AC Generator · 2020. 4. 2. · AC generator works on the principle of ”Electromagnetic Induction”. Parts of an AC Generator An Ac generator consists of two poles i.e is the north

AC Generator

How does the electric supply get into your house? The answer to this

is the AC Generator. But have you seen an ac generator working? And

do you know how does the mechanism behind it? Well, let us study

this more in detail.

Suggested Videos

AC Generator

An AC generator is an electric generator that converts mechanical

energy into electrical energy in form of alternative emf or alternating

current. AC generator works on the principle of ”Electromagnetic

Induction”.

Parts of an AC Generator

An Ac generator consists of two poles i.e is the north pole and south

pole of a magnet so that we can have a uniform magnetic field. There

is also a coil which is rectangular in shape that is the armature. These

coils are connected to the slip rings and attached to them are carbon

brushes.

The slip rings are made of metal and are insulated from each other.

The brushes are carbon brushes and one end of each brush connects to

the ring and other connects to the circuit. The rectangular coils rotate

about an axis which is perpendicular to the magnetic field. There is

also a shaft which rotates rapidly.

https://www.toppr.com/guides/physics/moving-charges-and-magnetism/torque-current-loop-magnetic-dipole/

Learn more about Biot-Savart Law.

Working of an AC Generator

When the armature rotates between the poles of the magnet upon an

axis perpendicular to the magnetic field, the flux which links with the

armature changes continuously. Due to this, an emf is induced in the

armature. This produces an electric current through the galvanometer

and the slip rings and brushes.

The galvanometer swings between the positive and negative values.

This indicates that there is an alternating current flowing through the

galvanometer.

Learn more about Magnetic Force and Magnetic Field here.

Video on Electromagnetic Induction and Alternating currents

Emf induced in an AC generator

If the coil of N turn and area A is rotated at v revolutions per second

in a uniform magnetic field B, then the motional emf produced is e =

NBA(2πv)sin(2πv)t, where we assume that at time t = 0 s, the coil is

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perpendicular to the field. The direction of the induced emf is given by

Fleming’s right-hand rule or the Lenz’s law.

Fleming’s right-hand rule states that, stretch the forefinger, the middle

finger and the thumb of the right hand such that they are manually

perpendicular to each other. If the forefinger indicates the direction of

the magnetic field, rhumb indicates the direction of the motion of the

conductor. The middle finger indicates the direction of the induced

current in the conductor.

Learn about Motion in Combined Electric and Magnetic Field.

3-Phase AC generator

In a symmetric three-phase power supply system, three conductors

each carry an alternating current of the same frequency and voltage

amplitude relative to a common reference but with a phase difference

of one third the period. The common reference usually connects to

ground and often to a current-carrying conductor that is neutral.

Due to the phase difference, the voltage on any conductor reaches its

peak at one-third of a cycle after one of the other conductors and

one-third of a cycle before the remaining conductor. This phase delay

https://www.toppr.com/guides/physics/moving-charges-and-magnetism/motion-combined-electric-magnetic-fields/

gives constant power transfer to a balanced linear load. It also makes it

possible to produce a rotating magnetic field in an electric motor and

generate other phase arrangements using transformers.

Learn more about Domestic Electric Circuits.

Questions For You

Q1. What replacement is required to convert an AC generator to DC

generator

A. Armature with coil

B. Concave magnets with horseshoe magnet

C. Slip rings with split rings

D. All of the above

Answer: C. The slip rings in an AC generator maintain a connection

between a moving rotor and the stationary rotor results in the periodic

change of current in the loop making it an alternate current. However,

the DC generator is consisting of split rings makes the current change

direction every half rotation which causes no change in direction of

the current.

https://www.toppr.com/guides/physics/magnetic-effects-of-electric-current/domestic-electric-circuits/

Q2. What determines the frequency of a.c. produced by a generator?

A. The number of rotations of coil in one-second

B. A speed of rotation coil

C. Both A and B

D. None of the above

Answer: C. A frequency of ac, v= w/2π, where w is the speed of

rotation.

