🟡If you like my work & effort then please help me complete 100 Followers🟡
Hi, myself Sufal Kumar, Physics Faculty. Dear friends, viewers & students, my channel is about Physics Education. I am to concentrate mainly on JEE, NEET, CBSE & ISC in near future. #sufalphysicsforum #jee #neet #physics #cbse #iitjee #igcse #cbse12thexam Pls like, share & subscribe, if you like my educational video....
00:00now important graphs related to EMI here we'll have around five six graphs just very normal
00:10first magnetic flux versus current phi versus I phi is directly proportional to I it implies
00:23that phi is equal to Li or phi is equal to Mi now here comes second graph induced EMF versus di by dt by dt there
00:45could be two possibilities or my first is equal to minus L di by dt because of this negative sign
00:56fourth quadrant negative and direct proportionality hence straight line incline now another possibilities
01:07again induced EMF this time straight line parallel to x-axis that means di by dt access when current
01:19is increasing at constant rate that means same e versus di by dt will have two graphs when it is
01:29given current increases at constant rate then parallel to x-axis otherwise in general
01:37then here comes third magnetic energy stored versus current this would be exponential graph you know
01:46why I'm going to give you the reason because u is equal to half Li naught square it implies that u is
01:59proportional to i naught square that's why graph would be like this current magnetic energy stored hence the
02:11topic is over now coefficient of coupling
02:16the coefficient of coupling of two coils two coils gives a measure of the manner in which
02:39the two coils coupled together the two coils coupled together k is m upon root under L1 and L2 where 0
02:51k that means this k always lies between 0 and 1 such that such that L1 and L2 are self inductances of the two coils
03:07the two coils and m is the two coils and m is the mutual inductance mutual inductance L1 and L2 M when the coupling is perfect
03:19m is maximum and k is equal to 1 but when there is no coupling m is equal to 0 and it implies that k is also equal to 0
03:33and then I think last would be combination of inductors so here comes combination of inductors this is series combination and in this series also we would be discussing three formats first discussions involving equivalent L in series and then thereafter in series only we would have when both the
04:03inductor coils are in the inductor coils are in the inductor coils are having same direction of current but another series would be when both the currents are in opposite direction so let's consider one by one
04:17firstly in general series x y i in series current remains same this is L1 L2 L3 E1 E2 E3 and suppose this combination is replaced by a single one x y e l a this is L equivalent in series now E is equal to sorry e
04:19series x y i in series current remains same this is l1 l2 l3 e1 e2 e3 and suppose this
04:32combination is replaced by a single one x y e l a this is l equivalent in series now
04:44e is equal to sorry e1 is equal to because in series potential varies so e1 is equal to l1 t i by t t e2
04:56l2 now we will be substituting all these three values of e1 e2 e3 in this
05:04y because vxy is equal to from the diagram e is equal to it implies that e is equal to e1 plus e2
05:20plus e3 m t i by t equal to and hence in general this was series but now series in general but
05:34when two inductor coils inductances l1 and l2 and mutual inductance m here also
05:48we'll have two situations when both the inductor coils are in series with same polarity of current
05:59here e equivalent is equal to e1 plus e2 here e1 is equal to minus l1 d i e t minus m also
06:16because now we'll have to include this factor also of m because here we are to include mutual inductance
06:26also already in the question in the situation we have included capital m that's why we are bound to
06:36consider and same way e2 also minus l2 d i by d t remember there is no m1 and m2 only one m is there
06:49always and e equivalent is equal to minus l equivalent d i by d t negative sign in all these expressions
07:02signify induced emf having opposing tendency now let's combine minus l equivalent d i by d t is equal
07:14to minus l1 minus m d i by d t minus l2 let us take out common and cancellation even minus sign will also
07:26cancel out and what we are left with l1 plus l2 plus 2m this is series same direction of current this
07:39result is useful for j related questions then thereafter when two in the inductor coils now third
07:48situation of series with opposite sense of series where opposite sense of current that is fluxes get
07:56subtracted in contact to the above diagram e1 is equal to minus l1 d i by d t plus m d i by d t this time it
08:09is positive sign because both the coils are having opposite direction of current fluxes are also opposite
08:18that's why m d i by d t is positive similarly for induced emf in second coil second inductor coil e2 is
08:29equal to minus l2 d i by d t m d i by d t but e equivalent is equal to minus l equivalent d i by d t and also e
08:43e equivalent is equal to e1 plus e2 therefore minus l equivalent d i by d t is equal to minus l1 d i by d t plus m
08:59again minus l2 plus m d i by d t firstly d i by d t d i by d t d i by d t all these are cancelled
09:11minus l equivalent is equal to minus l1 minus l2 plus 2m it imply that is l1 plus l2 minus 2m opposite
09:26current series now series discussions is over combination of inductors in parallel series thing
09:37is done opposite currents this was series same direction of current l1 plus l2 plus 2m opposite l1
09:46plus l2 minus 2m now separate heading i have started with with combination of inductors in parallel again
09:55this time we won't have three because uh firstly simple general parallel that is like this these three l1
10:07l2 l3 inductor coils i1 i2 i3 are in parallel x y i1 i2 i3 now this time e
10:21it is converted into equivalent circuit like this l x y from both the circuits if we write the expression
10:32for equivalent or total e e x y is equal to l1 d i1 by d t is equal to l2 l3 and here e x y is equal to l
10:51d i y d t why negative sign why can't we use later on we automatically cancel so everywhere we would have
11:00negative sign also and here i could have written i also here main current since i is equal to i1 plus
11:13i2 plus i3 according to parallel rule it implies that d i by d t is equal to d i1 d t d i2 by d t d i3
11:27by d t now some rough work is needed since e is equal to minus l d i by d t therefore d i by d t is equal to
11:40minus l minus e by l according to this parameter can we substitute this equation to new equation on the
11:50basis of this conversion so for left hand side i would be writing minus e x y upon l is equal to
12:03d i1 d i1 e x y by negative of l1 then d i2 by d t on the same line we'll keep on minus e x y upon l2
12:15minus e x y upon l3 this will be cancelling this also will be cancelling it implies that
12:281 by l equivalent is equal to 1 by l1 plus 1 by l2 plus 1 by l3 this is parallel now last heading
12:42what will happen to the expression when capital m will also be included but if there is any mutual
12:53inductance m between the coils then l equivalent is equal to l1 l2 minus m square upon l1 plus l2
13:10plus minus n hence for this there was no derivation hence finally we are done with total electromagnetic
13:22induction so i hope you must have enjoyed whole lot of electromagnetic inductions thanks for joining my
13:32videos and enjoying my channel throughout and thanks a lot for having great patience during these videos
Be the first to comment