hello good evening my dear lovely Lions my Warriors to the vant English Channel and this is your captain Shas your capto your physics Master teacher who has been guiding and training kids for more than 12 years guys and here we are on this channel make sure that you are liking the video and also subscribing to the withu need English Channel the number one channel for need English in the country so today we are already on chapter number three the current electricity chapter make sure that you attend all the ncrt line by line Series this will not only help in your board exams but obviously you know NDA is going to pick up ncrt they are going to go through the text and make the questions from ncrt so make sure that you know every important line and every single example from ncrt hi Krishna hi Jasmine welcome atluru nice to see you back hi Mel hello sumati welcome nice to see that fire in the chat box awesome super duper hi somia good evening I hope you guys had your dinner and are full of energy I know sleep will come in the may but we are not going to give up we are neat Warriors we are future doctors so we have to fight it we will struggle we will win this war of need 2025 okay so stay with me till the end I hope you marked your attendance if you have not marked it do that and smash the like button right away right now and also do not forget to check out this particular scholarship link for all of you mvat examination is nearby I hope you're preparing really well the link is there down in the description box below the biggest scholarship exam where more than two lakh students are going to give it and you too can get your National level ranking and Just for participating you will get free study materials and also chances of getting scholarship and even if you're enrolled in a course already so you can get that refund amount because of this particular scholarship right so lot of prizes to be won lot of goodies to be given offline as well as online the dates are mentioned syllabus everything I have already cleared it out in a live class so make sure you're registering by entering your mobile number right over here so that you know when the test is and you are preparing for it that will be our first step towards KN 20 25 or 26 and if you have your friends who are not yet you know enrolled in the test encourage them to give mvat cool thank you guys for all the fire really I feel really warm looking at all your chats thank you so much thank you so much sat Krishna thank you so much siia hi vs vetri present glad so in this chapter of current electricity it starts off with basic current parameters like density drift speed relaxation time resistivity resistance EMF all these things then slowly we move on from those to you know circuit problems where you talk about batteries in combination resistors in some combination we ston bridge and the power so that is the basic flow of the chapter if you remember little bit from your 10th standard I hope you yeah probably I don't know maybe it has been a while uh this is a much better extension of that chapter which you might have studied back in 10th Grade all right so okay so this introduction part is just about telling you how current electricity is there everywhere I mean they talk about uh natural situations like lightning as well as uh you know a artificial man-made situation like a torch so if you talk about you know your fans your AC your light your torch your computer your mobile all of them work on the principle of current electricity and naturally occurring phenomena are like lightning so when lightning occurs current basically flow of charges happens from the clouds to the Earth so that is naturally occurring current and if you ever wondered what a current is current is like a river that's what they say but a river which is instead of carrying water it is carrying charges so a river which is like carrying charges is that phenomenal is being called as the current now we know that River will flow through a path same way the current will also flow through a path which is a conducting path or else we wouldn't be able to survive or live just imagine somebody turns on the light but instead of the current going inside the bulb it flows through our body it doesn't because there is air there is some insulation rubber wood so many non-conducting materials are there so which stops the flow of current and you know it only allows the current in a certain path which is the wire which is a conductor so that is what the basic introduction is that's not so great or important so just to build up the mood like warming up just like you guys warm up the chat box by putting those fire emojis hello K tamis hi scientist of India welcome welcome hi prant yep now the main things start from here which is basically the electric current imagine a small area which is held normal to the flow both the positive and negative charges May flow forward backward in some intervals some charges move this way some charges move that way and you might see that the total charge which flows is this much then the current is given by Q BYT which is defined to be the current across the area in the forward direction if it turns out to be negative number it implies the current is in the backward Direction now the main things which you need to highlight over here is basically this and is defined to be the current across the area in the forward Direction the net amount of charge the net amount of charge flowing in the area forward Direction in that time interval T is basically this much then this is the value okay now I'll explain you what this means say for example say for example there is a positive charge it goes like this and it goes like that through some maybe cross-sectional area maybe through some crosssectional area over here so if that particular charge was let's say q and this moved in a time in a time of T then I will say that the current is Flowing I will say that the current is flowing in this direction in the direction of the positive charge and the value of the current is basically Q BYT I will say that the value of the current is the charge which flows in a unit time now just imagine the same cross-section but this time but this time what happens is you have instead a negative charge you have instead a negative charge negative Q which goes through that particular cross-section in a time of in a time of T now now if you ask me what is the current current will still be Q BYT but it won't be here current is always assumed in the direction of the positive charges here negative charge goes this way it is same as saying if evil is going out of me I am becoming better if good is coming into me I am becoming still better I hope you understand both of them are creating the same kind of effect if something good is coming into me I'm becoming a good person if evil is going out of me you might say Sir something is going out of you but it's okay it's the evil which is going out of me still it is making me into a better person so same way if negative charges go here is the same as saying the positivity is going on this side hence the current will still be charged by time only Q BYT but the direction will be here is that making absolute sense to all of you same way now imagine just imagine there is this cross-section and what happens is there are there are two positive charges which go like this through that particular cross-section okay and there is one negative charge which basically goes through the cross-section like this you might be like sir this is uh you know combination of multiple charges now what is the current exactly I'll tell you these two charges going here will make the total charge going this side Q Plus Q this charge going here is same as saying a positive charge going this way this is same as saying a positive charge going the left way so actually the charge is not going right side it is going left side so I will put minus q and this whole thing divided by time let's say there was one more charge over here which was going this way then I would have put one more Q over here so this will be the total current so in this case it will be 3 Q minus Q which is 2 Q / T is that okay my dear students how this works and then what if this is the scenario let's see if you guys can figure this out but before that the direction of the current in this scenario the direction of the current in this scenario was here this was the direction of the current come on my dear students I want everyone to answer this there are two positive charges which are going like this and there is uh there are two negative charges which are basically going like this there is one negative charge which is going like this okay so tell me in this particular scenario in this particular scenario uh let's say there will be three charges now tell me in this particular scenario what is the total current in the circuit what is the the total current in the circuit so if you notice over here three charges positive charges are going towards the right hand side so q and Q and Q charges went to the right hand side these negative Charges going right is same as saying two positive charges went to the left two positive charges it's same as saying two positive charges went towards the left these two negative Charges going towards the left is same as saying two positive charges went to the right so won't these two end up cancelling out each other won't they end up cancelling out each other that's it the whole thing divided by time is the current so these two cancelled the positive charges went here hence the current in this scenario is towards the right hand side so this is exactly what has been explained in this paragraph So this formula might look simple but you should know how to exactly apply it through these examples I hope you have understood how this formula has to be applied or how you will actually use these things is this absolutely clear finally yep all right very good very good awesomeness awesomeness now in the next part after this in the next part after this okay but before going ahead they also tell you one more thing let's say I tell you that the current in this is 2 units is two units and I show the arrow Mark like this and there is another diagram where I show the current is like this and the current I will say it is minus three units what's the difference in these two the