature of the conductor, the resistance and resistivity will increase, the conductance and conductivity will decrease.

But if I talk about the semiconductor, then the matter is opposite in the semiconductor. In the case of semiconductor, if you have increased the temperature, then the resistivity will decrease. The resistance will decrease when the temperature increases. The resistance will also decrease. Whereas the conductance and conductivity will increase.

You will say, sir, now tell me why this behavior is happening? After all, sir, why is it happening that it is different in this and in that? So, my dear children, the conductor has a lot of free electrons.

When you increase the temperature, they start colliding with each other. Collision increases. Due to increasing collision, the resistivity and resistance increases.

But if I talk about the semiconductor, then it does not have free electrons. So now when you heat, their bonds break. And when bonds break, free electrons are generated. And when free electrons are being generated, then we will say that now free electrons have grown. Now they are born, so now they will flow.

Now they will generate current. That means now its resistance and resistivity will decrease. Right?

So see the graph, it is very important, it is asked. Now let's talk about electric cell. Till now we were talking about passive element, that is, resistance.

ke baare mein baat kar rahe the. Ab hum log... element of any circuit, i.e. cell or battery.

So, what is a cell? The principle of a cell is that it converts chemical energy into electrical energy. What is an EMF of any cell?

If a cell is not giving current, then its total potential difference is called EMF. So, EMF of a cell is defined as the maximum potential difference when no current is being drawn from the cell. If the cell current is not giving, then its total potential difference is called EMF.

What is the terminal potential difference? If the cell is giving current, then the potential difference across it is called terminal potential difference. So terminal potential difference is defined as the potential difference when current is being delivered to the external load resistance.

That means if the cell has given current, then across it is the potential difference, the terminal potential difference, which is slightly less than EMF. And when it is not giving current, then the potential difference across it will be maximum. That is called EMF. Now, when it is giving current, then why is the value decreasing? The reason is that in any cell, there is some internal resistance which is due to its electrolyte.

That electrolyte is offering internal resistance there. So, its voltage. The total EMF of the cell, the total potential difference, some of that voltage it consumes on its own.

This is exactly the same thing that when you bring a 256 GB mobile, whose ROM is 256 GB, so when you buy it, it is written on the box 256 GB, but when you buy it at home, you find out that 20-30 GB is filled with Android. Now if we want to use it, if we want to fill movies, songs, if we want to fill anything, then how much space do we have to fill that? So you never get 256GB, you can check it in your mobile.

If you are bringing a 128GB mobile, then 15-20GB is filled with Android. You will get only 110GB, 112GB maximum usable. Right?

So the same thing is that if any cell is of 10V, then 1V, 2V, whatever is there from 10V, that consumes internal resistance. So we will get only 8V from 10V for external circuit. So that 8V is called terminal potential difference and 10V is called EMF of any cell. Right?

So what is internal resistance? Internal resistance of the cell is the hindrance offered by the electrolyte of the cell. That means any cell's electrolyte, which we generally call Tejaab, the battery of the inverter, in which generally people say Tejaab is filled. So that is not Tejaab, that is electrolyte.

The electrolyte which offers resistance is called internal resistance. Internal resistance depends on many things. It is very important, you can ask.

Note these things very carefully in your copy. man. If the distance between the electrodes increases, then the internal resistance will also increase. If the area of the electrode increases, then the internal resistance will decrease.

So everyone knows that resistance is proportional to length and inversely proportional to area. If the concentration of electrode increases, then also resistance will increase. If the temperature increases, then the internal resistance will decrease. So if you are talking about electrolyte, then internal resistance will increase when concentration increases.

and increasing the temperature of the internal resistance will reduce our Now let's talk about any cell. If any cell is being discharged, discharge means that this cell is giving current. If this cell is giving current, then dear children, here EMF is more and the terminal potential difference is less, that is, V is equal to E minus IR. That is, if we reduce IR from EMF, then we will get the terminal potential difference.

