Comprehensive Overview of Current Electricity for NEET 2025

hello everyone welcome back to PW English medium Channel and welcome back to umid neat English series friends as

you know in this series we are completing each and every chapter of class 11th and 12th specifically for

neat 2025 exam in these one-hot lectures we are going to cover theoretical Parts as well as pyqs from the last year also

some of very most important questions right so stick with me stay till last till end of this chapter

because trust me if you're going to attend this current electricity lecture you are going to need no more lecture

right because I'm going to give you all the important notes all the important derivations all the important formulas

each of the things from this class all right so without any delay let's first look at the topics that we are going to

do in today's class obviously we are going to start with current then the most important part of the first section

of this chapter is current density drift velocity and along with this we are going to also talk

about ohms law and all the relations right and then we are going to discuss numericals Also regarding that then

another part of the lecture is now now the numerical portion starts that is battery and EMF KCl kvl combination of

resistors power and Jewel slw and instruments so even if if you if you think that there might be uh one or two

more topics we are going to cover all of those things like for example is dependence of dependence of resistance

on temperature I not written it over here but surely we are going to cover each and everything not going to miss a

single topic right so let's start today's class let's start with what we were talking about let's start with

current and let me give you a little bit of of a brief revision whatever you have been learning till current electricity

see Class 12 started with electrostatics is that correct in

electrostatics we basically said that charge is not going to move charge will remain at rest right

this was the this was the fundamental principle this was the fundamental principle of

electrostatics that the charge was at rest and we discussed kums force and all of those things that you have done in

chapter 1 and chapter 2 now when we are going to talk about current electricity we are going to say the rate of flow of

charge we are going to start our chapter with this thing that the rate of flow of charge

rate of flow of charge is current a very easy peasy

definition Doo right a rate of flow of charge is known as current now you can say Sir okay that means that let's

suppose if we have got a conductor over here if you have got a wire and please from the very start whenever we are

going to talk about a wire now it's going to be a metallic cylinder is that clear it's going to be a metallic

cylinder and we will say that let's suppose that we have got some charges over here we have got some charges over

here and if this starts to flow in a direction we say that the the wire has got current the material has got some

current right and then we are going to we are going to talk about all of the other aspects also so don't worry now

the first uh question is that why do charges move right why do charges move why do charges flow what I mean what

what what makes these charges move from one place to another place so the answer for that is is potential difference

let's suppose that this side is positive is is is having positive potential this side is having a negative potential

right so potent because of potential difference charges moves and now the next thing comes what do you really mean

by charges sir what what are the charges over here in a metallic conductor see when we are going to talk about a

metallic conductor let's suppose we are discussing Metals the charges because of which we

are saying that there is current are known as charge carriers so so don't get confused when we'll when we'll say that

what are charge carriers in metals or in in metallic conductors or in wires we mean to ask what are those charge

particles which are flowing because of which Cent we are stating that there is current so those things are known as

charge carriers in metals we know that we have got Loosely we have got loose electrons in the outer shells right you

you know you know all of these things better than me so we have got electrons which are actually Loosely bound and

these electrons will have a tendency to move towards the positive potential so this is how the

electrons are going to move so in this direction there will be flow of electrons is that clear so we have we

have till now we have studied that rate of flow of charge is going to be known as current that means I can Define

current as I equals to and see whenever whenever something like this comes up now whenever something like this comes

up that is rate we Define two types of Formula One is average current so average current is going to be called as

the um number of charges flown in a unit time between let's say two points the these are the two points right between

two points or if I would have said that okay let's talk about the instantaneous current so instantaneous current will be

written as limit delta T tends to zero d q by DT all right all right don't have to worry about this is nothing but

d d q by DT please please don't ever panic when whenever you see something like this

this is nothing this is your easy peasy derivative of charge with respect to time that's what we are talking about

you have done this numerous of times you have studied that velocity can be written as rate of change of

displacement with respect to time is that clear so you differentiate the equation of displacement with respect to

time and you get velocity similarly if you have got an equation of charge at as a function of time T and if you're going

to differentiate it you are going to get current so all right so this is quite easy for all of

you now what are the different things regarding current obviously I can see that the SI unit of current is going to

be Kum per second or known as ampere now current is actually a fundamental fundamental quantity current

is a fundamental physical quantity and ampere is a fundamental unit okay so whenever someone's going to ask you what

is the dimensional formula of current obviously you know it it's going to be m0

l0 t0 and A1 so it's a

fundamental quantity and has got fundamental unit right now let's quickly move on hopefully now now now you are

with me we are on the same page we have talked about what do we mean by current why current is basically rate of flow of

charges charges can be different in different types of mediums like for example as we were talking about Metals

so in metals the charges were electrons and the direction of flow of electron is something like this and the direction of

current will be opposite to the flow of flow of electron this is by convention okay you must be knowing this that that

this is the direction direction of current which is it should be opposite

to opposite to that of opposite to that of flow of electrons flow of flow of electrons or negative charges

right not going to bore you all with all of those things that uh electrons have the mobility protons cannot move you

know all of those things right there is going to be no current uh because of protons unless and until there is a Hy

hypothetical question I mean they can anyone can frame an a hypothetical question saying that we have got like

