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 = V_{p}× I_{p}

Where,

V_{p} is the emf od primary coil,

I_{p} is the current in the primary coil.

Given,

Power = 550 W

The voltage supplied , V = 220 V

⇒ I_{p} = 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 r_{1} and r_{2} such that, r_{1} < r_{2,} and place the two coils coaxially, we have,

Φ_{21} α I ,

⇒ ϕ_{21} = M2 I1

Where ,

M_{2} is the coefficient of mutual inductance of two coils.

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

B1 = μn_{1}I_{1}

Where,

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

Thus, ϕ_{21} = B_{1}A × n_{2}I

⇒ ϕ_{21} = μn_{1}I_{1}× A× n_{2}I

⇒ ϕ_{21 =} μn_{1}n_{2} AI I_{1}

⇒ M_{21} = μn_{1}n_{2} AI

Thus similarly we can have:

M_{12} = μn_{1}n_{2}AI

And then

We have, M_{12} = M_{21} = M

M = μn_{1}n_{2}AI

(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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