So the example I gave, if our EMF is 10 volts, If the EMF is 10V and the internal resistance voltage is 2V, then the terminal potential difference will be equal to 8V. So, my dear children, it is simple here that the value of EMF is high. If it is being discharged, then EMF is high and the terminal potential difference is low.

But if the cell is being charged, we are charging the cell with an external battery, we are using a charger, So now what will happen here is that the external battery... The terminal potential difference should be more. So, my dear children, this time V will be equal to E plus IR. And here it is clear that the terminal potential difference is more than the EMF of the cell. Now think for yourself, if there is a 10V battery whose total EMF is 10V, then will we charge it with a 10V battery?

No, we will charge it with a bigger battery than that. Say, if there is a 10V cell, then we will charge it with a 20V battery. We will charge it with a 50V battery. charging from the battery, so simple to say means This is the case here, right? That here the terminal potential difference is more and the value of EMF is less.

Now let's talk about the combination of cells. First of all, think about what is the work of the cell. The work of the cell is to provide current or to maintain the potential difference.

If that cell is not able to give us the desired current, then we will do the combination of cells. There are two or three combinations of cells in your syllabus right now. First of all, the series combination of the cells.

In series, you will keep connecting the cells in a line. So, in this case, the current that we are going to get here, the value of current is NE upon R plus NR. Where N is the total number of the cells which are connected in series. And E is the EMF of all these cells. That is, if I assume that E1, E2, E3, E4, all are equal to each other.

And all of these are equal to E. Means we have considered such cells whose EMF is equal to each other. And I am taking all internal resistance equally. So in this case, NE upon R plus NR will be.

So what is this R? What is capital R? This capital R, my dear children, is external resistance.

Right? This is external resistance. Any bulb you have connected, any fan you have connected, motor you have connected, all that is called external resistance.

So NE upon R plus NR. You will say, sir, where did this formula come from? Son, look, all these cells are giving current on the left side, that is, all these cells are supporting each other.

So all of them will add EMF, E plus E plus E plus E plus E. And if there are N cells like this, then NE will be formed. So NE divided by total resistance.

Total resistance, look, this one is capital R, all these small R are in series. So, Nr plus capital R will be done. The thing is, sir, when will we do series grouping of cells?

When the external resistance of the circuit and the internal resistance are more. If the external resistance is very high and the internal resistance is very low, then in this way, we are doing series grouping. Now, let's talk about our parallel grouping.

In parallel grouping, we have combined cells in parallel as shown in this figure. and here the current is E upon R plus small r by n. You will say, sir, how did the formula come? Son, look, if you talk about parallel, then all EMFs are the same.

So net EMF is also equal to our capital E. Understand, it's done. Right? Divided by, now these small r, small r, small r, small r, such n cells are there. All of them are in parallel.

So we can say, 1 upon r dash is equal to, all of them are in parallel. So 1 by r plus 1 by r plus 1 by r such n terms are there. So son, this will become n by r. 1 by r dash is equal to n by r.

So from here, you can take out r dash. which is R by N. This is the net internal resistance of all the cells. So, my dear children, the net internal resistance of all the cells is corrected in this series with R.

So, R plus R by N. This is our internal resistance, this is external resistance, this is total resistance and above is EMF. So, E upon this value.

When will this be used? When the value of internal resistance is very high in comparison to external resistance. Remember this, when it is used, you should remember the conditions. In parallel combination, the numerical chance of coming this year, remember this, this slide can be your numerical. The thing which is important, understand that it is really very important, it can be asked in the exam.

And there are many chances of being asked this time. So, assume this is your one cell, which has EMF E1, internal resistance R1, this is E2, this is R2. Look carefully, this is also giving current on the left, this is also giving current on the left. There are two cells which we have connected in parallel. in the world.

So, the formula of net EMF is something like this. E1 by R1 plus E2 by R2 upon 1 by R1 plus 1 by R2. And the formula of internal resistance, you must have understood. It is very simple.

That is 1 by R1 plus 1 by R2. All the cells, if you combine them in parallel, then you will get net internal resistance from here. And from this formula, you will also get net EMF.