100 protons moving but generally generally speaking we'll always have electrons and if electrons are moving in

a particular direction direction of current is going to be opposite to opposite of that that's it now if if

someone is talking about an electrolytic cell right surely we can talk about an electrolytic cell let's suppose you have

got a positive electrode you have got a negative electrode and then you have got an electrolytic solution over here then

we have got both the things we have got both ions we have got positive and negative ions is that clear we have got

positive and negative ions and these are going to be your charge carriers these are the charge carriers in the case for

an electrolyte so it's not like if someone is going to ask you what are charge

carrier it's not like always electrons are going to be charge carriers electrons are charge carriers in the

case of a metal when we are going to talk about an electrolytic cell charge carriers are going to be what charge

carriers are going to be both positive and negative ions hopefully everything is clear right now if someone ask you

what about Sir if if I want to find if I want to find out the uh flow of if I want to the amount of charge flown so

let's suppose we want to know the amount of amount of

charge loone so now this is very easy as I've told you that current can be

written as in I'm talking about the uh instantaneous current it can be written as DQ by DT so the charge flown can be

actually written as integral of DQ further we can rewrite it as I * DT and let's suppose they are talking about

from time T1 to T2 that's it right so this is going to be uh the way by which you can find out the

charge flown between two time interval hopefully everything is clear till this

point current is really really simple uh always remember that current is actually a scalar quantity right so it's

a it is a scalar quantity although we we uh we do talk about its direction but when we say

when we talk about direction we really mean to talk about the direction between the direction in in in a circuit right

we really don't mean to say that okay if uh if the if we are talking about if the direction is going to change we are not

going to say that it becomes a different uh we are not going to treat it as a different physical quantity like we used

to do it in in uh velocities or uh or any other vector quantity also there are some re reasons behind it sometime most

of the time you're going to uh see that because current doesn't follow the vector addition but but let's it's not

it is not the absolutely correct answer for that but surely current is actually a scalar quantity

right and also please don't get into all of those tensor and tensor kinds of things uh that that's also absolutely

wrong uh explanation now let's move on let's talk about a vector quantity right so that we can really understand why

current is actually a scalar quantity let's discuss what do we really mean by current density it we can Define current

density as it is the current current per unit per unit Normal

area it is the current per unit Normal area now definition is very easy let's understand it by a diagram let's suppose

we have got a we have got a w a wire and this wire has got let's suppose this has got a

cross-sectional area of this has got a cross-sectional area of a right this is this area is a and let's

suppose I'm saying that the current flowing through this wire is actually I right now no matter what happens with

this with with the shape of this wire the current will always remain same this is the main part so let's suppose even

after some time let's suppose the wire turns out to be something like this or it moves something like

this at all points the current will be same that is 1 ampere only or or or sorry I ampere only I have not used any

number over here but it's going to remain the same why is that because current is rate of flow of charges the

number of charges which are passing through this point will be exactly equals to the uh number of charges

passing through this point per second and same for this point as well why we are saying that because we we are not

assuming that the I mean you you you reason me out why would the number of charges will change number of charges

will change only because either we going to increase the number of charges we are not doing that e either either someone

is going to take some charges out of the wire uh neither this is happening right so we are going to say that the current

Remains the Same now what we are saying is let's suppose initially I mean if you're going to

closely look at look at this uh uh area let's look at this area this is this has area a now hopefully till now everyone

of you know that yes sir area is actually a vector quantity and if area is actually a vector quantity we are

going to say something like sir this is actually the vector quantity that is a right so I'm going to say okay so that

means for for this particular part current density will become J1 I'm talking about J1 J1 will become current

I divided by per unit area that is a is that clear hopefully this is clear now let's talk about some another area

let's talk about let's not say that we are drawing the same type of uh area now let's say I've tilted this by an angle

by an angle Theta something like this right and that angle is let's suppose this angle

is is Theta by which actually I have tilted it so this angle is let's suppose this

is Theta all right now can you tell me this whole thing now this whole of this uh

surface has got now area a now if I'm going to ask you what is the current per unit Normal area now now

area is not a area is going to change why because now we are going to take the component of this area and that will

actually become this will actually become something like this and

this area will be a COS Theta hopefully you're getting it right absolutely I mean this is the area about through

which current is actually passing through which current is actually passing something like this is it clear

so now I'm going to actually Define Uh current density as J equals to J equals to and J is a vector

quantity current current upon area vector or I can write current as the dot product of two Vector

quantities and hence we can say that current is a scalar quantity right again let's not let's not waste a lot of time

on talking about vector and scalar over here uh but still this is a way better explanation than just saying that

current doesn't follow uh uh the vector law of vector addition all right also if you're going to talk about the magnitude

of uh J so magnitude of J can be written as I upon a COS Theta same

thing I mean now you won't find it surprising if I'll write that it is a vector

quantity the SI unit of this one is going to be ampere per meter square and I'm not going to waste time writing its

dimensional formula you are smart enough to write it down right but still the diagram is uh through this diagram you

can clearly understand what do we really mean by Uh current density and what is its relation with current right now

let's move on hopefully everything is clear now now what I want uh us to understand is when we are going to talk

about uh materials like when we are going to talk about uh different types of material we are going to categorize

materials into three types that you have been doing through uh since the junior classes that we have got conductors we

have got semiconductors and we have got insulators now we actually Define them in such a way that we talk about the

order of free electrons density all right so the order of free electrons density we have got density over here in

conductors is actually 10 the^ 28 per M Cub so this is actually number of electrons in uh number of electrons per

unit volume right whereas in semiconductor this drops to 10 the power 16 all right and uh for insulator it

would be way smaller than the semiconductor as well but still it's an important and that's what I was saying

if you're going to stick with me till the end of this lecture you going to get many such important notes and these

notes are it it is important for you to like for example as NTA might give you a match the column and they might throw

some data over there right obviously they'll never ask you this question in McQ I mean in normal your normal uh uh