difference in these two is see when I say the current is+ two and I show the arrow mark means the positivity is going like this the positivity is going like this or I can say alternatively the negative charges are going like this that is what it means and the answer being positive tells whatever I have assume is correct if something is positive that means whatever I assume is correct but here it is negative means whatever I assumed is wrong so actually charges are not going here so the charges positively are going here or same as saying the negative charges are going this way that is the meaning of negative value of the current don't get scared thinking sir current became negative am I wrong no that's what they say if the current is negative then it just means the current is in the backward Direction so that is what they just say over here so another important point over here if it turns out to be negative number it implies the current is in the opposite direction or the backward direction that is what I have explained now the next part talks about the derivative of the charge with respect to time and they have given one formula over here which is the same as DQ by DT and why they have given this is because current need not always be study and it may increase and decrease sometimes more current goes sometimes less current goes everybody might have uh turned on the fan and be like Oh sir it is very hot increase the fan more current will come uh AC is not making me cold enough make the AC speed fast so you'll make the AC stronger to blow more cold air so it will take in more current or sometimes you are feeling very cold you reduce the AC so current can change with time and when current changes with time the charge which is going through it is also changing at different different rates sometimes more charge sometimes less charge sometimes constant charge sometimes again more charge and even more charge and again even less charge so the rate at which the charge flows can change with time so that is why you write it in the derivative form which is the rate of flow of charge and the unit of current also has been defined right over here the unit of current is basically ampere and ampere is nothing but how much current sorry how much charge flows per unit time it is a of charge which goes in 1 second so remember this 1 ampere is nothing but 1 Kum which goes in 1 second now this is a very informal definition the formal definition comes in magnetism chapter you will see why later on but don't worry about it okay now if you ask me how big is an ampere let me tell you you are mobile phone when charging takes few milliamp of current yes milliamp the AC the heater your Kettle water kettle all those things takes a few ampers like 2 ampers 3 ampers 5 amp or even up to 10 to 15 amp not more than that but lightning which strikes the Earth which is very dangerous that is thousands of ampers that is why it is considered to be very very dangerous got it so a charger typically in milliamp your laptops milliamp but you know heaters and all of that go in ampers and Lightnings in thousands of ampers that is what you should understand the scale of ampere now to give you an example of this to give you an example of this just say for example these kind of questions have been asked in the neat previous year papers they give you charge is equal to let's say t Cub minus 2 t² + 5 Kum question will be find the current at time is equal to 1 second this kind of question can come so what you will do you will see the given information and realize oh the charge is changing with time to find current I have to differentiate it I have to take the derivative of this DQ by DT okay no issues current is nothing but derivative of the charge which means I have to take the derivative of this entire thing T Cub minus 2 t² + 5 what might be the derivative of T to 3 3 comes here power reduces by one so it will become two minus 2 will come as it is it is a number T s's derivative two will come outside times power will reduce by one five being a constant the derivative is zero so therefore the current in general will become 3 t^ 2 minus 2 2 4 T the question is at 1 second so i1 so i1 will be substitute the value of time as 1 - 4 into 1 so what is the answer 3 into 1 is 3 - 4 which is -1 amp now you will be scared sir I got the answer as negative will I get Negative marks don't be worried you will see the options if it says minus one you'll just mark it what does this minus sign indicate it just indicates that whatever Direction you had assumed is probably wrong if you say this is the direction of current actually the current is not that way the current is going this way having a magnitude of 1 amp that is what it means is that clear everyone very good Krishna vs madhumati excellente Su long time I'm very good suganya yes I was not able to take the classes when I was back in Pune I was meeting all lovely students just like you yes correct moving on to the next concept electrical currents in conductors electric charge will experience for okay now in this uh entire paragraph I'll tell you what they have exactly done so there are some many lines in this section entire section 3.3 before 3.4 going to ohams law this entire section is talking about how exactly the charges move and what exactly conductors do in helping the current flow let's just go through it let's just read through it okay calmly and then we will understand it okay first let's read calmly don't worry whether I'm understanding or not forget it let's just read through it so when a charge will experience a force when an electric field is applied if it is free to move it will move in contributing the current in nature free charge particles exist like atmospheric uh straight up the ionosphere however atoms and molecules the negative charges which are basically the electrons and the positive charges which are the nuclear bound to each other hence they're not free to move bulk matter is made up of many molecules in fact a gram of water itself has so many molecules now these molecules are packed and the electrons are no longer attached to the individual nuclei in fact in some of the materials the electrons will still be bound and they will not accelerate even if you apply a f in some materials like Metals these electrons are practically free to move and they will you know move inside the conductor when electric field is applied if you consider solid conductors then of course the atoms are tightly bound to each other so the current is carried by the negative charge electrons and there are however other types of conductors like electrolytic solutions where both can move in our discussions we only focus on solid conductors consider the first case when no field is present okay before going here let me just start underlining few things uh an electric charge will experience Force if electric field is applied if it is free to move it will contribute to the current okay in some materials the electrons will be bound they will not accelerate even if the field is applied whereas in other materials notably Metals some of the electrons are practically free to move within the bulk material these materials are basically called conductors and they develop electric current when electric field is applied okay uh okay so that the current is carried by the negatively charged electrons okay um we only focus on our solid conductors okay consider the first case when no electric field is present and the electrons will be moving to the thermal motion will collide with the fixed ions and Elon colliding with other ion emerges with the same speed as before the Collision however the direction of the Velocity is random at a given time there is no preferable direction of the velocities thus on an average the number of electrons traveling in any direction will be equal to the number of electrons traveling in the opposite direction so there will be no net current this is considering the first case when there is no electric field present and they will be moving due to the thermal motion okay I will just read it and then I'll explain don't worry let us now see what happens to such a piece of conductor when field is applied when electric field is applied this is the next case when electric field is applied okay now you take a section and you see that some positive charge which is distributed on one disc negative charge on the other disc we attach the two dis on flat surface of the cylinder electric field will be created in the direction from positive to the negative charge the electrons will be acceler ated okay they will thus be moving to neutralize the charges electrons as long as they are moving will constitute electric current hence in the situation considered there will be current for a very short duration and not after much time we can also Imagine see guys ncrt will try to complicate things but wait a minute St s is going to decode this entire ncrt for you we can also Imagine a mechanism where the ends of the cylinder are supplied with fresh charges so that you know continuous flow is there in that case there will be a steady electric field in the body okay so imagine where ends of a cylinder are supplied with fresh charges to make up for any charges neutralized so that in that case there will be a steady electric field in the body and this will result in continuous current this will result in continuous current rather than a short current this mechanism by which you make a study current is basically called as cells or battery now called as cells and Battery we shall study them later all right so what is all of this let's decode imagine there is a house imagine there is a house this house this house okay this house is basically the nucleus this house is the nucleus which is basically positively charged in that house there are many kids maybe four five kids okay these kids which are there these tiny mini pandus which are there okay these kids are basically negative charges basically the electrons basically the electrons now just imagine maybe your favorite hero or heroin has come maybe talapa VI came in the neighborhood that way or maybe maybe dhoni came okay near our house maybe in a coffee shop for some reason or maybe some beautiful actress came okay so what will happen is these kids are like I want to go out of the house I want to go to the house I want to meet duni I want to