But if one cell is giving current here and the other cell is giving current here, there, sir. then what will happen? So, my dear children, then minus will be applied here. E1 by R1 minus E2 by R2. But plus will remain below because the formula of parallel combination is the same.

It never applies minus in this. Okay? So, you must try these types of numericals.

I have also asked you such questions in the curriculum batch. And for the children, when they will bring the marathon class, then I will bring these types of numericals for you. Right?

So, now let's talk about combination of cells, a little bit out of syllabus, i.e. I am talking about mixed grouping of cells as well. Where there are some cells which are connected in series and we have some rows like this. In such cases, the current value is total EMF upon total resistance, i.e.

MNE upon MR plus NR. Where M and N are, look at this carefully. We have M rows and every row has N cells. So, how many cells are there in every row?

N cells. In one row. And how many such rows are there? M. We have total M rows.

Right? So if someone asks the total number of cells, it is equal to Mn. Okay? So, Mne divided by Mr plus Nr. If someone asks the total internal resistance of the circuit, the total internal resistance is equal to Nr by M.

You will say, sir, how did you come up with this? Tell me a little. So, in one row, Small r, small r, small r, small r.

How many cells are there? N cells are there. So how much is the resistance of every row? Nr. R plus R plus R plus R plus R, how much will be N R?

And N R, N R, N R, N R, N R, there are such M rows, my dear children. So 1 by R dash is 1 by N R plus 1 by N R plus 1 by N R. How many M terms will there be? Such M terms will be there. So 1 by R dash will be M upon N R. So from here, the value of R' will be N R by M.

This is net internal resistance. You will say, sir, when do we use mixed looping? So my dear friends, you will use mixed looping when the external resistance and internal resistance of the circuit will be equal.

And if these two are equal, then let me tell you, here the current will be maximum. And in that condition, the power loss that was happening in the circuit will be maximum. This is called maximum power transfer theorem. which is also called B-Tech. For now, let's talk about Kirchhoff's laws.

So, Kirchhoff had made two laws to analyze the circuits of direct current. The first law is based on the conservation of charge, which we call Kirchhoff's current law, Kirchhoff's junction rule. Nodal law is also called this, which simply means on any joint, any junction, any node. What is a joint junction or node?

Where some wires are getting. So, the current coming at this point is equal to the current going from this point. Right? So, the coming moment is going to go.

It is a simple thing. The current that is coming here, it will go from here. So, I current has come. I1, I2 is going. So, I is equal to I1 plus I2.

That means, if I write it here in short form, then I can also say that summation of the total current passing through this junction is always equal to 0. Right? Then, come on, there is the second law, which we also call loop law, which is based on conservation of energy. And this says that across any loop, The more active elements provide the potential, the more voltage they provide, the more passive elements will consume the voltage. If it has given a potential of 10 volts, then this 10 volts will be consumed completely. So my dear children, try to understand the method of applying the loop law carefully because children have a lot of problems in this.

The big line in any cell is plus, the small line is minus and the current always goes from high voltage to low voltage. So when current is going from here, then this is high voltage and this is low voltage. Current goes from high to low. High is shown as plus and low as minus.

So the first thing, no matter how big the loop is, you have to do this first. Make plus minus in all the cells and make plus minus in all the resistances. Now consider any loop.

Loop means any closed path of the current. So my dear children, this is our loop which is a closed and continuous path. Now start running from one side to one corner.

Start running from here, here, here, anywhere. Okay. If I am starting to run from here, then see, I am reaching minus. Right.

So, what will be the voltage in resistance? Minus IR. Say, V is equal to IR.

We all know that. Right. So, what does it mean? Because we reached minus, we took the sign of minus.

Minus VR. Okay. IR. Then move forward, move forward, move forward.

We have reached plus. So, plus V is equal to zero. Right.

Total voltage, sum of all the voltages across all elements is always equal to zero. That means the amount of voltage supplied by the active element, the passive element will consume that much voltage. So delta, sorry, sigma V, summation of V is always equal to zero across any closed loop. So you can apply it this way.