Eddy Currents

Suppose you are traveling in a train and the motorman applies the

brakes all of sudden. Do you know how the brakes are been applied in

order to stop the train? The answer to this is eddy currents. Let us

study what eddy currents are and its different uses.

Eddy currents

An eddy current is a current set up in a conductor in response to a

changing magnetic field. They flow in closed loops in a plane

perpendicular to the magnetic field. By Lenz law, the current swirls in

such a way as to create a magnetic field opposing the change; for this

to occur in a conductor, electrons swirl in a plane perpendicular to the

magnetic field.

Because of the tendency of eddy currents to oppose, eddy currents

cause a loss of energy. Eddy currents transform more useful forms of

energy, such as kinetic energy, into heat, which isn’t generally useful.

(Source: Geocities)

Some Practical Applications

In The Brakes of Trains

During braking, the brakes expose the metal wheels to a magnetic

field which generates eddy currents in the wheels. The magnetic

interaction between the applied field and the eddy currents acts to

slow the wheels down. The faster the wheels spin, the stronger is the

effect, meaning that as the train slows the braking force is reduces,

producing a smooth stopping motion.

Electromagnetic damping

Used to design deadbeat galvanometers. Usually, the needle oscillates

a little about its equilibrium position before it comes to rest. This

causes a delay in taking the reading so to avoid this delay, the coil is

wound over a non-magnetic metallic frame. As the coil is deflected,

eddy currents set up in the metallic frame and thus, the needle comes

to rest almost instantly.

Thus, the motion of the “coil is damped”. Certain galvanometers have

a fixed core made up of nonmagnetic metallic material. When the coil

oscillates, the eddy currents that generate in the core oppose the

motion and bring the coil to rest.

Electric Power Meters

The shiny metal disc in the electric power meter rotates due to eddy

currents. The magnetic field induces the electric currents in the disc.

You can also observe the shiny disc at your house.

Induction Furnace

In a rapidly changing magnetic fields, due to a large emf produced,

large eddy currents are set up. Eddy currents produce temperature.

Thus a large temperature is created. So a coil is wound over a

constituent metal which is placed in a field of the highly oscillating

magnetic field produced by high frequency. The temperature produced

is enough to melt the metal. This is used to extract metals from ores.

Induction furnace can be used to prepare alloys, by melting the metals

at a very high temperature.

Speedometers

To know the speed of any vehicle, these currents are used. A

speedometer consists of a magnet which keeps rotating according to

the speed of our vehicle. Eddy currents are been produced in the drum.

As the drum turns in the direction of the rotating magnet, the pointer

attached to the drum indicates the speed of the vehicle

Question For You

Q. Eddy currents are produced in a metallic conductor when

A. The magnetic flux linked with it changes

B. It is placed in the changing magnetic field

C. Placed in the magnetic field

D. Both A and B

Answer: D. They are produced when the magnetic flux passing

through the metal object continuously changes. This may happen due

to many reasons. 1. The object is placed in the region with changing

magnetic field. 2. The object continuously moves in and out of the

magnetic field region.

Energy Consideration: A Quantitative Study

We all know what is force and energy. But what provides the link

between the force and the energy? The answer to this is energy

consideration. Newton problems can also be easily solved using

energy consideration. Let us study more about them.

Energy Consideration

We all know that Lenz’s law is consistent with the law of conservation

of energy. Lenz’s Law states that, when you induce a current in a wire

via a changing magnetic field, the current flows through the wire in

such a direction so that its magnetic field opposes the change that

produced the current.

Now let us understand energy consideration in a better way

Suppose there is a rectangular conductor. now from the above figure,

we can say that the sides of the sides of the rectangular conductor are

PQ, RS, QR, and SP. Now in this rectangular conductor, the three

sides are fixed, while one of it’s side that is the side PQ is set free.

Let r be that movable resistance of the conductor. So the resistance of the other remaining sides of the rectangular conductor that is the

resistance of side RS, SP and QR is very small as compared to this movable resistance. In a constant magnetic field, if we change the flux, an emf is induced. i.e E =

dΦ

dt

If there is induced emf E and a movable resistance r in the conductor then, we can say that I =

Blv

R

. As the magnetic field is present, there will also be a force F acting, as F = ILB. This force is directed outwards in the direction opposite to the velocity of the rod, given by F =

B²l²v

R

Power = force × velocity =

B²l²v²

R

Now here the work done is mechanical and this mechanical energy is dissipated as Joule heat. This is given as PJ = I²R =

B²l²v²

R

. Further, the mechanical energy converts into electrical energy and finally into thermal energy. From the Faraday’s law, we have learned that, |E| =

Δ

Φ

B

Δt

So we get, |E| = IR =

ΔQ

Δt

R

Hence we get, ΔQ=

Δ

Φ

B

R

Solved Examples For You

Q1. A circular coil of radius 8.0 cm and 20 turns is rotated about its

vertical diameter with an angular speed of 50 rads -1 in a uniform

horizontal magnetic field of magnitude 3.0 × 10 -2 T. Obtain the

maximum and average emf induced in the coil. If the coil forms a

closed loop of resistance 10, calculate the maximum value of current

in the coil. Calculate the average power loss due to Joule heating.

Where does this power come from?

Solution: Maximum induced emf e = NwAB,

N = number of turns w = angular speed

A = Area of the coil B = Magnetic filed

e = 0.603 V

Over a full cycle, the average emf induced in the coil is zero.

Maximum current, I = e/R = 0.0603

Average power loss due to Joule heating is P = eI/2

= 0.018W

Answer: The average power loss due to Joule heating is 0.018W

Q2. A rectangular wire loop of sides 8 cm and 2 cm with a small cut

is moving out of a region of a uniform magnetic field of magnitude

0.3 T directed normal to the loop. What is the emf developed across

the cut if the velocity of the loop is in a direction normal to the (a)

longer side, (b) shorter side of the loop? For how long does the

induced voltage last in each case?

Solution: A = 8 × 2 = 16cm²

emf, e = d(A × B)/dt = 0.32 × 10-4 V

Induced curent, i = e/R = 2 × 10-5 A

Power, P = i²R = 6.4×10-10 W

Faraday’s and Lenz’s Law

You must have always come across the security checks at airports or

at railway stations. You must have also used tape recorders to record

your voice and to listen to the music. All these things work on the

principle of Faraday’s law. Now, what is Faraday’s law? We will

study this law in detail.

Faraday’s Experiment

To understand the Faraday’s law, let us first carry out an experiment

in which we have a coil attached to a galvanometer and a bar magnet.

Now, this coil does not have a source of current, that means there is no

battery attached and no current circulates inside the coil. When the

bar magnet is moved towards the coil, the galvanometer starts

showing deflection. That means there is a current induced in the

circuit. Was there any battery? NO!

But just because the bar magnet was in motion, emf has been induced

in the coil. This is an electromagnetic induction. Now let the magnet

move towards the direction of the coil with velocity ”v”. What is

observed is that, till the bar magnet was in motion, only at that time

the galvanometer shows deflection.

The moment ”v” becomes 0 again, the galvanometer shows ”0”

deflection. So if v = 0, emf = 0. Here we have observed that greater

the velocity, greater is the induced emf. Also when the direction of

”v” is changed, the galvanometer shows deflection in the opposite

direction, that is the current moves in opposite direction.

The bar magnet is associated with the magnetic flux and the emf

which gets induced inside the coil, it’s because of the magnetic flux.

From this above experiment, we get two laws:

Faraday’s Laws

Faraday’s First Law

Whenever there is a change in the magnetic flux associated with a coil

and emf is induced in the coil.

E

∝

dΦ

Because of this magnetic flux, current is flowing through the circuit

and if the current flows through the circuit there is some emf which is

getting induced in the circuit.

Faraday’s Second Law

The magnitude of the induced emf in a circuit is equal to the time rate

of change of magnetic flux through the circuit.

|E|

∝

dΦ

(dt)

|E| =

dΦ

(dt)

● dΦ is the change in magnetic flux

● dt is the change in time

● the proportional constant = 1

Rate of change of flux=

dΦ

(dt)

According to the Faraday’s law, there would be an induced emf. So, E =

dΦ

(dt)

Lenz’s Law

Faraday’s law does not give an explanation to the direction of the

current. However, the Lenz law specifies the direction of the current

induced inside the coil. Let us understand the Lenz law.

Lenz law of electromagnetic induction states that, when an emf

induces according to Faraday’s law, the polarity (direction) of that

induced emf is such that it opposes the cause of its production.

According to Lenz’s law,

E = –

dΦ

(dt)

The negative sign shows that the direction of the induced emf and the

direction of change in magnetic fields have opposite signs. Suppose

we have a coil and a bar magnet.

The moment we take the bar magnet towards the coil, emf is induced

in the coil that is the galvanometer shows deflection. The direction of

the induced current will be such that it opposes the motion of the

magnet towards the coil.

Questions For You

Q1. Lenz’s law of electromagnetic induction corresponds to the

A. law of conservation of charge

B. The law of conservation of energy

C. Law of conservation of momentum

D. The law of conservation of angular momentum

Answer: B. Lenz’s law of electromagnetic induction compounds to the

law of conservation of energy.

Q2. Two identical coaxial coils P and Q carrying an equal amount of

current in the same direction are brought nearer. The current in

A. P increases while in Q decreases

B. Q increases while in P decreases

C. Both P and Q increases

D. Both P and Q decreases

Answer: D. Two identical coaxial coils P and Q carrying an equal

amount of current in the same direction are brought nearer. The

current in both P and Q decreases as per Lenz’s law.

Inductance

Have you seen a motor working? And do you know how does it work?

Well, it works because of ‘inductance’. But actually what it means?

Let us find out!

Inductance

It is the current production in a coil due to change in magnetic flux in

itself or new coil. Whenever there is a coil, and you have a change in

magnetic flux or change in magnetic field, an induced emf is

generated in that coil or wire. This very property is inductance.

Here Φ ∝ I, where, Φ is the magnetic flux and I is the current. In ‘n’

turns of the coil, N Φ ∝ I. It is a scalar quantity and it’s SI unit is

Henry. It is denoted by H.

Dependency of Geometric Parameters on Inductance of a Coil

● The number of wire wraps or turns in the coil: When there are

a greater number of turns of wire in the coil it will result in

greater inductance. And vice versa.

● Coil area: If the coil area is more, the coil (as measured

looking lengthwise through the coil, at the cross-section of the

core) results in greater inductance and vice versa.

● Coil length: The longer the length of the coil, the inductance

will be less. If the length of the coil the is shorter, the

inductance will be greater.

Self Inductance

Self-induction means the coils induce the emf themselves. There is a

change in the magnetic flux through that coil and because of this, the

current will be induced in the coil by itself. So once the current get

induced, the current tries to oppose the flux. Here NΦ ∝ I

NΦ = LI ( L is the self-induction)

Induced emf, E = -N

dΦ

(dt)

= -N

dI

(dt)

[ L/N]

E = -L

dI

(dt)

This is the self-induced emf. A coil having self-inductance ”L” is said

to be the induction coil.

Mutual Inductance

Here, there are two coils placed near each other. The first coil will

make turns and carry the current which results in the magnetic field.

As both the coils nearly close to each other, the magnetic field through

one coil will all pass through the other coil. So one coil causes the

change in magnetic flux because of which current is induced in the

other coil.

Here there is the primary coil and another one is the secondary coil.

This type of induction mainly depends upon the number of turns, size,

and shape of the coil and medium between the two coils.