McQ questions but they can ask anything in match the column right now let's solve some questions

Also let's solve some questions till what we have studied question says the current I in a conductor is expressed as

I equals to 3T s by the way this is a pyq this is a pyq question not from neat but from JW Mains AA if we are studying

for neat why are we talking about JW Mains two reasons I'm I'm repeatedly saying to my students who are who who

are studying uh who are studying from me that if you want to prepare really good for your neat

2025 along with neat previous year questions please also solve JW Mains previous year questions why is that

because first of all the difficulty level is is ABS is uh we can say it is approximately same also we are expecting

most of the faculties and uh we are expecting that neat 2025 must be slightly difficult than the

past year and which will which will be on our side I mean this is this is something which will be good for us

right so if that happens now it is good for us to solve some pyqs from JW Mains as well now let's see what this question

is talking about the current in a conductor is expressed as I = to 3T ² 3T ² + 4 T Cub all

right where I is in Amper T is in second the amount of electric charge that flows from a section of a conductor during

this time see we know that that this thing can be actually written as DQ by DT and if someone is asking you about DQ

I'm I'm going to just say that let's just integrate it and if I'm going to quickly integrate it can I quickly do it

if I'm going to quickly integrate it this will become 3T Cub by 3 + 4 t^ 4 by 4 and since they are talking about the

two limits I'm going to just put from 1 to two right three can be canceled out four can be canceled out and this will

become cube of 2 + 1 to ^ 4 minus then I have got cube of uh 1 and plus

I've got 1 to the power 4 right so definitely this thing can be canceled out by anything so this will this will

be nothing but 8 and this is uh minus one that is going to be your 7 kums so the answer for this question is going to

be 7 Kum now please understand that uh this is the same uh level that you can also expect in JW Ms sorry in NE 2025

right now quickly let's quickly understand oh here they have given us current we just integrated it this

becomes 3T Cub by 3 this would become 4 T the^ 4 by 4 now from lower limit 1 to two we have just put 2 ra to the^ 3 that

is 8 and 1 ra to the^ 4 then minus then lower limit hopefully everything is clear till this point now let's move on

to the next one also I'll I'll try to give you some homeworks as well please write down

those answers in the chat box right the next question says the electric current Through the Wire varies

with time as I equal to I plus beta T where I not is 20 aamp and beta is 3 amp per second the amount of charge flown

through this in 20 second is can I give give this question in homework can you do it similarly over here as well I'm

going to write charge as the integration of I KN I not is 20 so this becomes 20 + beta is actually 3 so it becomes

3T and from 0 to 20 right so they they have not talked about the lower limit so it will be zero so 0 to 20 right

whatever the answer is please write down in the chat box and by the way this is DT over here so this is going to be 20t

+ 3 t² by 2 that's it whatever it's going to be doesn't matter from 0 to 20 again this is from previous year JW

Mains right easy peasy questions friends now let's move on to the next one this question is saying now this is

not from previous year this question is saying current passing through a wire decreases linearly decreases linearly

basically means if someone is going to ask you to draw its graph this looks this will look something like this let's

say we have got current over here we have got time over here although we don't have to draw a graph for it just

for your sake just for the sake for understanding so they are saying that it linearly decreases from 20 to 0 so let's

suppose at tal to 0 it was 20 aamp and at T equals to what in 4 seconds this drops to zero they are saying that what

is the total charge the reason also for drawing me this diagram was that if you'll find out the area under the it

curve right so area under the it curve area under the

it Curve will give you the charge isn't it and why not because the thing is that charge is actually the integration of I

do DT so integration means area under the curve right so this would basically

means that if you have got the graph for uh the curve for charge and time the slope will give you the current very

easy peasy thing Doo all of these things you have been studying uh since mathematical tools so we are not talking

about anything new so the area of this is going to be that's also going to be the charge is

going to be half base time height so that's going to be 40 Kum everything is SI

unit good you tell me everything's fine till now uh I mean under 25 minutes we have

completed the basic part of this chap the basic part of the first portion now let's talk about that is something that

is called as drift velocity right because it's a one shot video I'm going to straight St away dive into what drift

velocity is obviously then going to explain each uh aspect of it see the drift velocity can be actually defined

as it is the average velocity average velocity of

electrons average velocity in electrons in presence of or I'll simply say average velocity of

electrons when electric field is applied when electric

field is applied right what are we talking about let's see the thing is let's

suppose that we have got a metal over here we have got a metallic surface over here

and let's talk about two cases the two cases are the first case is a when there is no electric