Start running from one side, take the sign wherever you reach. If I reach negative, I have taken minus IR. If I reach plus, I have taken plus V, which is equal to zero.

So this is Kirchhoff's second law. It is important, my dear children. Practice these two laws a little.

You can be asked. On the last topic, let's come to Wheat-Stones Bridge. Sir, what is Wheat-Stones Bridge? It is a formula to calculate the value of resistance.

Wheat-Stones Bridge is used to measure any unknown resistance. In Wheat-Stones Bridge, this method is... There are quadrilaterals on each side of the quadrilateral.

There are resistances on each side of the quadrilateral. That means we have four resistances. There are two diagonals in any quadrilateral.

One diagonal has a cell on it. On the other diagonal, we have a galvanometer. Galvanometer is a device that tells us that the current is...

or not? It means it takes the attendance of current. It represents whether current is present or not. So, my dear children, what will be happening here?

It will be happening that from here, I current will be coming out of the cell. As soon as I current will reach here, that I current will be divided. I1 went here, I2 went here. As soon as I1 reached here, now it became known that we consider Wheatstone Bridge to be balanced when there is a current in the galvanometer. If no current goes in this galvanometer, then my dear children, where will all the current go?

In the Q, because it does not have to go here. So all the current went to the Q. When the I2 current reached here from here, now again he remembered that the current did not go in the galvanometer, so all the current went to S. So I1 came from here, went here, I2 came from here, went here, and finally both together again became I current and went back. Remember one thing about any cell, the more current the cell gives from its positive, and takes back the rent in negative.

Clear? So, it means that any wheat stone bridge will be balanced when P upon Q R upon S is equal to this resistance upon this resistance equal to this resistance upon this resistance. Or this resistance upon this resistance equal to this resistance upon this resistance.

Right? So, R1 upon R2 equal to R3 upon R4. Or P upon Q equal to R upon S. Or P upon R equal to Q upon S.

All the ways are the same. Write as you want to write. Write.

Okay? In Charbis, it's... you will know three resistances, you will not know the fourth, you can calculate that. There is no problem in it. But remember, the wheat stone bridge will be balanced only when the current is not going in the galvanometer.

That means, no deflection is showing in the galvanometer. Right? Now, sir, the null point of the galvanometer, does it depend on the resistance?

No, it doesn't. Galvanometer and E, E means cell's EMF. Right?

It is not dependent on the EMF and the resistance of the galvanometer of this cell. It is not even affected if positions of galvanometer and cell are interchanged. That means, if you lift this and put it here, if you lift the cell and put it here, there is no difference, brother.

Right? So, let me teach you one more thing. Whenever in any circuit, in any question, in numerical, how will we recognize that, sir, that is a galvanometer? So, for that, there is a method, this one, right? Yo-Yo Singh's method.

So, this is positive. If you check the positive cell, you should have two resistances connected. If two resistances are connected from the positive part of the cell, if two resistances are connected from the negative part, if there is a resistor or galvanometer connected between them, then there is a possibility that it can be our wheat stone bridge. But you have to check whether that wheat stone bridge is balanced or not.

So, my dear children, This was your Wheatstone Bridge. This was your chapter number 3. I have revised the entire chapter for you. Chapter number 3 has been revised very quickly.

I hope you have understood everything. Everyone, please comment and tell us how you liked this lecture. Then we will meet in our next chapter, which is Magnetic Effect of Electric Current. It is a very beautiful chapter.

And we are going to revise that chapter as well. Your homework is to revise the chapter with me. Now you solve the numericals of this chapter. And per day, 10 numericals are your homework.

That means when you are watching the lecture of next chapter, then I am giving you at least Sunday's leave. At least 60 numericals you have solved on your copy. Right? So brother, let's meet in our next class. Till then, goodbye and take care.

Transcript for:Current Electricity Overview

Transcript for:
Current Electricity Overview