meet this person my favorite hero heroine has come they will try to go but the parents will be like no you can't go you have to stay in the house so usually in an atom the electrons are bound the electrons are bound they cannot go outside this door agree or disagree but inside the house they can keep moving randomly they running around like mad people they're running around like mad people inside the house that random motion happens within the bounds of that vicinity of that atom but not far away from the house or that atom itself that random motion of the electrons is associated with the temperature or the thermal energy so when you take let's say copper or gold or aluminium inside that so many electrons are there and they're moving randomly here and there they're colliding that random motion is associated with temperature if you heat it up there is more Randomness imagine there is more heat in this these kids are running around like crazy they are they are they're going nuts they're going mad is that clear okay now imagine many such houses imagine many such houses obviously with houses come many such kids out here many such kids if for example our beautiful Champa has come all these pandus are at home okay this is a beautiful Juma all these kids are like all these pandus are like I want to meet my hero I want to meet My Heroine I want to meet my Superstar these houses are not letting them go this cha this Superstar is like that external field what is that cha or that external Superstar like the field electric field what does electric field do electric field applies force on the electrons is that right force on the electrons so now now what happens is if it's a nonconductor basically an insulator like rubber wood paper marble Stone soil bad conductors no matter which Superstar comes no matter which Champa comes these electrons can never leave their houses their kids will be crying but they can't leave so for non-conductors like rubber Etc the electrons can't leave the atoms they cannot flow even if there is a electric field because of which they do not conduct electricity but in a conductor the parents are little lenient okay our superstar has come go here take some money okay enjoy okay eat something okay maybe drink some juice okay here have some chips so the parents gave some money okay go meet your Superstar so these kids run and meet the Superstar so there is a flow of charges these electrons flow so there is a flow of charges because of an external influence and that's what constitutes current where does it happen in conductors example Metals copper silver gold aluminium iron so all these substances you will see the parents of their houses basically the nucleus the nucleus is lenient and they have let the electrons free to roam around now if few of the kids meet the Superstar the other kids will think are already this Superstar is surrounded with so many kids over here what will I go and do they will get demotivated already this Champa is giving bow is giving you know importance to the few pandus around whatever that star so the other kids are like okay my role is not there it's okay Papa I will stay at home it's okay Mom here take this money I'm going to stay stay at home so the other kids do not have motivation but imagine one more cha comes one more Champa comes over here one more Superstar comes then the next few kids will get motivation and they will go towards the Champa is that right but then again other kids will be like okay already the Champa is surrounded by pandus I will not do anything then you need one more cha imagine there is a continuous supply of Champa imagine there is a continuous supply of Champa what will happen kids will keep coming kids will keep coming got it my dear Warriors so what they explain in the paragraph is that if you apply the electric field using you know some plates or anything then the charges will get attracted and then the charges are neutralized after that there is no current but if you constantly maintain the electric field if you constantly maintain the supply of electric field how do you do that by connecting a battery a cell then charges always have that motivation because of that electric field to leave the nucleus they are free and they continuously flow inside the conductor and that's how current gets established is that absolutely clear what they have explained in these three four ridiculous Pages or paragraphs I have marked all the important lines for also for all of you this is the main thing what they have explained clear have you understood it are you able to visualize this now what happens inside a conductor electrons they want to live but they can't live for a um nonconductor like you know rubber or wood but for conductor they can leave free to move once they move the charges get neutralized then there is no motivation for the new electrons so the current will be only for a short duration so to continuously maintain the current we need to continuously give the electric field that external motivation has to be there so that comes through a battery a cell you buy those cells you connect it across a wire continuous electricity flows okay clear awesome Yesa clear very good now let's come to basic Ohm's law so now that you have understood what current is Ohm's Law is a law which was given almost like 200 years back guys okay and he he said that uh you know whenever he applied a uh whenever he connected a battery or a cell across different devices and he changed the batter's voltage or he increased the power supply he found that the current was proportional to that voltage and that is exactly what Ohm's law is all about so a conductor in which a conductor through which current I is slowing and voltage V is the voltage difference between the ends of the conductor then Ohm's law says voltage is proportional to the current or the constant of proportionality the constant of proportionality is basically called R which is the resistance how much does it resist the flow of the current the unit of resistance the unit the SI unit of resistance is basically Oham and is denoted by the symbol this Sigma over here the resistance not only depends on the material but also the lengths the breads everything and we will see how it is determined in the next slide so basically what Oham said is that if you have some device and he passed different values of current so he see what is the current and he also notices what is the voltage difference across the ends first you saw when there is Zer volts then there is two volts then let's say there is uh 4 volts okay then let's say there is 10 volts the currents that he saw for example no current over here then let's say there is5 current over here then he saw basically you know 1 ampere current over here okay so then he saw basically you know 2.5 aamp current over here he saw that the current is directly proportional to the voltage and if you notice over here if I write V is equal equal to I * R take any value for example I take the value of 2 okay is equal to current is nothing but .5 multiplied by the resistance I will get the resistance as 2x5 which is 4 ohm which is basically 4 ohm so this tells me the resistance of this device is 4 Ohms if the resistance was more then this won't be the current the current would be less if the resistance is less for the same voltage there would be more current which would be flowing that is exactly what Oham set yep all right very good now this is only true for something called as ohmic devices ohic devices you will see later on in semiconductor chapter that there are nonohmic devices as well which do not obey Ohm's law which means means if you increase the voltage current increases but not proportionately suddenly there is a sudden Jump Then it is not increasing so much so that weird Behavior can happen at that time imagine this happened you know in 1828 the knowledge of semiconductors was not there so he gave the law although this law is only valid for mainly conductors not for semiconductors is that absolutely clear everyone adesh obviously J means is tougher but gold is tough if you do not understand the concepts yeah now how does it depend on the dimensions of the uh how does the resistance depend on the material as well as the dimensions so we'll come to that as well so the resistance depends on material of the conductor as well as the dimensions of the conductor how does it depend that is what they have explained in these few paragraphs right over here now what they have written down in these two paragraphs I will just have a look at it okay and I'll explain and decode it for you so first they take a single slab of conductor of certain length and area then they increase the slab's length and what happens is basically they put another slab along with it to increase the length and and they apply the same voltage they find that the current has become uh you know less that's because the resistances have become more okay so they conclude from here that the resistance is proportional to the length and next time instead of placing one slab after other they cut the slabs or place it besides each other then they find that the resistance has increased and then they conclude that okay resistance is inversely proportional to the area so how they are doing this let me tell you imagine this is the conductor imagine this is the conductor and what they do is they have passed in some current over here because there is some voltage difference because there is some voltage difference so they find out what is the resistance and the resistance comes out to be let's say V by I because V is equal to i r will be V by I next time what they do they take the same conductor but they put another similar conductor in front of it so that the length becomes basically double so now the length is double or you can think as if there are two conductors side by side what they find is if they apply the same voltage now across this the current which passes through through this becomes I by2 the current which passes through this will become I by2 so this resistance this new resistance will be voltage by current voltage by current so it will be V by I multiplied 2 but V by I is nothing but R so it will become two times of R so the new resistance has become two times and the new length was twice the old length from this what they concluded resistance is directly