# (i) Draw a labell

(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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses