AC Generators

Ac Generator

An AC generator (also known as an alternator) is an electrical machine that converts mechanical energy into alternating electrical energy. It is the primary device used in power plants to generate the alternating current electricity that powers our homes and industries.

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Principle of an AC Generator

The working principle of an AC generator is based on Faraday's Law of Electromagnetic Induction. Specifically, it relies on the phenomenon of motional EMF. When a conductor (like a coil) is rotated in a magnetic field, the magnetic flux linked with the conductor changes continuously. According to Faraday's Law, this change in magnetic flux induces an electromotive force (EMF) across the ends of the conductor, and if the circuit is closed, an electric current flows.

The induced EMF is given by $\mathcal{E} = -\frac{d\Phi_B}{dt}$, where $\Phi_B$ is the magnetic flux linked with the coil, and the direction of the induced current is given by Lenz's Law.

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Construction of a Simple AC Generator

A simple AC generator consists of the following essential parts:

1. Armature: This is the rotating part. It consists of a rectangular coil having a large number of turns of insulated copper wire wound on a soft iron core. The coil is mounted on a rotor shaft.
2. Field Magnet: This provides the magnetic field. It can be a strong permanent magnet or an electromagnet. The armature coil rotates within the magnetic field produced by the field magnet.
3. Slip Rings: These are two metallic rings (R1 and R2) connected to the ends of the armature coil. As the armature coil rotates, the slip rings also rotate along with it. They provide the electrical connection between the rotating coil and the stationary external circuit.
4. Brushes: These are two stationary carbon brushes (B1 and B2) which are kept pressed against the slip rings. They collect the induced current from the slip rings and pass it to the external load circuit.
5. Shaft: The armature coil and slip rings are mounted on a shaft, which is mechanically driven by a prime mover (e.g., turbine, engine) to rotate the coil.

Simplified diagram showing the essential parts of a simple AC generator.

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Working of a Simple AC Generator

Let the armature coil PQRS rotate in a uniform magnetic field $\vec{B}$. Let the area of the coil be $A$. Suppose the coil rotates with a constant angular velocity $\omega$ about an axis perpendicular to the magnetic field.

Let's consider the position of the coil at time $t$. Assume at time $t=0$, the plane of the coil is perpendicular to the magnetic field. At time $t$, the coil has rotated by an angle $\theta = \omega t$. The angle between the magnetic field vector $\vec{B}$ and the area vector $\vec{A}$ (normal to the plane of the coil) is $\theta = \omega t$.

The magnetic flux ($\Phi_B$) linked with the coil at time $t$ is:

$ \Phi_B = \vec{B} \cdot \vec{A} = BA \cos\theta = BA \cos(\omega t) $

If the coil has $N$ turns, the total magnetic flux linkage is $N\Phi_B = NBA \cos(\omega t)$.

According to Faraday's Law, the induced EMF ($\mathcal{E}$) in the coil is given by the negative rate of change of magnetic flux linkage:

$ \mathcal{E} = -\frac{d}{dt}(N\Phi_B) = -\frac{d}{dt}(NBA \cos(\omega t)) $

Since $N, B, A, \omega$ are constants:

$ \mathcal{E} = -NBA \frac{d}{dt}(\cos(\omega t)) $

The derivative of $\cos(\omega t)$ with respect to $t$ is $-\sin(\omega t) \cdot \omega$.

$ \mathcal{E} = -NBA (-\omega \sin(\omega t)) $

$ \mathcal{E} = NBA\omega \sin(\omega t) $

This equation shows that the induced EMF is a sinusoidal function of time. The term $NBA\omega$ is the maximum value of the induced EMF, as the maximum value of $\sin(\omega t)$ is 1.

Let $\mathcal{E}_0 = NBA\omega$ be the peak or amplitude of the induced EMF.

$ \mathcal{E}(t) = \mathcal{E}_0 \sin(\omega t) $

This is an alternating EMF, which varies sinusoidally with time.

Induced EMF varies sinusoidally with time.

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Role of Slip Rings

The slip rings (R1 and R2) are permanently connected to the respective ends of the armature coil. As the coil rotates, R1 and R2 rotate with it. The stationary brushes (B1 and B2) maintain contact with the slip rings.

For example, let one end of the coil (say, P) be connected to slip ring R1 and the other end (S) be connected to slip ring R2. Brush B1 is in contact with R1, and brush B2 is in contact with R2.

As the coil rotates, the current induced in the coil reverses direction every half rotation. However, since each brush is permanently connected to its respective slip ring, the current collected by brush B1 always flows in one direction relative to the external circuit terminal connected to B1, and the current collected by brush B2 always flows in the opposite direction relative to the external circuit terminal connected to B2.

This results in the current flowing in the external circuit reversing direction periodically, hence producing Alternating Current (AC). The slip rings ensure that the alternating EMF induced in the coil is transferred as alternating voltage to the external circuit.

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Frequency of Induced EMF

The angular frequency of the induced EMF is $\omega = 2\pi f$, where $f$ is the frequency.

$ f = \frac{\omega}{2\pi} $

The angular velocity $\omega$ is related to the speed of rotation of the prime mover. In India, the standard frequency of AC supply is 50 Hz. This means the coil in the generator rotates at a speed that produces 50 cycles of alternating voltage per second.

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Factors Affecting Induced EMF Magnitude

The peak value of the induced EMF, $\mathcal{E}_0 = NBA\omega$, depends on:

• N: Number of turns in the coil (more turns, higher EMF).
• B: Magnetic field strength (stronger field, higher EMF).
• A: Area of the coil (larger area, higher EMF).
• $\omega$: Angular velocity of rotation (faster rotation, higher EMF).

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Practical AC Generators

Practical generators are much more complex than the simple model described. They often use rotating field magnets and stationary armature coils, employ electromagnets for the field, and have multiple coils to generate smoother and more powerful output. However, the fundamental principle of electromagnetic induction due to changing magnetic flux remains the same.

AC generators (alternators) are the backbone of power generation in thermal, hydro, nuclear, and wind power plants.

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