E = -M

dI

(dt)

Questions For You

Q1. What do we call the phenomenon of production of back emf in a

coil due to the flow of varying current through it?

A. Self-inductance

B. Electromagnetic Induction

C. Magnetic flux

D. Magnetic moment

Answer: A. Self-inductance is that phenomenon in which charge in

electric current in a coil produces an induced emf in the coil itself.

Q2. Two coils A and B have L= 2×10-2 Henry. If the current in the

primary is i = 5 sin 10πθ then maximum value of emf induced in coil

B is:

A. Π volt

B. Π C. 2 D. volt

E. Π F. 3 G. volt

H. Π I. 4 J. volt

Answer: A. Given that, Current i = 5sin (10πt), Mutual inductance L =

2×10-2 and H =0.02H

Induced emf, E = -M

di

dt

∴ |E| = M × 5 (10π) cos (10πt)

= π volt

Motional Electromotive Force

Did you know that the Electromotive force is essential for an

electronic circuit to drive currents through the circuit? The

electromotive force also like a charge pump. Let us learn more about

them.

Motional Electromotive Force

An emf induced by the motion of the conductor across the magnetic

field is a motional electromotive force. The equation is given by E =

-vLB. This equation is true as long as the velocity, field, and length

are mutually perpendicular. The minus sign associated with the Lenz’s

law.

(Source: Exam.com)

For us to understand the motional electromotive force, let us make a

particular setup. Let us take a rectangular coil, a metal rod of length L,

moving with velocity V, through a magnetic field B. There is a

magnetic field at some location.

Length, velocity and magnetic field should always be at a right angle

with each other. The direction of the magnetic field is going inside.

Assume the metal rod is frictionless that means there is no loss of

energy due to friction and we apply a uniform magnetic field. The

conductor rod is moved with a constant velocity and placed in the

magnetic field.

ΦB = Blx

But ‘x’ changes with time,

E = –

d

Φ

B

dt

= –

d

dt

(Blx) = -Bl

dx

dt

E = Blv

The induced emf Blv is motion electromotive force. So we produce

emf by moving a conductor inside the uniform magnetic field. The

power required to move a conductor rod in a magnetic field is,

P =

B²l²v²

R

Where,

● B is the magnetic field,

● l is the length of the conductor

● v is the velocity of the conductor

● R is the resistance

The magnetic flux associated with the coil is given by Φ = BA cos θ.

We know that cos θ = 0, so Φ = BA. The motion of electromotive

force can be further explained by Lorentz force which acts on free

charge carriers. The Lorentz force on charge is:

F = qVB

Solved Questions For You

Q1. A coil having n turns and area A is initially placed with its plane

normal to the magnetic field B. It is then rotated through 180º in 0.2

sec. The emf induced at the ends of the coils is

A. 0.1 nAB

B. nAB

C. 5 nAB

D. 10 nAB

Answer: D. Total change in flux = ΔΦ = 2 nAB

Total time of change = Δt = 0.2s

Emf induced =

ΔΦ

Δt

= 10nAB

Q2. A straight line conductor of length 0. 4m is moved with a speed

of 7ms-1 perpendicular to a magnetic field of an intensity of 0.9wbm-2

The induced emf across the conductor is:

A. 25.2 V

B. 5.24 V

C. 2.52 V

D. 1.26 V

Answer: C. The induced emf across the conductor E= Blv

= 0.98 × 0.4 × 7 = 2.52V

Q.3 Two conducting rings of radii r and 2r move in opposite directions

with velocities 2v and v respectively on a conducting surface S. There

is a uniform magnetic field of magnitude B perpendicular to the plane

of the rings. The potential difference between the highest points of the

two rings is:

A. Zero

B. 2rvB

C. 4rvB

D. 8rvB

Answer: D. Replace the emf in the rings by the cells.

E1= B2r(2V) = 4Brv

E2 = B(4r)v = 4Brv

V2 – V1 = 8Brv