proportional to the length of the conductor longer the conductor more is the resistance is that absolutely clear everyone how they were able to conclude this by putting another conductor and if you put three conductors the resistance will become three times the current will become 1/3 if you put four conductors resistance will become four times one after the other now they did the same experiment but this time they put another conductor besides it another identical conductor besides it so instead of one after the other instead of one after the other they put another identical conductor besides it like this and they applied the same voltage say for example the same voltage like this what they found was now the current had two paths to go like this in fact the current became 2 I the current became double so from this if you find what is the new resistance voltage is V current is basically 2 I so it will be half into V by i v by I is R so it will be R by 2 so what they found is the resistance has become half when the area is two * the old area from this they concluded resistance is inversely proportional to area area doubles resistance becomes half resistance becomes half exactly so that is how they were able to finally write down they were able to finally write down okay resistance is proportional to length resistance is inversely proportional to area therefore resistance is proportional to L by a therefore I need a constant of proportionality instead of proportionality I put a symbol called row what is this row this row is that constant that constant which is called as resistive it resistivity understand that so this is called as the resistivity this is resistance this is resistivity resistivity is of a material aluminium will have some resistivity copper will have some resistivity no matter where you find the copper copper will have the same resistivity but resistance depends on resistivity length and area if you take more copper the resistance might be more or less depending on whether area is more or length is more but resistivity is a material specific property if I take a Long Rod of copper then the resistance will be more but resistivity will still be the same if I take a wide copper maybe the resistance will go down but resistivity will still remain the same that is what they have written down right over here so this is a very very important formula guys R is equal to row L by a and this constant of proportionality this constant of proportionality row depends on the material like I said whether it is copper aluminium Etc of the conductor and very very important not not on the dimensions and this row is basically called as resistivity okay that is what it is so if if you write Oh's law instead of V is equal to I you can write r as row L by so it will become I row L by a that is what they have done this is not so important if you know this and homes law it's more than enough till this point clear very good ATU Krishna madhumati chitra suya understood clear shall we move ahead my dear students everyone okay cool cool now now they derive another expression called e equal to RJ and there is a very funny way they do it see V is equal to current into resistance correct what if I write resistance as row L by a and then they write current by area separately okay row over here and then that length they take it over here voltage per unit length what is it DV by Dr it is nothing but electric field if you remember this definition which we have learned before electric field electric field was negative DV by Dr so here we are just concerned about the magnitudes don't worry about the minus sign rate of change of voltage with distance so voltage per unit length gives me the magnitude of the electric field what is this current per unit area telling me this is telling me listen if you have a cross-section if you have a cross-section okay and in that cross-section for example some current is flowing through it versus the same current flows through a larger cross-section here the current per unit area is more here the current per unit area is less so I get a term called as current dens density so the current is more dense more current more current density in this case versus there is low density of current low density of current in this case because the area is more for the same current so this current per unit area is given a symbol J so remember this J is current density which is I by by a guys which is nothing but I by a very very important so that is how they get electric field is J row electric field is nothing but jro that is what they have got right over here so you might be wondering sir what is this electric field that we are talking about this electric field is the electric field inside the conductor inside the conductor which causes which causes the free charges the free charges to move to move very very important without this electric field remember this electric field is like that cha or that Superstar giving that motivation for those electrons to move so that electric field is inside the conductor which causes the motion of the charges J like I have told you before is nothing but your current density this current density will have a unit of unit of ampere per M Square how many ampers is going per unit area that is nothing but your current density now this equation was completely in magnitudes like you see the minus sign everything was ignored but actually it can be written down in the vector form now current density is actually a vector quantity and you can rephrase this as J Vector is your or rather electric field Vector is your J Vector into row and then the another quantity called as conductivity okay so we'll come to that but before that let's block all the important statements over here and they write Sigma is 1 by row which is nothing but called as conductivity okay and they have also defined the current density Vector over here the current density which you have defined the current through the unit area normally to the current is also directed along e it is a vector it is a vector okay so now what have they basically told over here let me tell you see understand this okay very carefully observe this was our area this was our area let's say the current flowing through it was like this the current flow going through it was like this the current value was I current density is a vector which is perpendicular to that area in the direction of that current okay and it is a vector in this direction of the current itself it is in the direction of the current itself so that's how it has been defined now if you talk about the conductor sorry if you look at the conductor this let's say is our conductor inside the conductor who moves which charge moves positive or negative nucleus does not move electrons Mo which direction do they move which direction do they move think about it which direction do they move yes they move opposite to the direction of the current these electrons obviously move opposite to the direction of the current this is how the motion of the electrons is and that is the reason why the current was in this direction okay that is how the current was here so actually the electrons are moving in the opposite direction so in which direction the electric field is applying the force obviously the force applied by the electric field on the electrons is in this this direction hence the electric field itself must be in this direction because electric field on a negative charge applies a force in the opposite direction so hence electric field was in this direction so can you see electric field Vector electric field Vector is basically parallel to the current density Vector is parallel to the current density vector so that is why this equation which we had e is equal to e is equal to row J row J row was your resistivity row was your resistivity okay it can be written down in Vector form also because the directions are same for J vector and E Vector if I put J Bar here there is no harm in putting e bar over here it's fine it's perfectly fine got it everyone why I'm able to put the bar over here because electric field is parallel to the J Vector now what they do in the next step is they take this e bar and this row which is there they just put it over here they just put it over here and they get J Bar this one by resistivity 1 by resistivity they are calling it conductivity so conductivity conductivity is one by resistivity meaning if something is more conductive it will have less resistivity if something has more resistivity it will have less conductivity so they are just inversely proportional to each other that's all if somebody is less bad that means he's more good if somebody is more good that means he's less bad so they are inversely proportional so it's just a way of looking at it in a different way so this is then called as Sigma which is conductivity these people come over here as it is and is equated to J bar is that understood how this expression comes how this expression comes and what they mean over here absolutely clear my dear warriors cool very good if you have understood it till here if you have understood it till here awesome awesome now let's go to 3.5 where they talk about drifting they talk about drifting and then they have given some interesting paragraphs here here here and okay till here okay these three pages let's have a look look at it let's read it and obviously then let's decode it okay cool let's start reading guys start an electron suffers collision with different things but after Collision it will emerge with the same speed in random direction if you consider all the electrons their average velocity will be zero very important line all the electrons their average velocity will be zero since their directions are are random very very important so if there are n electrons the velocity of the I electron at any given time is this blah blah blah so the average is zero okay no need to byard this consider now the situation when the electric field is applied electrons will be accelerated by this particular formula and then you know if you take it for any particular uh electron okay the velocity After Time T is given by chematic equation final velocity is initial plus acceleration into time since uh okay um since starting with its last Collision it was accelerated with the acceleration given by for time T the average velocity for the electrons at the time T is the average velocity of all the uh VTS okay the average blah blah blah since immediately after any Collision direction of the velocity of an electron is completely random the Collision of the electrons do not occur at regular intervals but at random times let us denote to the average time between the successive collisions then over a Time some of the electrons would have spent more time than to and some Less in other words the time T will be less than t for some and more blah blah blah then the average value will be this and this uh okay you will get something called as the drift velocity in this last result is surprising it tells us that electrons move with an average velocity which is independent of basically um independent of time although all electrons are accelerated this is the phenomenon of drift and this is called as the drift velocity okay so again this particular formula of drift velocity very very important tells us that electrons move with an average velocity which is independent of time and this is called as the drift velocity over here okay so what is basically explained over here let's understand if you look at the life of any electron it goes like this hit somewhere hit somewhere hit somewhere this is inside that you know solid it is moving randomly over here so there is random motion of the electron of the electron in fact if you look for a decent amount of time let's say 1 minute or 2 minutes or maybe 30 seconds you will see on an average these electrons have zero velocity these electrons have zero average velocity so I can say the average velocity is basically zero because the displacement is zero for a decent amount of time for a for an you know time interval for a time interval if you look at it on an average the velocity is zero okay now if it was a stationary electron and if somebody applied an electric field like this that electron will experience a force in this direction because of which it will end up accelerating and that force will be nothing but the charge let's say the charge is e multiplied by the feed multiplied by the feed so hence now there will be acceleration which is given by force by mass so the acceleration will be Force divided by mass the force itself is capital E into small e field into e because because of which what will happen the velocity will continuously continuously what increase after some time it will become 2 m/s Then 10 m/s 20 40 100,000 one lakh if the field is continuous there is nothing to stop it but inside a conductor even when you apply the field because you connect a battery or a cell it does not continuously increase the speed after some time what happens is after some time what happens is this electron which was being accelerated this electron which was being accelerated yes the velocity might increase yes the velocity might increase for some time but it will collide it will collide with something it loses everything and again it starts from rest again increases the velocity maybe for a longer time and again now Collide and then again it starts increasing the velocity maybe the Collision happens sooner here again it starts increasing the velocity so if you see it's like going inside the traffic it's not on a express way which is continuously accelerating so it increases the speed t Okay full one tight slap it gets again it accelerates t slap it gets stops that slap corresponds to Collision every time it collides loses its velocity again it accelerates again loses its velocity so if you see it is not continuously increasing the velocity rather I would suggest that it is on an average going with some average velocity it is going with some average velocity it's basically getting drifted slowly and all of this was happening because of the field which was pulling it accelerating it and the Collision which was again bringing it bringing its velocity down so this is basically called as the drift velocity what is this called This is called as the drift velocity did you understand what is the meaning of this word drift velocity VD everybody till this point yep very good excellent now now what they say is see if you look for only one atom if you look for only one atom this on an a this final velocity is basically initial velocity plus acceleration into time but if you look for many atoms this final velocity on an average which is initial velocity on an average plus acceleration into time on an average this velocity after the Collision is going to be zero on an average this velocity on average is going to be zero this final velocity on an average by which they keep on moving they keep on moving that is basically your drift velocity VD over here acceleration we just figured it out right over here it is e e by m it is nothing but e e / M this time sometimes longer sometimes even longer sometimes shorter it accelerates for more less depends but on an average if you take that time that time that time over here is called as tow which is called as your relaxation time relaxation time relaxation time means it it gets slapped T again it accelerates slapped again it accelerates T SLA so it is relaxing one slap now no slap it is accelerating T so that time on an average is called as relaxation time got it my dear Warriors clear so that is how they get this expression VD is equal to e by Mt VD is equal to e by Mt where did it go e by m to sounds only so nice no to say e by Mt VD is equal to e by Mt okay e by Mt is equal to VD VD is equal to e by Mt maybe some jingle will be made if somebody is some musician you can make some nice music out of it VD is equal to e by Mt cool understood o Clearo VD is equal to e by m i feel like saying it again and again it sounds so interesting VD is equal to e by m to great now moving ahead what have they done such nice paragraph they have written something and all they got and don't worry about this I'll explain you they have not mentioned anything significant but they have done some derivation in a very textual format I will explain everything over here and then they get current density in the form of relaxation time okay how did they do it see I'll explain this before going ahead imagine you take a conductor of some area some length Okay and it has some amount of current so basically some charges some charges will go through this cross-section from here to here in a time of delta T and as they are moving they are moving with a velocity on an average of drift velocity okay how long does this session take as long as it takes to complete this okay if needed we'll break it down into Parts but okay as long as it takes to complete this guys okay if needed we'll break it into Parts also H all right all right so now my dear students over here over here okay observe this carefully in this small time interval these charges cross this cross-section so can I say that the amount of that the amount of charge flowing upon the time taken being the current I can say that charge upon delt T is equal to I rather Q is equal to I delta T Q is equal to I delta T this is one way of looking at the charge second way is second ways this conductor will have some free electrons per unit volume if you take a good conductor it will have many free electrons in one unit volume if it's a very bad conductor not so many free electrons per unit volume so I Define a number called as n which is number of free electrons which are participating per unit per unit volume so can I say this n is equal to the total number of electrons upon the total volume now the total volume can I say it is area multiplied by the length area multiplied by the length okay perfect now what I will do is that I'll think if each electron has a charge e the total charge which I was talking about about this Q This Q will be the number of electrons multiplied by each charge has a charge e so this Q which was there inside which flows through that conductor will be number of charges into e but what is that number of charges which we can see right from here it is nothing but n a l n a l so guys Q is equal to n a l e q is equal to n e Nali so but Q is also I delta T Q is also I delt T so therefore I can write it as n a l and then e over here is that absolutely clear my dear Warriors everybody till this point clear that is what they have done in this particular thing current into time on this side and n a l e now what they do later on is that instead of writing length instead of writing length length they write it as speed into time speed multiplied by time that's it and here on the left hand side you still have I delta T you still have I delta T So this length which is there what they have done this length which is there they have written it down as speed multiplied by time length they have written it down as speed into time so now what and all will get cancelled what and all will get cancelled delta T and delta T got cancelled that is what they do over here okay they will basically cancel that delta T and delta T and they bring down this particular area below the current the rest of the things as it is n v d and e n is there VD is there and e is also there what is I by a it is nothing but J what is drift speed drift speed we just got it over here it is e by tow M or e e by m tow okay e by m and the whole thing multiplied by to so e e by m the whole thing multiplied by to and this e is as it is so from this we get J is equal to n e s e by m and down that is the formula is this derivation clear now how they got it that's the derivation guys that is exactly what they have obtained right over here okay that's all you should know okay so I've explained this in a very simple manner this is paragraph manner you will not understand it if you read it also rather I have tried to keep it as simple I found the charge here I also found the charge other way and then I just equate it from here and here okay so at this particular step I have equated it cool let's go ahead now they also say that this is exactly Ohm's law if we identify the conductivity as this blah blah blah so what they have done over here is this is uh J and uh remember there was an equation where did it go okay let me write it down over here J is equal n² T by m n e s to by m n² to by m into e but long time back we also wrote down J is equal to e * Sigma if you have forgotten where we wrote it down right over here J is equal to e MTI Sigma I wrote it down just some time back so comparing these two so just by purely just by purely comparing both of them what do you get just by comparing both of them Sigma is equal to n² to by m n e s to by m that is what they have also done n e s to by m clear okay so that is what they have obtained shall we go ahead my dear students shall we go ahead my dear Warriors ready cool okay great let's go ahead to some questions okay there is a question over here now how to solve this question I will definitely help you out with it so they say that there is a wire of some cross-section some current and uh each atom contributes one electron density is also given atomic mass is also given compare the drift speed thermal speed and speed of propagation of electric elect field and what causes okay fine now see guys over here what and all values are given to me I'll just write it down first of all I am given the area of cross-section area of cross-section is 1 into 10^ - 7 so 10 ^ - 7 m squ then current is 1.5 amp current is 1.5 amp then each C atom contributes one electron okay density is given as 9 into 10^ 3 density is 9 into 10^ 3 Kg per M Cub atomic mass number also they have given how much is it 63 so 63.5 G are there per mole okay that is what they have given and what we have to find is basically the drift speed and other things before solving anything else this third part speed of the probation of the electric field in the conductor yeah sorry the second part which we can do very easily this part what is the speed at which the electric field moves inside anything electric field guys if you remember light light light is a electromagnetic wave and electromagnetic wave or light travels at what speed the speed of light so electric field magnetic field if there is a charge Z the information will travel the field will travel everywhere at what speed speed of light so the this answer the speed of propagation of the field along the conductor which causes the drift motion should be the speed of FL I think the answer should be mentioned as it is yes yes the electric field travels exactly at the speed of light okay which is nothing but 3 into 10 ^ 8 m/s so electric field travels at the speed of light so that is that particular answer that is that particular answer and we have done this now let's go to the thermal speeds of the atoms versus the drift speed so for the drift speed I think I will need all this information how do I do this how do I solve for the drift speed think about it I feel to find out the drift speed to find out the drift speed what do I need what do I need there is a beautiful equation actually there is a beautiful equation actually which comes down as current is equal to n vdr this equation although it is not there in ncrt please remember it it will help you and it will solve the problems in a much simpler manner so remember this formula so because of which drift speed will be current multiplied NE E A now you'll be like sir what is the value of the current the value of the current is nothing but 1.5 a okay what is the value of e it is is 1.6 10 power -9 what is the value of a sir area is basically 10 the power minus 7 what is this small n it is not given to you that value is basically not given to you so how do I find this small n becomes the next challenging part this is number of free charges number of free charges per unit volume since it was mentioned each atom contributes one electron can I say it is basically the number of atoms the number of atoms upon the volume Now volume can be written down as mass see mass by volume is density so volume is nothing but density density density divided by mass so Mass goes on the top density is mass by volume so volume becomes mass divided by density uh sorry I think I missed this I wrote it perfectly know density is mass by volume so volume will be mass by density I wrote it Ulta guys I'm so sorry the this should be the mass and here should be the density okay now once I get this once I get this yes Envia graphics card company yes is it there in ncrt no it is not there directly in ncrt but you can use it okay it is not there in NC but use it you can get it by again modifying these drift speed formulas if you modify these drift speed formulas now you again get the same thing only okay so we don't have to worry about the derivations but just remember Nvidia graphics card company now the mass the mass which is there Mass can be written down as mass of each atom into the number of atoms I can write it down as mass of each atom multiplied by the number of atoms multiplied by the number of atoms and this density will come over here this n and this n cancels what will be the mass of each atom that will be nothing but your molar mass molar mass molar mass this density is on the top only density is on the top m divided by avagadro number avagadro number so hence this small n becomes avagadro number multiplied by the density multiplied by the density whole thing divided by the molar mass that's it that's it so this thing is not mentioned but you know they are using it ncrt so that is why I am explaining this to you how this came once you get this small n can be easily found out as 6 into 10 ^ 23 density is how much 9 into 10 ^ 3 molar mass be very careful it is G so 63.5 convert it into kg by multiplying by 10 ^ minus 3 so that will be per mole that's it so I think you will get the answer from this so whatever value of n you get right from here so just substitute it over here just substitute it over here and that's how you finally get the drift speed that's how you finally get the drift speed is it clear yes okay and this value this value comes out Out close to 1.1 mm/s this value comes out close to 1.1 mm/ second guys this is very small okay as expected okay don't expect the electrons to move with hundreds of meters per second they'll move very slowly very very slowly but the electric field gets sets uh sets up instantly speed of light that is the reason when why when you turn on something although the wire might be long it's not like sir the electron is moving at millimeter per second sir it took 5 hours for the electron to reach the fan so when I turned on the switch sir after 5 hours the fan turned on no it turns out turns on instantly it turns on instantly because the electric field reaches there and all the electrons in that wire are moving at a very slow speed everywhere it is moving instantly but at a very low speed keep that in mind and then there was the second part of question which talked about what is the speed of those electrons which are moving here and there that is usually the thermal speed which you will learn in thermodynamics of 11th standard that is of the order of few hundreds of m/ second there the Boldman constant comes you don't have to remember it as such this particular thing but in thermodynamics you might have learned kinetic energy is equal to kinetic energy is equal to 3x2 KT temperature is given boltman constant is given half MV s is equal to 3x2 KT from that you can find that speed okay but you should know it is you know in the order of few hundred of m/ second so these electrons move randomly few hundred of meters per second but as they move randomly they are moving ahead very slowly 1 1 mm/ second so they move really fast like this but they slowly drift like this after few minutes they slowly go here they slowly go here they're moving very fast but their effective output is that they're moving slowly drifting slowly at few millimet per second so that is why this question was even there to compare three different speeds the first one being the drift speed which is in very small values then you have your actual speed of the electrons which is decently large and the final speed was your light speed which is very very large I hope this is clear cool awesomeness awesomeness awesomeness let's go to the next thing let's go to the next example example 3.1 the electron drift speed is estimated to be only a few for the currents how then is the current established almost instantly this answer I gave you uh that time only how come the fan turns on or the light turns on instantly even if the electrons move in very small speeds like millimeters per second it's because the electric field sets up really quick it asks all the electrons throughout the circuit to start moving everybody is moving slowly but they are moving that's very important that's why current begins instantly so that's the answer of the first question I hope this is clear okay next the electron drift arises due to force inside the conductor but the force should cause acceleration why do the electrons acquire steady average speed this part I explained over here how is it that an electron does not continuously accelerate does not continuously accelerate rather it goes with constant speed it's because of the collisions it increases the speed loses the speed because of the Collision so that is why it moves with a average speed called as the drift speed so that is the answer for the second question okay that is the answer for the second question clear everyone next one if the electron speed is so small and electron charge is small how can we still obtain large amounts of current in the conductor electron speed is small electron charge is also small how come the current is in ampers the reason for that there are too many such charges even in a small gram of a conductor even few grams is like an avagadro number which is 10 ^ 23 number so the charge is small that's okay the speed is small that's okay but the number of those charges huge 10 ra to 22 10 to 23 that's the reason why the currents are in few ampers or milliers that's the answer for the third question clear everyone okay all right when electrons drift in a metal from lower to higher voltage does it mean that all free electrons of the metal are moving in the same direction so when we say current is moving like this is it true all the electrons are moving opposite to the current no all the electrons are not moving opposite to the current few of them might be moving even in the direction of the current but they are very few in number majority of them so maybe thousand are moving opposite to the current maybe some three or four are moving in the direction of the current so as a whole if you take the effective number of electrons they are moving opposite to the direction of the current I hope this is clear I'm so glad lucky thank you so much and I'm so happy that I'm your favorite teacher means a lot and uh I'm so glad you love physics because of me means a lot thank you so much are the paths of electrons straight lines between successive collisions with positive of the metal in the absence of electric field presence of the electric field so what about the paths okay how are the paths going to be now usually the paths are going to be straight lines even though the positive charges are there they will cause small deflections but they are too negligible but usually they are straight lines between one Collision to the next Collision so they go like this Collide go like this Collide Collide Collide but due to the nucleus there will be a very small deflection but not so much and approximately straight lines okay so all these same answers are um written down over here in your ncrt as well all right let's go to Mobility guys let's complete this let's do the resistivity part also okay all right resistivity part also let's do this okay now they have defined a new quantity called as Mobility Mobility means if I connect a battery how fast are these electrons drifting for the same battery meaning a field is applied if they are moving very quick they are very mobile if they are not they're less mobile so they defined it as drift speed by field if their speed is large that means their Mobility is more if I have to apply more electric field that means I have to push them more they are very lazy so they are not so mobile so Mobility is less that's the reason why Mobility is defined Mobility is defined as the drift velocity per unit field electric field okay per unit electric field drift speed formula we already know it is e to e by m so if you substitute it over here Mobility will become just e to by m okay so Mobility will just become e to by m because remember drift speed was e to e by m this e and this e can cancel out and that's why you will just be left with this so this can be also the formula where T is the relaxation time or the average time of collisions so this is something which you should know which is given over here this part if you remember I had explained it while explaining Ohm's law itself let me go back let me go back where is Ohm's law where is Oh's law where is Oh's law yes I told you this law is only valid for conductors which is basically ohmic devices there are devices where voltage is not proportional to current that is why they have mentioned about this which is basically the limitation of Ohm's law there are some deviations some materials do not obey proportionality they have some nonproportional behavior and such places they are said to be nonohmic devices so very clearly mentioned over here Ohm's law has been observed to be followed by many materials there are devices where voltage and current are not proportional to each other there do exist materials and devices where the proportionality does not hold they are nonohmic devices okay this happens for example in a diode which you'll study in this chapter chapter 14 that's basically semiconductors so semiconductors are a good example of materials where Ohm's law is not obeyed okay something which you should be aware of they have shown how the current and voltages changed this is for a diode you can see it's crazy the voltage and current relationship then it is like this it's very very crazy it is definitely not proportional these are just graphs given then there is a g there is a material called as G gallium and arenic how does the current change with voltage it's even more crazy it goes up then even comes down again goes up so we can see again nonproportional Behavior okay so they have just given examples please remember these graphs they might just ask you which of the following graphs is the behavior of voltage versus current for gas some options will be given if you know this graph it is there in ncrt you will immediately tick mark the correct option same thing for this this you will learn in chapter 14 so don't worry semiconductor chapter cool clear all right great okay so they just mentioned what is Ohm's law where it is obeed and we'll be mainly studying those devices where Ohm's law is obeed okay that's fine now again they come back to resistivity of different materials the materials classified as conductors semiconductors and insulators are based on the resistivities and of increasing values uh so if you talk about conductors which are basically metals they have very low resistivity obviously in the range of this much 10 the ^ - 8 to 10 the^ - 6 obviously metals are conductors so their resistances should be less resistivity also depends on the material remember that so they have very low resistivities which kind of makes sense then you have other materials like uh what do you say which are insulators like Ceramics rubber wood plastic paper Etc they will have very high resistances something like 10 to the^ 18 times greater than the metals so it's much much larger than the metals in between both of them in between both of them you have basically semiconductors they have decent resistivities but the funny part is their resistances you know change with temperature and also with what kind of materials are added in it so we'll study that in the separate chapter don't break your head how can resistance change by adding some amount of some impurity in it that is called as doping that doping you will study in chapter number 14 don't worry about it right now but it also depends on the temperature semiconductors like you know silicon germanium their you know resistivities also depend dep on the temperature and also something on the impurities which is called as doping which you'll be studying later on now how does it depend on the temperature is what we are going to study how does it basically depend on the temperature now usually if you take a conductor usually if you take a conductor what happens is when you basically heat it when you basically heat it what happens is these electrons which are there which are going randomly these electrons which are there their thermal energy their thermal energy increases so what happens is their collisions increases because of the collisions which are increasing what will happen they're colliding very frequently guys they are colliding very very frequently that means they will not have enough speed their relaxation time is less let's go back a little bit to see what happens let's see what happens guys over here maybe yeah their time will be less oh sorry where did it go H here their time will be less they will collide very frequently so relaxation time will be less what will happen to the conductivity conductivity will decrease so resistance will increase they will collide more frequently time will reduce less time between every Collision so conductivity will decrease so resistivity will increase hence you will notice hence you will basically notice that the resistance the resistance will increase is that clear the resistance will increase but for semiconductors it is exactly opposite why it happens we'll study that later on in that separate chapter don't have to break your head now but remember for semiconductors it is different how does it change for a conductor that formula is given right over here the resistivity is Row 1 + Alpha Delta T where where row T is the resistivity at some temperature at some temperature R KN is the resistivity at some reference temperature let's say t and Alpha is basically and Alpha is basically called as the temperature coefficient of resistivity this implies that when you plot the graph it would be a straight line and at temperatures much lower than 0 deges the graph how deviates okay that's this can be us approximate limited range okay fine now from this it should be clear it should be clear that if on the horizontal axis you plot temperature this is your temperature this is your resistance the graph should probably look like this as you increase the temperature the resistance will also increase Mak sense usually the graph is not a straight line it is a slight curve but if you take a small range if you take a small range it approximately looks like a straight line so for a small decent range decent range of temperatures it is approximately a straight line otherwise it is slightly curved it is slightly non linear it is not a straight line it is nonlinear so that is why for small ranges the graph will will be directly dependent on the temperature so you can see temperature is there here not t² or t Cub or root of T all those things are not there rather only direct single power of time is there that is what it is yes yes I hope this is absolutely clear row not 1 + Alpha Delta T this equation this equation is very very similar to if you remember final length is initial length 1 + Alpha Delta T where did you study this equation if you have studied 11th standard physics you will remember this was linear expansion of solids you Heats a solid it will expand or contract exactly so same kind of expression is even there for temperature dependence on Resistance so the resistivity at any temperature is resistivity at some reference okay into 1+ some constant into the change in the temperature this is called as your coefficient of thermal resistance like you had coefficient of linear expansion Alpha Beta gamma this is Alpha but for resistances exactly okay I hope this this is clear okay I have reduced the thickness of the pen don't worry I have reduced the thickness of the pen clear everyone till this point so that is why this expression has come and by the way I've also mentioned over there also that it is approximately a straight line for a small range thus this equation thus this equation can be used as an approximately over a limited range of temperature around any reference temperature whereas the graph is an approximately a straight line approximately a straight line and they have given that examples also see this here they have given the example of copper how the resistivity changes with temperature you can see it is nonlinear but if you take a small range it is straight line straight another straight line but big range no so from 20 to 30 yes 20 to 50 also is okay but 20 to 500 then I feel it's a problem because it's a huge range of temperature you can see it's for decent temperatures whereas for nichrome it is almost like a straight line there are not many deviations this is for Semiconductor this is very weird instead of increasing the resistance the resistance goes down why this happens we will see it in that particular chapter not here but you should should know that it is weird instead of increasing it decreases that's why there is a dedicated chapter only for that there is a dedicated chapter only for that okay great some materials okay magnitude and constant these materials have th a widely used in wire blah blah blah would change very little with temperates unlike Metals res okay okay so this special example of nichrome is what you should know nichrome you can see it is a constant line it is a almost like a straight line oops what just happened it's almost like a straight line so unlike copper or maybe aluminium where the graph is nonlinear for a wide range here it is a straight line that is why they have clearly mention some materials like nichrome okay you can see there is hardly any dependence very weak dependence with temperature and that is why they are usually used you know they are widely used in wires because you know how the temperature will affect the resistance it's a linear relationship okay this particular part like I have been telling again and again resistivity of semiconductor decreases with the temperature this you will study later in chapter 14 of semiconductors don't worry about it right now okay as we increase the temperature I think this explanation I already give what happens okay if you increase the temperature collisions increase relaxation time will go down so conductivity will go down and that's why resistivity will go up because the number of collisions number of collisions go up that is something which I explained right over here why the resistance increases they have explained it right over here so mentioning it here again okay as we increase the temperature as you increase the temperature the speed of the electrons okay increases so frequent collisions so the average time of collisions reduces okay something which you should understand from this which I have explained right over here how heating it increases the temperature increases the collisions reduces the temperature hence increases the resistance that is what they have explained over here same thing again cool great okay uh well this is fine okay now this part what they say is n is not dependent on the temperature to any appreciable extent hence the value of time plays a role but for semiconductors n changes and that's why you will see resistivity also depends on that okay now if you notice this equation the resistance not only depends on the time but also on the number of electrons which are free but when you change the temperature this nend does not change meaning if you take copper if you heat it don't expect more free electrons will come getting my point if you take copper aluminium which are conductors if you heat it if you heat copper or aluminium or gold don't expect there are suddenly more number of electrons already it has done enough it won't give new free electrons so that's why for conductors you will see it is generally not dependent on any but for Semiconductor like devices which you will again study later on you will see this changes drastically this changes drastically upon heating n changes so resistivity depends on N also that is what they have mentioned so again an important Point regarding conductors n is not dependent on the temperature in metals basically conductors basically conductors to end any appreciable extent and okay but this is an exception now this is an exception now for semiconductors for insulators semiconductors and changes with temperature and changes with temperature we'll come to that again in chapter 14 don't worry we'll study that later on today only let's focus on conductors and that is what they have also told somewhere over here see in most of these chapters we will study currents in materials that obey Ohm's law very very important guys we study we study currents in materials that obey Oh's law which means basically conductors so except for that semiconductor chapter everywhere else we study normal devices like conductors so you increase the temperature resistance increases ohms law is obeyed okay everything is smooth that is what they have told also clearly okay there is a toaster which uses some wire some small current passes and the resistance is found to be this much when the toaster is connected to this Supply uh and there is some new current what is the temperature of the uh nichrome element the temperature coefficient is also given to us read the question again and again and let's see how do we solve this particular question okay now here obviously resistance must be changing because you can see the current has changed because the current has changed and because of that I feel you should be able to use the formula for how resistance changes with temperature and then you can find out what might be the new temperature so ready to solve this ready to solve this question usually usually our equation used to be resistivity is original resistivity 1 + Alpha Delta T but there is no harm in replacing resistivity with resistance but then make sure here also you put resistance on there is no harm in this now resistance is voltage by current voltage is I think the same voltage is I think the same so voltage by the current at time T voltage divided by original current 1 + Alpha Delta T do you see that this voltage and this voltage just cancelled out and I get this equation I get this equation I think I know the current at time T sorry at some new temperature what is the current when a small current passes through it the resistance is found to be this much for this much Supply the current settles and oh I can't cancel the voltage my bad guys so sorry because voltage only initially is given my bad sorry sorry what they have given is at room temperature the resistance is given so R not is given to me at some new temperature for that voltage the new current is given so voltage at some temperature and current at that temperature is given to me this is my complete equation now it's just about substituting values 230 volts this much current is at that new temperature so put 230 over here current is basically 2.68 original resistance 75.3 1 + alpha alpha is also given 1.7 10^ - 4 into delta T what is this delta T actually final temperature minus original temperature which is 27° C so from this you will get the temperature the temperature comes out to be some 847 de C it comes out to be 847 de C now if you look at the solution given in ncrt you will get 100% confused but if you look at my solution it is very simple and elegant very simple and elegant I just said this is the resistivity formula so resistance formula will also look similar old resistance already given new resistance indirectly given because voltage and current is given oh now I know this this this this I just need to find what is the new temperature got it everyone yes I hope this is clear I hope this is clear okay let's go to the next question maybe or next concept okay resistance of a wire is 5 ohms at steam Point uh sorry at ice point is 5 ohms and at steam point is this much when it is inserted in the hot bath the resistance is this much calculate the temperature of the bath very interesting question guys very very interesting question see one thing we know resistance for a decent range is going to be like a straight line for a decent range ice Point means 0° C steam Point means 100° C means 100° C at I Point what is the resistance 5 ohms steam Point what is the resistance where is it 5.23 ohms they have asked you now if the resistance somewhere is 5.7 95 that means it is much Beyond than this somewhere over here maybe this is 5795 OHM then what is the temperature then what is the temperature that is what they have asked is that absolutely clear what the question is now one way to do the problem is using equations one way of solving the problem is using equations other way is using straight line equation but don't break your head on the straight line equation let's just use resistance at temperature T is original resistance 1 + Alpha Delta T let's rearrange RT by R is equal to 1 + Alpha delt t Okay so RT by R uh min-1 is Alpha delt T take r on the top RT minus r0 minus r0 divided r0 bring that delt T below is equal to Alpha why did I write this because Alpha is not given to me in the question Alpha is not given to me in the question that is the reason why I did this now whether I do from here to here or from here to here change the temperature from here to here or here to here Alpha should be the same so for this part the yellow part final resistance would be 5.23 original resistance was 5 ohm divide it with the change in the temperature 0 to 100 the change is basically 100 multiplied by the original resistance original resistance was 5 ohm that is for the yellow part if you do it completely for that orange part including right from here final resistance is 5 point is 5795 old resistance is 5 ohm whole thing divided by older sorry change in temperature change in temperature means T minus 0 so T minus 0 this is old resistance old resistance is 5 ohms do you see everything in this equation I know except for T solve this I will get the value of temperature did you understand what we just did Alpha was not given so first I wrote down what Alpha is then I wrote this equation two times one one here one here but for different ranges first for this and then for the whole thing that's all so from this I get the value of temperature as 345.8 345 65° C clear how to solve this isn't this method much simpler isn't this method much simpler yes or no yes or no guys correct very good great so we will continue with this second part of the class in lecture number two okay so we have spent a good amount of time in 3.1 to 3.8 today okay 3.9 onwards in lecture number two okay so I hope you will be marking your attendance quickly for lecture number two as soon as the session goes live but till then make sure quickly you have liked the session yes and mention part one done waiting for part number two okay see you very soon we'll be completing electrical power resistance in parallel series batteries in parall series Wheat Stones Bridge Etc properly in deta okay take care guys bye-bye have a great time