field when there is no electric field and if there is no electric field that means there is no potential difference

obviously we have got many electrons over here those free electrons right and both of these things are kept at room

temperature around 300 Kelvin both of them are kept at room

temperature now at at room temperature also these electrons have some velocity right and you can find out that velocity

by the way you can find out that velocity using your uh half M v² = to 3x2 KT by that formula that you

have learned in in ktg right for a for a single electron of course so uh you can find out that velocity and that velocity

is is is of really high order so over here these electrons are moving quite fast these electrons are moving actually

quite fast and in complete random Direction in complete random Direction well you can surely ask me why

are they moving the reason is because of thermal agitation they are kept at room temperature they have got certain energy

because of the energy they are gaining because of ther energy uh gaining from room temperature and

because there is no electric field they are not moving in in any particular direction they are not flowing in any

particular direction they are just drifting and they are uh they are colliding with with another uh electrons

or with another fixed positive ions right uh so this is what happening at uh at room temperature one more thing that

the the order of these uh the average speed of the of the these electron is going to be

of 10^ 5 m/s that means quite quite high right they are moving quite fast but what will happen if I'll apply some

electric field over here so let's suppose that I I give some positive potential to this side and some negative

potential to this side now let's suppose an electron was actually an electron was was initially

moving in this direction so the initial path was something like this obviously I'm not saying that it it would have

moved in a clearly in in a very straight path it would have collided with any other particle but at this point the

initial velocity was in this direction right now what's going to happen because and because we have applied an electric

field and by the way electric field is in this direction from positive to negative we have applied an electric

field what's going to happen is that a force will act so this is the B part where electric where we have applied an

electric field so a force will uh a force will get applied on an electron and that force is going to

be that force will be actually minus E * e that means the charge of an electron times the electric field that we have

applied further we can rewrite that so that means it will also have an acceleration nothing so difficult about

it right and if it has got acceleration by the way in which direction the force

will act so on on electron the force will act on in this direction and by the way on each and every electron the force

will act on this Direction only so this is the direction of force right so it was moving it was

about to move in this direction but because of this force it will start to actually move in this direction so this

is going to be the direction of the direction of electron because of electric field now obviously it will not

move because it will not collide with any other particle after some time and so so the similar thing will happen with

every other electron so every other electron which was let's suppose an electron was moving in in in uh straight

direction from the very start so it will accelerate and it will get accelerated and it will strike with some another

particle so in a way every electron will start to drift in a particular direction right so it's not a very uh a very uh

harmonic motion or a very uh what we can say a streamline motion that that we see like like for example if this pen is

moving like this that's not how electrons moves right electrons moves something like this that they move then

they Collide and and then uh they transfer their energy and then some another electrons obviously all the

other electrons are moving in in in a particular direction right so I mean if I'm going to apply some basic kinematics

over here the basic kinematics over here let's suppose I'm applying a basic kinematics for one of the electron so

I'm going going to say that let's suppose its initial velocity was U1 that means when when uh there was no electric

field it experiences an acceleration of a and it collides after a Time T1 with any other particle

right so the thing is the the speed with which the velocity with which it gets collided is written by V1 similarly I

can write it for many other particles so V2 can be written as U2 plus acceleration is going to be same

and T2 now please tell me what is T2 T2 is not the mean free mean uh time T2 is the time for which the second electron

traveled and T2 was the time after which second electron got collided so there are like number of electrons similar to

this so we can rewrite it for like n number of particles so straight away let's write for nth particle so it's

going to be written as un n + a n time TN now let's do a very simple mathematical operation and that is let's

add them and take a take average of it right so if I'm going to add all of these

things and I'm going to also take an average of it so that's what the drift velocity is average velocity of all the

electrons when electric field is applied so that that that is what I'm going to write

V1 + V2 and so on VN all divided by the total number of

particles that is n equals to U1 + U2 + u

n and whole divided by n plus acceleration is common right and

obviously I don't have to write this a n over here acceleration is same so I'll take a as

common and I'll write T1 plus T2 and so on plus TN whole to the power n hopefully everything is clear till

this point please have a look after this let me write it somewhere else let me write it over here on the new page I'm

going to just say that if this is the case can I write V1 + vs2 + V3 as drift velocity

VD equals to acceleration can be written as just minus E E by m and T1 + T2 + T3 the average of all the time can be now

written as relaxation time tow so you must have seen this formula so that's why I've directly written

it so over here tow is going to be called as the relaxation relaxation time that is the mean mean

time between two Collision or average average time

between two successive Collision all right hopefully everything

is clear now from this you you can have actually like many questions uh there can be many questions uh developed from

this particular formula that is VD is equal to minus E to by m right so now the first thing that we are going to do

after this is after drift velocity we are going to actually derive uh we are going to actually State ohms law then

we'll try to prove ohms law using the using all of all of this formula right but first of all let's have a look what

will happen if I increase the temperature right so if I'll increase the

temperature if I increase the temperature uh frequency of collision will

increase so temperature is actually directly proportional to frequency of collision and IF frequency of collision

will increase this this would mean that tow will decrease is that clear it's quite logical if more number

of collisions taking place in a given time that means the average time for Collision is going down so so if

temperature increases star actually decreases so this is a very important relation please remember it after

