Alternating Current Generator-Construction, And Working

An alternating current generator is a device that is used to produce current electricity. An alternating current generator is a device that produces an electric potential difference.

Alternating current generator

It is a device that converts mechanical energy into electrical energy.

Alternating current generator Principle:

The principle of alternating current generators is based on Faraday’s law of electromagnetic induction. When a coil is rotated in a magnetic field magnetic flux through the coil changes and an emf has induced in the coil.

Alternating current generator Construction

It consists of the following major parts:

Armature

A number of coils are wound around an iron cylinder which is rotated in the magnetic field.

Slip rings

The ends of the coil are attached with the metal rings R and R^/ called the Slip Rings. These rings are concentric with the axis of the loop and rotate with it.

Carbon Brushes

The slip rings RR^’ slide against stationary carbon brushes connected with an external circuit.

Alternating current generator Working

A rectangular loop of wire of area A is placed in a uniform magnetic field B. The loop is rotated about the z-axis through its center at constant angular velocity. To calculate the induced emf in the loop consider when the coil is rotating anti-clockwise. The vertical side ab is moving with velocity v in the magnetic field B if the angle between v and B is θ

then the motional emf induced in the side ab has the magnitude

 ԑ_ab =v BL sinθ

It should be noted that the direction of the induced current in the wire ab is the same as that of the force F experienced by the positive charge in the wire from top to bottom. Similarly current through the side cd is

ԑ_cd =v BL sinθ

Now the direction of the induced current is from the bottom to the top. The emf through the sides bc and da is zero because these sides are parallel and anti-parallel to the field.

So the total emf through the loop is

 ԑ=ԑ_ab+ԑ_cd

ԑ= v BL sin θ +v BL sin θ

ԑ=2vBL sin θ

For a coil of N turns we have

ԑ=N v BL sin θ

ԑ=2N(r) ωBL Sin θ

ԑ=N ω (2rL)B sin θ

Let L be the length and 2r be the width of the coil. Then the area of the coil will be

A=2rL

ԑ=N ω AB Sin θ

θ= ω t

ԑ=N ω AB Sin (ω t)

The equation shows that the induced emf varies sinusoidally with time. It will be maximum for Sin θ (ω t) =1 so

ԑ_o=N ω AB

Where ԑ_o is the maximum induced emf. The equation can be written as

By Ohms law

ԑ=IR

I=ԑ/R

I= ԑ_o Sin (ω t)/r= ԑ_o/R*Sin (ω t)

The angular speed ω of the coil is related to its frequency f as

ω=2π f

ԑ= ԑ_o Sin (2 π ft)

I=I_o Sin (2 π ft)

The graph between the Current and angle

When the angle between v and b is 0 the plane of the loop is perpendicular to B and so the current is zero.

When θ=90⁰ or 3π/2 radius the loop is parallel to B and the current is maximum.

When θ=180⁰ or π radius the loop is again perpendicular to B so the current is zero.

When θ=270⁰ or 3π/2 radius the loop is parallel to B current is maximum.

When θ=360⁰ or 2π radius current is again zero.

It should be noted that the current increase twice in a cycle but in the opposite direction. Thus the current alternate in direction once in one cycle. Such a current is called an alternating current.

Role of Armature

In actual practice, a number of coils are wound around an iron cylinder which is rotated in the magnetic field. This assembly is called Armature.

The magnetic field is usually provided by an electromagnet. The armature is rotated by a fuel engine or a turbine run by a waterfall. In some commercial generators, the field magnet is rotated around a stationary armature.

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