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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