this after this my dear friends we are going to say also please note this thing that VD is actually quite less this is

actually really small right really small uh if you remember when there was no electric

field the average velocity was of the order of 10 to the^ 5 this is going to be in 10 the minus 3 - 4 something like

that now next let's move on let's move on and let's talk about relation between current and current

density now the relation comes out to be relation between these things comes out to be see current is nothing but total

charge flown divided by total time T now let's just suppose that we have got a

conductor let's suppose we have got a conductor something like this having length L area of cross-section

a so this has area a length L right and there's also one more thing that is small n

which is actually number of electrons per M Cube number of electrons per meter cube

so DQ will be actually written as the total charge so what is the total charge so one electron has got charge

e and how many charges how many electrons are there so in 1 M Cube there is n number of charges and how many how

much of volume is there so the volume is actually a into L divided by what is the DT so D delta T is

basically the time taken by an electron so let's just say because we have already defined what

drift velocity is I'm going to just take an electron I'm going to say it drift velocity is VD so the time time is going

to be just L by VD so L can gets canceled out so the relation comes out to be n e a v

d so very important relation please remember it NE e a VD all right where n is the number of

electrons per M Cub now we have got two things we have got two formulas one is drift velocity can be written as e by

the way I'm just writing the magnitude e to by m another formula is I equal to NE e a

VD so can I put instead of VD can I put e e t by m so I would get I equals to

n² A to by m and and instead of electric

field my dear friends electric field would be if electron is moving in this direction this would be positive

potential this would be negative potential so the potential difference between these two points can be actually

written as it can be actually written as e into L isn't it right because I'm assuming

that electric field is uniform so e into l so that means e can be written as V by L so this thing can be written as V by

now please understand we can rearrange all of this thing and we can rewrite this thing as V equal to M into L

divided n e s to into a have a look at it have a close look at it and see

that's what I was saying I know that this is a one short lecture we we we can actually skip derivations but we'll

we'll not call this as a dation why because this is just putting this is just plugging the value of VD into I

then find plugging the value of e in terms of v and that's it right so V is the potential difference and all I can

see obviously I I should write current also so current over here now if you if you'll closely see

for a given wire for a given wire what I'll say is

I'll write it over here for a given

wire m l n

e to and a are all constant isn't it I mean if I've got this wire I've

already taken this wire this its length is not going to change area is not going to change n is the number of electrons

per Meer Cube it is a property of the material that is not going to change right tow is the relaxation time now you

can say that a tow can change right so that's why if you if you remember even from even in grade 10th we used to say

under same physical condition so when we are talking about tow right so this is we must also state that this happens at

same temperature so there's a caveat to it there's the temperature should be same right so that's why we

say that under same temperature under same physical condition

under constant physical condition we we'll say that potential

difference is directly proportional to current because everything else is a constant and now the proportionality

constant over here is actually nothing but R so in this case resistance will be

actually equals to ml divided by n e s n e s to * a so this is the value of resistance have a

look almost derived it isn't it hopefully everything's clear till this

point ml n e s to time a what is resistance resistance is the property of a material to offer hindrance to the

flow of current right AA also we know that when we'll talk about resistance resistance does depends

upon it directly depends upon the length inversely depends upon the area through this we can say that resistance

can be written as something that is called as resistivity time length into area so resistivity is nothing but

resistivity how how you are going to Define resistivity see resistivity is the resistance of the material having

unit length and unit cross-sectional area so again equating the formula resistivity will come out to be row will

come out to be M upon n² * St all right

so now let's again come back if you are going to say what is what will happen if you if you are going

to actually increase the temperature so we are going to actually divide it into two parts if you're going to talk about

conductors if you're are going to talk about the conductors for a conductor if you're

going to increase temperature if you're going to increase temperature that will actually decrease resist

decrease relaxation time that we have already talked about right so if you're going to increase temperature that will

decrease decrease uh Tow and that will increase resistivity right so to is also also I'm going to write

also to is inversely proportional to resistivity so this means that that is resistivity directly depends upon

temperature for a conductor for all of those metals that you have talked about so in layman terms

if you're going to increase the temperature a good conductor will move towards becoming a bad conductor its

resistivity will increase so will its resistance is that clear hopefully everything is clear so that was about uh

that was about conductors in semiconductors something different will happen see I'm not saying that in

semiconductors this is not true still this statement will hold to still in semiconductor temperature is

actually inversely proportional to relaxation time but along with this Factor there is also one more factor

that is with increase in temperature the number of free electrons per unit volume increases now please don't get confused

that sir just now you said that n is not going to change I was talking about conductors in semiconductors n is well n

is the number of free electrons so in semiconductor what happens is I'm just I'm just briefly explaining it to you

you'll you'll learn it uh in detail in semiconductors Band Theory what happens in semiconductor is when you're going to

increase the temperature more number of electrons will be able to fall will will be able

to actually jump the energy gap and they will they will be able to take part in the conduction right so the number of

electrons will change so because of this and and by the way this Factor actually uh overpowers the

other right so we we this Factor overpowers the other so we are going to say okay so two things is happening with

increas in temperature to is actually decreasing and N is increasing is that clear so if in the denominator Ator n is

increasing and this factor is overpowering the another one so we are going to say okay we are we are going to

