AC Generator

An A.C. generator, or alternator, is a machine that transforms mechanical energy into electrical energy through electromagnetic induction. Its operation is based on Faraday's Law of Electromagnetic Induction. A.C. generators are used in power stations to generate electricity for the grid, provide electrical power to vehicle systems, and charge the battery.

1.0Definition of AC Generator

An alternator/A.C. Dynamo is an electrical machine that converts mechanical energy into alternating electrical energy.

2.0Principle of AC Generator

The operation of an AC generator is based on Faraday's Law of Electromagnetic Induction. As the coil spins within a magnetic field, the magnetic flux through the coil varies, generating an alternating electromotive force (EMF) in the coil.

3.0Diagram of AC Generator

4.0Construction and Parts of AC Generator

The main components of A.C Generators are given below

1. Armature: The armature coil (ABCD) is composed of numerous turns of insulated copper wire wrapped around a soft iron core.
2. Strong Field Magnets: These consist of a powerful permanent magnet or an electromagnet with cylindrical poles labeled N and S, used as field magnets. The armature coil rotates between these poles. The field magnet creates a uniform magnetic field that is normal  to the axis of rotation of the coil.
3. Slip Rings: The two terminals of the armature coil are attached to brass slip rings, $R_1$and $R_2$, which rotate in tandem with the armature coil.
4. Brushes: Two carbon brushes ($B_1$ and $B_2$) make contact with the slip rings. While the slip rings and armature rotate, the brushes remain stationary. These brushes are linked to the external load, through which the electrical output is delivered. 

5.0Working Principle of AC Generator

• As the armature coil ABCD rotates within the magnetic field created by the strong field magnets, it intersects the magnetic lines of force.
• The rotation of the armature alters the magnetic flux linked with the coil, thereby inducing an electromotive force (EMF) within the coil.
• The direction of induced EMF or the current in the coil is determined by the Fleming’s Right Hand Rule.
• Consider the plane of the coil to be perpendicular to the magnetic field $\vec{B}$. Let the coil be rotated anticlockwise with a constant angular velocity .
• Angle between the normal to the coil and $\vec{B}$ at any instant t is given by  $\theta =\omega t$
• Magnetic flux $\left({\varphi }_B\right)$ linked with the coil having n turns is given by, ${\varphi }_B=n(B\mathrm{Cos}\omega t)A=nBA\mathrm{Cos}\omega t$
• According to Faraday's Law of EMI, the induced EMF generated in the coil is described by $ϵ=-\frac{d{\varphi }_B}{dt}=-\frac{d}{dt}(nBA\mathrm{Cos}\omega t)=-nBA(-\omega \mathrm{Sin}\omega t)=nBA\omega \mathrm{Sin}\omega t$

$ϵ=nBA\omega \mathrm{Sin}\omega t$, this is the expression for induced EMF produced in the coil at any instant t

• Instantaneous Current In the Circuit is given by $I=\frac{ϵ}{R}=\frac{{ϵ}_0}{R}\sin \omega t$, R = Resistance of the Circuit and ${ϵ}_0=nBA\omega$

6.0Variation of Induced EMF with different position of coil w.r.t Magnetic Field

1. When =0°, the plane of coil is perpendicular to the magnetic field, then $ϵ={ϵ}_0{\sin }^{\circ }=0$
2. When $\theta =90^{\circ }$, the plane of the coil is along the direction of the magnetic field, then  $ϵ={ϵ}_0\mathrm{Sin}90^{\circ }={ϵ}_0$
3. When $\text{ When }\theta =180^{\circ }$, the plane of the coil is perpendicular to the magnetic field, then   $ϵ={ϵ}_0\sin 180^{\circ }=0$
4. When $\theta =270^{\circ }$, the plane of the coil is along the direction of magnetic field, then $ϵ={ϵ}_0\sin 270^{\circ }=-{ϵ}_0$
5. When $\theta =360^{\circ }$, the plane of the coil is perpendicular to the direction of the magnetic field, then  $ϵ={ϵ}_0\sin 360^{\circ }=0$
6.  When the coil rotated from its position at right angle to the magnetic field through 180°,the induced EMF and the current increases from zero to maximum (0) and then decreases from maximum to zero in the same direction.
7. When the coil is further rotated through the next 180°,the EMF and current rises from zero to maximum and then decreases from maximum to zero in the opposite direction.
8. Current supplied by an A.C Generator is sinusoidal like its emf i.e., $I=I_0\sin \omega t$

7.0Application of AC Generator

• AC generators are used in power stations to generate electricity for the national grid. 
• In automobiles, AC generators (alternators) are employed to charge the battery and supply power to the vehicle's electrical systems.
• In renewable energy systems, AC generators are used in wind turbines and hydroelectric power plants.
• AC generators are used in locomotives to supply power to various systems onboard the train, including lighting, communication systems, and traction systems.

8.0Diagram of Variation of Coil w.r.t Magnetic Field

9.0Losses in AC Generator

1. Copper Loss: These losses are associated with I²R loss in copper windings of armature coil.
2. Flux Leakage Loss: The useful flux is that which effectively links between magnet and armature. In practice, some of the flux will escape, or otherwise fail to link properly  and will constitute flux leakage loss.
3. Iron loss: This loss takes place in soft iron core of armature. It is of two types

Magnetic hysteresis loss in the iron core

Eddy current losses in the iron core.

• Mechanical Loss: This loss takes place due to friction between moving parts.
• Eddy current: This current is generated in a conductor when there is a change in the magnetic flux associated with it. It is a group of induced currents which are produced, when metal bodies are placed in time varying field or they move in external magnetic field in such a way that flux through them changes with respect to time.
• Some of the applications of eddy currents are electromagnetic damping,induction furnace,induction motor,electromagnetic brakes etc.
• Some of the negative impacts of eddy currents include that they oppose the relative motion ,involve loss of energy in the form of heat and reduce the life of electrical devices.
• To minimize eddy current,laminated cores are used.

10.0Advantage of AC Generator over DC Generator

1. They can be easily stepped up and stepped down through transformers.
2. Losses are less compared to D.C Machines
3. Size is comparatively smaller than a D.C Generator
4. A.C Generators are generally less expensive than D.C Generators.
5. They are more reliable than D.C Generator and also require less maintenance.

11.0Sample Questions on A.C Generator

Q-1. A rectangular coil with dimensions 0.10 m✕ 0.05 m and consisting of 1000 turns rotates at 3600 rpm about an axis parallel to its longer side. Calculate the instantaneous value of the induced EMF when the coil is oriented at 300 to a magnetic field of 100 gauss.

Solution:

Area (A)= $0.10\mathrm{m}\times 0.05\mathrm{m}=5\times 10^{-3}{\mathrm{m}}^2$

n=1000          

$\mathbf{v}=3600\mathrm{rpm}=60\mathrm{rps}$

$\omega =2\pi v=2\times 3.14\times 60=376.8{\mathrm{rads}}^{-1}$

$ϵ=nBA\omega \mathrm{Sin}\theta =1000\times 100\times 10^{-4}\times 5\times 10^{-3}\times 376.8\times \sin 30^0$

$ϵ=9.42\mathrm{V}$

Q-2. In an AC generator, a coil with N turns, each with an area A, and a total resistance R, rotates with a frequency \omega in a magnetic field B. What is the maximum value of the EMF generated in the coil?

Solution:

Magnetic flux passing through Coil $\left({\varphi }_B\right)=NBA\mathrm{Cos}\omega t$

$ϵ=-\frac{d{\varphi }_B}{dt}=-\frac{d}{dt}(NBA\mathrm{Cos}\omega t)=NBA\omega \sin \omega t$

induced EMF will be maximum if $\sin \omega t=1$

$ϵ=NBA\omega$

Q-3. If the rotational velocity of a dynamo armature is doubled, how does the induced EMF change?

Solution:

Value of induced  EMF produced in Dynamo            

$ϵ=NBA\omega$

New EMF if rotational velocity is doubled 

$\left(\therefore {\omega }_{\text{new }}=2\omega \right)$

${ϵ}_{new}=NBA{\omega }_{new}=NBA(2\omega )=2NBA\omega =2ϵ$

Induced EMF gets doubled.

Q-4.Determine the phase difference between the induced EMF and the magnetic flux in a coil that is rotating in a magnetic field.

Solution: Magnetic Flux linked with the coil is given by               

$\varphi =BA\cos \omega t$               

$ϵ=-\frac{d\varphi }{dt}=-\frac{d}{dt}(BA\cos \omega t)=BA\omega \sin \omega t=BA\omega \cos \left(\omega t-\frac{\pi }{2}\right)$

Phase difference between induced EMF and the magnetic flux is $\frac{\pi }{2}$