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00:00so hello friends now third part in the lecture series of electromagnetic induction in which i
00:12plan to do these four topics energy conservation relation between induced charge and change in flux
00:20eddy current and ac generator then then thereafter in fourth part i am planning to finish
00:28emi so let's proceed with energy conservation that means here we will be proving how law of
00:40conservation is relevant in electromagnetic induction
00:46same diagram i'm repeating from emotional emf here previously while talking about emotional emf
01:03we didn't consider forces but now magnetic force due to straight conductor f is equal to ilb we are to
01:13consider how let's see here induced current induced current i in the circuit i is equal to e by r here
01:28this e is induced and r is the resistance of the rod pq then e is equal to b l v upon r so this was the
01:42induced current so as current flows through the arm pq it will experience a force due to the magnetic field
01:58this f is equal to i l b and i is e by r it implies that f is equal to b square l square v upon
02:12r r and in the diagram we can see speed is in the leftward direction whereas magnetic force will be
02:25in the right direction let's check from flaming's left hand rule no force will be also in the left
02:33direction direction current into the field so that's why that means magnetic force is in the rightward
02:41direction on the rod
02:46so i must specify this point direction of this force will be towards right opposite to that of velocity
03:00from fleming's left hand rule remember while finding out the direction of this magnetic force uh induced current
03:11was not in the picture that's why we didn't apply fleming's right hand rule instead uh we have
03:21uh applying fleming's left hand rule for this purpose because this involves completely magnetic effect
03:29of current to to keep this rod to keep this rod moving against against rightward magnetic force equal and
03:41unlike force is needed
03:48to move this rod with constant velocity and for this purpose definitely power is needed
03:56and that power thing we are to discuss over here p is f v and f will be this p square l square
04:09v upon r therefore p is b square l square v square by r the power spent is dissipated
04:23as joule's heat that's why heading name is law of conservation of uh energy the power spent is dissipated same power
04:34whatever power we have put the power spent is dissipated as joules heat and is given by
04:43i square r and i we have blv upon r this is equation number two therefore from one and two the mechanical energy
04:58required to move the rod pq is converted to electrical energy
05:09energy and then thermal energy hence conservation of energy is completely relevant now next topic
05:24relation between induced charge and change in flux here we have from basic fundamental of this chapter
05:32the mod of e is equal to del phi b upon del t that means d phi by dt but on the other hand it is i r i could be written as
05:50the del u by del t and this can be cancelled out either this formula or simply it could be written
06:02or simply q is phi b upon r so same formula is relevant in both the formats in del format also and in
06:16full complete format also and here comes ad current has come up in which i plan to write a lot so what is ad
06:30current so there are currents induced in the bulk pieces of conductor when the amount of magnetic flux
06:45linked with the conductor changes how they work their flow patterns ad means swirling waves cyclonic waves
06:55circular waves it is special type of induced current generated in bulk piece of conductor earlier any type
07:03of induced current we had in our discussion we had always in the form of current in the conductor
07:11that is linear conductor that is linear conductor but now we'll have proper wavy current in the form of circular waves
07:21in solid bulk piece of conductor now we don't have current carrying wire type conductor we have full solid
07:32energy however however the flow pattern resemble twirling ades in water so that is why they are ad current
07:52disadvantages of undesirable ad currents are undesirable because they normally harm
08:02our circuits how ad currents are undesirable as they heat up the core and dissipate electrical energy
08:14in the form of heat this way we are able to create the picture in our mind towards ad current that it is
08:21not useful for us but interestingly there are some advantages they are having some practical applications
08:36in our everyday life we are going to discuss that small list also but before that methods of reducing ad
08:45current but after uh going through this uh paragraph uh what we are thinking that it's since it is
08:53disadvantageous to our everyday life so let's try to reduce these factors which are causing disadvantages so
09:05what are the methods of reducing number one holes or slits made in the plate reduces the area
09:17available for ad currents to flow if in the core some holes and slits are made whatever magnitude of ad
09:29current is generated some currents will be passing across the holes hence reducing number two
09:38laminations of a metal are used to make a hole the laminations are separated by an insulating
09:50layer layer like lacquer lacquer lacquer is a varnish type paint type thing which obstruct induction the plane of
10:01the laminations must be parallel to the magnetic so that they cut across ad current parts this reduces
10:15the strength of the strength of ad currents and hence the loss of energy the loss of energy as heat p is i
10:27spare r this way we have finished another subheading methods of reducing eddy currents and after that last
10:37subheading of eddy current is advantages of the uses of eddy currents pain of the elevation must be parallel
10:48so that they cut across the eddy current parts this reduces the strength of eddy currents and hence the loss of
10:56energy advantages of the uses magnetic braking in trains very important number one in trains
11:08strong electromagnets are situated above the rails when activated they produce eddy currents they produce
11:18eddy currents which oppose the motion of the train as there is no mechanical contact break breaking is
11:25smooth number two electromagnetic damping certain galvanometers have a fixed core made of
11:34non-magnetic metallic material when the coil oscillates the eddy currents generated in the coil opposes
11:43oppose its motion and quickly bring the coil to rest so these are the advantages
11:49number three induction furnace they are used to produce high temperature to make alloys by melting the
11:57constituent metals a high frequency ac is passed through a coil which surrounds the metal to be melted
12:07the eddy currents induced in the metals produce high temperature sufficient to melt it and number four
12:17electric power meters the shiny metal disc in the electric power meter rotates due to eddy currents
12:25electric currents electric currents are induced in the disk by magnetic fields produced by sinusoidally
12:31varying currents in a coil so whatever electric electricity bill is generated through electric power meters
12:39it is run with the help of eddy currents and last point in speedometer of automobiles and energy meters
12:53and yes last but not least thanks for reminding me every day i'm talking about this in front of all the students
13:06induction book so these are very important applications in everyday life
13:13if you do eddy currents only we are we take these advantages here comes ac generator all of us let me remind
13:26we are in a habit to study this topic from lower classes and it has been said again and again it is repeated again again
13:37that it is a device through which mechanical energy is transformed into electrical energy so it is the same discussion
13:52firstly i would like to share one diagram it converts mechanical energy to electrical energy
14:04okay and principle of working so before discussing into principle of working
14:20this is the diagram now we'll try to understand what its construction is basically let me give you some basic idea
14:46this is the rotor this central dotted line which is known as axle and it has to be rotated mechanically that's why
14:57from our side in the form of input mechanical energy is given to this system and because of this whole arrangement
15:08induced current induced current is being generated in this rectangular loop and hence electrical energy is
15:18generated that means mechanical energy is transformed into electrical energy but how let's see this is
15:26north pole and south pole strong pole pieces which is causing strong magnetic field
15:32in this direction in this direction and and and in which because of this axle rotation this rectangular coil
15:44rectangular coil is being rotated like this and because of this kind of rotation change in magnetic flux is
15:54happening across this coil and hence induced current is generated and
16:01that induced current direction is determined by following fleming's right hand rule how where my cursor is located right now
16:13at that line suppose magnetic field is like this
16:18this movement because this branch is going down in the process of rotating like this so thumb is pointing
16:28towards towards downward direction and index finger finger is suggesting the direction of magnetic field and then
16:38hence middle middle finger is suggesting the direction of induced current that means like this like this like this like this
16:49and and here this is slip rings arrangement and these are these two are slip rings and this and this are carbon brushes
17:01and here this way current after current appearance it will start going like this like this like this like this and here
17:13across these two and some load will be connected through which it would be transferred in argue forward direction and
17:22and after this this way this way going like this and see one hidden line behind these slip ring arrangement and this way
17:35as sugar k and this way meanwhile this loop will be moving further and completing half cycle after this half cycle this
17:47end end will come over here now again fleming's right hand rule this time this kind of current would be reaching
17:58here as sugar k would be reaching here and this way this time another that means in second half cycle current will be
18:08going this way that means after every half time cycle direction keep on
18:16reversing that means polarity will keep on changing all the time and hence it is ac current alternating current
18:26this type of induced current is known as alternating current which we'll be studying further in detail
18:34mathematically in chapter alternating current here this was the working in simple now some mathematical analysis
18:45is left very few minutes of discussions is left
18:52firstly few lines of construction magnetic field the axis of rotation
18:59of the coil connected external circuit with the help of slip rings and
19:07and brushes which is in the diagram axle strong magnetic field here is caused due to north and south
19:19forward the axis of rotation of the coil is connected to external circuit with the help of slip rings and
19:26and brushes slip rings these two are slip rings and these two are carbon brushes here comes working working
19:37i'll try to cut short very briefly i'm to explain basically
19:44i intend to write the expression for peak value of induced emf for that purpose i need to write the
19:56the expression few lines of mathematical discussion the flux through the loop phi is equal to b a cross theta
20:07where theta is omega d as s is equal to b t as the coil rotates theta hence the flux through the coil
20:20coil changes which sets up which sets up which sets up and induced emf in the coil e is equal to e naught sine
20:33omega t to be the instantaneous emf induced emf in the coil here theta is equal to omega t which is
20:46the angular velocity of the coil let the coil rotate constant angular velocity omega the flux that means
21:00magnetic flux at any time t would be e is minus d phi b upon dt that means rate of change of flux with respect
21:14time obviously n would be the number of turns e is equal to minus d dt of b a cos omega t e is minus n b a d dt of cos omega t
21:35it implies that e is equal to cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos cos
22:05and comparing this equation peak value of induced emf e naught is nba omega since value of sine
22:20function varies between plus one and minus one the polarity of the emf also varies hence direction
22:35of current also varies periodically with time therefore current is called alternating current
22:47previously just few minutes back we had had a discussion from that discussion we could learn
22:56through the instrument through the device how current is alternating but now here from this
23:04paragraph we are able to understand convince ourselves mathematically how the current is
23:13changing its polarity between the sine function from plus one to minus one minus one to plus one
23:21and so on so on hence the current is alternating this was the sine function and already we had been
23:32knowing from long time that sine function and cost function both lies between plus one and minus one
23:41lastly i am to include one more diagram and lastly we could see in this diagram also this was initial
23:53position of that rectangular coil then 90 degree means quarter rotation after this plane completely is in
24:03horizontal position then in the process of rotating now half cycle it is done then three quarter and
24:12then four quarter and one more thing here wherever i have used theta theta is the angle between b vector and area vector
24:23so now i guess nothing is left and this way i have completed third part of the electromagnetic induction
24:36so i hope you must have enjoyed this whole presentation and lecture now
24:42you keep enjoy our physics and bye see you take care until next video