say that okay the denominator actually increases so that means the resistivity will decrease so in short we are going

to say that with increase in temperature resistivity will decrease so simply going to write it something like

this resistivity decreases with increase in temperature for a semiconductor see in one page I have explained you

many things now this is going to be really really important for you if you want to uh I mean you you're going to

you're going to see many questions from this one single page right and by the way this is nothing but your oh SL and

pro of everything is been done now let's move on and let's move to a one more uh one

more note over here a very simple thing I've already written it this is actually if I've got a this is something that is

called as non-uniform cross-section non-uniform a wire which has got non-uniform area as we can say that as

we can see that A2 is greater than A1 so if A2 is greater than A1 what we'll say by we'll say that drift velocity at J1

will be greater at J2 drift velocity will be greater than at this point also sorry drift velocity and also current

density will be greater at at A1 why we are talking about drift velocity by the way

everyone knows obviously sir if area is less current density will be more because current density is current per

unit Normal area if you're going to decrease the area current density will increase but what is happening with

current D with drift velocity see whenever you are going to see some questions like this now uh it would be

even better if I'll say that a constant current is flowing through it this is actually

important if constant current is Flowing so I'll write it over here that I is constant so if I'm going to say

something like current is constant I'm going to say that uh current is written as

Nea Nea VD now because current is constant n is no matter it will remain constant that means the product of a and

VD is constant this means that VD is also inversely dependent on area but again we have got a condition

for it current should be constant current is not going to be constant then you'll use the formula of e to by m this

is a very important thing okay so this is for constant current if someone is going to talk about under uh for

constant potential difference for constant potential difference please

use something like VD equals to E T by

m so that means it is independent of area right so in this particular case VD is is independent of area as you can

see hopefully everything is clear till this point now let's move on and let's see

some more curves first one is linear VI curve that we often see right now see uh even if at

at really high temperatures now like for example this is at this is at low potential but at really high voltages

let's say this is I this is V something like this can also happen something like this thing can

also happen right so this is a nonlinear Behavior also you can have nonlinear behavior of of

semiconductors so in case for semiconductors you'll have something like let's say

this is this is actually now over here I'll write current over here it's in milliampere you'll you'll learn all of

these thing in detail in semiconductor this is microampere and this is how it's going to

be all right that part is forward by this is L this is reverse bi by the way I'm going to talk about something like

this even at these points ohms law is applicable all at at individual Point all right at individual points OHS law

is still applicable so don't don't think like okay OHS law is not following over here oh law this is omic devices which

follow OHS law for a particular range this is not omic devices because V is not directly proportional to I but at

these individual points you can still find out the value of resistance because you can find out the value of R Now by

taking the slope so now let's move on to something that is known as temperature dependency of resistance we have already

seen yes sir if you're going to increase the temperature see what what till now what we have seen we have seen that if

you're going to actually increase the temperature resistance will increase for conductors for conductors that means all

the metals if you're going to increase the temperature resistance will decrease for

all the semiconductors right this is what we we have we have studied till

now now the thing is let's just write a mathematical equations for it so that we can solve some problems now there is no

requirement of derivation over here the thing is uh I mean you you have seen this formula many times before also the

formula is look it looks something like this row equals to row not times a by the way first we can rewrite it for

resistance resistance equals to R * 1 + Alpha into delta T or row equal to

row * 1 + Alpha into delta T so these are the two formulas row not is the resistivity

at initial temperature at initial temperature let's say that's T

T1 this is at T2 that would mean delta T is nothing

but T2 minus T1 and the unit of alpha is going to be what's going to be the unit of alpha if

you'll closely see I can rewrite this thing as Al row minus row is that clear row minus row divided by row * delt T is

equals to Alpha to this is the formula for Alpha I have done nothing but I

multiplied R not with this bracket and I've written Alpha is something like this now if you'll closely see this is

actually nothing but ohm meter this is oh meter so Alpha's unit will come out to

be per de Celsius or or per Kelvin and you don't have to worry about units over here right because Alpha uh I mean

Kelvin and Celsius are linear scales so uh you you'll not face any trouble so you don't have to worry about

conversions okay now let's move on let's look at some of the questions over here before that also have a look at what

happens with with change in temperature this is a copper copper basically means we are talking about conductors so with

for conductors if you're going to increase the temperature this is some order of like 50

Kelvin then 100 Kelvin and so on at 0 Kelvin obviously resistivity will be zero but as you're going to

increase by the way see I'm also explaining you the or order of resistivity so order of resistivity for

a metal like copper is around 10^ minus 8 ohm meter when you're going to talk about nichrome which is a alloy it goes

to micro ohm meter right and can you please see over here that with increase in

temperature it's showing a very uh what we can say uh a positive relation with change in temperature as temperature is

increasing resistivity is also increasing what we are seeing over here is with increase in temperature

resistivity is increasing but that increase is actually quite small so if you want to use a if you

want to use a particular material which does doesn't show a very uh a very close uh what we can say a very sensitive

relation with temperature you should use nichrome because with increase in temperature Nikon's resistivity will not

not increase that much this is what we are going to call as semiconductor a this will actually also explain one

thing if you have talked about this Alpha what does it tells us this tells us that for

conductors and for all the metals Alpha is going to be positive because if you are increasing

temperature delta T is positive always we are increasing it that's how we call it delta T is positive and row is

greater than row not that means Alpha will be positive so for conductors Alpha will be positive but for

semiconductors we say that if temperature increases resistivity decreases so temperature increases delta

