Answer :

(i) Principle:


A transformer works on the principle of mutual induction. If the amount of flux inside the primary coil changes , a corresponding emf is induced in the secondary coil.


Working:


In a step down transformer, A primary coil with high number of turns and thus high voltage and low current is connected to an alternating current source , the current changes continuously in this coil, which in turn changes the magnetic flux through the secondary coil continuously. An alternating of low emf , though of same frequency is developed across the secondary terminals.


The faraday’s law of e.m.f induced in the primary coil can be written as:


…..(a)


Where,


E is the emf induced in the primary coil,


N is the number of turns of coil


ϕ is the flux through the coil


And the e.m.f induced in the secondary coil is given as:


…….(b)


Where,


E’ is the emf induced in the secondary coil,


N’ is the number of turns of secondary coil,


ϕ is the flux through the coil.


On dividing (a) and (b) we get,



For step down transformer we have, C<1


Therefore, E’ < E



(ii) The emf induced in the primary coil can be given as:


…..(a)


Where,


E is the emf induced in the primary coil,


N is the number of turns of coil


ϕ is the flux through the coil


And the e.m.f induced in the secondary coil is given as:


…….(b)


Where,


E’ is the emf induced in the secondary coil,


N’ is the number of turns of secondary coil,


ϕ is the flux through the coil.


On dividing (a) and (b) we get,



Where,


C is called the turn ratio or the transformation ratio.


(iii) If the transformer is ideal , then


The input electrical power is equal to the output electrical power.


EI = E’I’


Where,


E, E’ is the emf induced in primary and secondary coil respectively,


I and I’ is the current in the primary and secondary coil respectively.


Therefore, we get



Where,


C is called the turn ratio or the transformation ratio.


(iv) The power can be defined as:


Power = Vp× Ip


Where,


Vp is the emf od primary coil,


Ip is the current in the primary coil.


Given,


Power = 550 W


The voltage supplied , V = 220 V


Ip = 550 W / 220 V = 2.5 A


OR


(a) If two inductors are placed in proximity, and when the time varying current in one inductor changes, the flux changes with it and thus cuts the inductor nearby , which in response produces a onduced voltage in both the inductors.


We consider coils P and Q . We take a time varying current I flowing through one of the coils, let it be P, then we get,


ϕ α I


ϕ = MI


where,


ϕ is the magnetic flux through the coil


M is the coefficient of mutual inductance,


The induce emf can be written as:



We take mutual inductance of the coils of radius r1 and r2 such that, r1 < r2, and place the two coils coaxially, we have,


Φ21 α I ,


ϕ21 = M2 I1


Where ,


M2 is the coefficient of mutual inductance of two coils.


The magnetic field of the first coil can be given as:


B1 = μn1I1


Where,


Magnetic flux linked with the second coils B1 times the cross section of the first coil.


Thus, ϕ21 = B1A × n2I


ϕ21 = μn1I1× A× n2I


ϕ21 = μn1n2 AI I1


M21 = μn1n2 AI


Thus similarly we can have:


M12 = μn1n2AI


And then


We have, M12 = M21 = M


M = μn1n2AI


(a) The number of turns on the rectangular coil is supposed to be N . Let A be the cross sectional area which is placed under the magnetic field of magnitude B, The magnetic flux linked with coil can be given as:


ϕ = NBA cosθ


Thus, the emf induced in the coil can be given as:


E = -dϕ /dt



E = NBA.sin θ (2πf)


Where,



We can see, For maximum emf induced we must have ,


Sinθ = 1,


Therefore,


E = NBA (2πf)


Which is the maximum emf induced in the coil.


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