T is positive but row row is less than row not that means Alpha will be negative so for semiconductors Alpha

will be negative so again you have got two more points and all of these are very very

important done hopefully everything is clear till this point now let's move on and let's have a look at some

questions now I think it's a good time you should pause this video Sol take a look solve it by yourself and then

unpause it right question says a current I flows through a uniform wire of diameter D when the electron drift

velocity is V the same current will flow now can you please check they are talking about that the same current will

flow through a wire of diameter D by2 that means if they have said that the same current is flowing and they want us

to find out drift velocity at another Point use the equation of I I equals to NE a v

d right so because same current is Flowing so so we are going to Simply write NE e

a uh by the way uh D with area it means NE e Pi d s times drift velocity is

V right drift velocity is V and this will be also equals to NE E A so Pi D ² by4 because now it becomes D by2 times

VD Dash new drift velocity NE e Pi can be cancelled out d square can be cancelled out hopefully everything is

clear right so D VD Dash will become 4 V so D is going to be the correct answer

have a look quickly let's move hopefully everything is clear moving on to the next

one have a look this is for you this is for homework very easy non-uniform drift speed just now we have did we have did

it right so it is quite easy for for us to Now understand because drift velocity also depends inversely upon

area so that means VP will be greater than VQ C let's

move next question is saying the resistance of a platinum wire the resistance of a platinum wire Platinum

resistance thermometer at the ice Point all right so what do you mean by Ice point so ice point is nothing but 0°

C and steam Point steam point is 100° C steam point is 100° C are 8 ohm and 10 ohm so that means

resistance at 0° C is 8 ohm and resistance at 10° cius is sorry uh at 100° cus

is is 10 ohm and we have to find it at 400° C so what I'll suggest you to do it

always for for questions like this you can find out what Alpha is now easily take the reference as 0° C that will

help you so I'll simply say I'll simply use this equation that R is equal R into 1 + Alpha into delta

T so I'm going to write R equals to so I'm going to first take these two things so 10 = to 8 * 1 + Alpha into 2 what

I've have done I've taken uh 0° celius to be be my initial temperature and final temperature as 100° Celsius so

sorry final temperature is 100° cus so this is going to be 100 change in temperature so final temperature final

resistance is 10 initial resistance is 8 1 + Alpha that I need to find out times 100 right times 100 is the change in

temperature from this I can find out what Alpha is going to be so this is actually it's going to be

uh see 10 minus 10 - 8 that is 2 equals to Alpha into 800 so Alpha will

come out to be 1 upon 400 per de celius you can rewrite this thing as something like this done so we have got

what Alpha is now let's apply now let's take these two and let's write resistance at 400°

cius is equals to again I'm taking the reference at resist reference at temperature 0° cius that that that's why

I have marked it down so this is will be 8 1 + Alpha times change in temperature now is

is 400 so this gets cancelled out and this will be actually this will be 2 this

will be 16 so the answer should be 16 ohm option b have a look hopefully you have paused it please try it by yourself

anyway I'm going to do it then you can unpause and you can check your answer please quickly

see now moving on to the next question please have a look read it the question says two wires A and B

are made up of the same material same material would mean that they have got same resistivity

all right and have same mass all right so we are going to use this fact also so they have got same

mass wire a has radius 2 mm wire B has radius 4 mm the resistance of wire B is 2 ohm the resistance of wire a is

question is quite simple why they are saying that they have got same mass the reason is that see we know that mass can

be actually written as density is Mass upon volume so Mass can be written as

density into volume right if they are saying that their mass

is same their density is also going to be same that means their volume is same please understand that volume of a will

be actually equals to volume of B because they have got same mass they are made up of same material so same

material means same resistivity and density right so if volume is same we are going to say that area that is

PK R1 s * L1 = PK R2 s into L2 Pi can get cancelled out after this they are saying that uh they are saying that

radius is 2 mm so this is this is actually 2 mm I'm just going to just simply write two not going to change

unit what about length are they talking anything about length two wires A and B made up of same material having same

asass wire radius is this radius is this so L1 equals to R2 is 4 mm and this is

L2 so this would basically mean I can cancel out one of the four with this so that means L1 is actually equals to four

* of L2 all right and they are also saying resistance of B is actually 2 ohm so

resistance of B is actually equals to 2 ohm this would mean row into l so L is L2 divided by A2 so A2 is going to be Pi

R2 s right so this is actually equals to two so uh I mean if we are going to find

out R A that will be row instead of L1 can I write four * of L2 right and if you'll also closely see

R1 is also equals to half of R2 right so R2 can be written as double of R1 so instead of R1 can I also write it as

half of R2 so this would mean Pi R2 2 * 4 so this would mean 16 * of

row a L2 / PK R2 s so this would mean 16 * 16 * 2 that is 32 so 32 should be your answer for this particular case 32

should be your answer you can do it I mean more quickly it's up to you right so now let's move on to the next

question before moving on let me give you one more uh uh note over here you might have also seen questions like

stretching of the wire right whenever whenever a question comes in which they talk about stretching of

wire so stretching stretching basically means that the volume will remain constant volume will remain constant

right so if volume will remain constant and they are saying that it has been stretched to n times of its original

length so let's suppose that initially the length was L and now we have stretched it now the length becomes n

times of original length so the resistance will become n square of the original resistance this is something

which you should be able to understand it we can derive it definitely because see uh if uh we are saying that A1 * L1

is actually equals to A2 * L2 so let's say initial area is a initial length is L and now they are

saying that length becomes n times so this would become NL so A2 would become A2 would become

a by n and now the new resistance will become row L which is now n * divided by new area which is a by n so that's how

we are going to get it becomes n square right I've def I've derived it for you but you must remember it to save time

similarly if they are going to talk about that if it is if it is stretched in such a way that the radius becomes 1

upon n times now the radius will now the resistance will become n to the^ 4 * are this is really really important if

you're going to derive these things in neat it's going to cost you some time so it is it is recommended that please just

remember these things all right after this my dear friends we have got one more topic which is related with drift

velocity and electric field that is called as Mobility a very small topic Mobility is actually defined

as the drift velocity per unit electric field and this is just we are going to talk

about its magnitudes it is drift velocity per unit electric field so if you'll substitute

the value of drift velocity it would be e e to by m and divided by E so e can get canceled out so this will come out

to be e to by m all right so please understand that this will just talk about that drift velocity

depends upon the charge which I have just written as e and depends upon the mass so if you're going to talk about an

example if you're going to talk about a proton and an electron right so we know that mass of proton is greater than the

mass of electron so because of this and they both have same charges because of this mobility of electron will be

greater than that of mobility of proton that's it right a simple example nothing to worry about you can

also Define its unit very easily now let's come back let's come back to some important topic which is actually

battery and EMF right so we must have seen uh a battery something like this let's suppose that we have got a battery

over here and it is connected with some load res resistance this this

thing is actually known as load resistance the main electrical Appliance for which we are using our

battery and also over here we have got some internal resistance so let's say the EMF of the

battery is e that's what we are going to Define right now also and this is the load

resistance by the way this battery or or the uh batter is actually comb of cells if you're going to talk about a cell

let's let's look at an example of a cell let's suppose that you have got an electrolytic cell over

here a basic electrolytic cell you have got two electrodes something like

this and then external circuit attached with this and let's say this is positive electrode

this is negative electrode right that is uh anode and cathode and current flows outside from the circuit something like

this and inside the circuit current flows from the negative from the uh from the cathode to anode right now the thing

is if we are going to say if you're going to Define what EMF is so we are going to say that em EMF is

basically the potential difference the potential difference between the between

the between the terminals terminals of the cell terminals of the

cell this is one of the definition another definition can be also it is the potential difference

across the cell across the cell in an open circuit in an open

circuit you can also Define it as the energy energy it gives to to a to a unit charge to move through the complete

circuit and through the cell right but these two definitions are going to do the job now the thing is let's suppose

that current total current I is flowing in this circuit right and see from this particular topic

now you must understand the concepts of potential drop potential difference and potential also I'm going to use this

concept the main the main uh thing that we are going to use this battery and EMF is to understand what do we really mean

by potential potential difference and potential drop all of those things right now please see

here if current is Flowing from the battery first of all this thing is actually known as when current comes out

of the positive terminal of the battery and goes inside the uh negative terminal this thing is actually known as

discharging of battery next thing is let's suppose that we are we are talking about the

potential difference between these two electrodes is let's say 100 volt so 100 volt becomes the EMF of the

battery right and now let's say that you you you ask me sir okay does this means if I'm

going to use an voltmeter something like this will this voltmeter give me a reading of 100 volt or a little less

than that so the answer is going to be this volt meter will not give you a reading of 100 Vol it will give you a

reading a little less than that the reason is out of this 100 volt there is also a

potential drop at R now first let's understand what do we mean by potential drop right and even before that let's

understand why do we actually I mean what does electrical appliances use if you have got if you have got a

resistance something like this if you have got a resistance something like

this and current I is flowing in this direction and let's say current is 2 Amp and the resistance is of 5 ohm let's

just take an example all right let's take an example now what does this

mean this basically means let's say this is actually 2

ere and this is five 5 ohm sorry 5 ohm first of all as soon as you see the direction of the current you know that

okay sir this is the low potential this is the high potential all the electrical appliances

which means all the resistances do not use current they use potential difference right so there's going to be

a potential drop when you are going to move from point let's name this as Point P to point Q there is going to be a

potential drop why because this device of resistance 5 ohm will consume a potential what's going to be that

potential that potential will be found out using V = to 2 into 5 that is 10 Vol

that means these two points have a potential difference of 10 volt which means that VP minus VQ is

actually equals to 10 now I have no interest in finding out what is the potential of Point P what is

the potential of Point Q I know that potential of potential difference between these two points is 10 volt now

I can imagine anything I can say that let's suppose the potential of this point is actually 200 volt so this would

mean the potential of this one is 190 volt that's it I really don't know what this

individual potential is are you getting so I can assume anything to solve my question or what what I can usually what