Talha's Physics Academy
Electromagnetic Induction - AC Generator
AC Generator (Alternator)
"An AC generator is a device that converts mechanical energy into electrical energy in the form of alternating current (AC) based on the principle of electromagnetic induction."
This fundamental law was first formulated by Michael Faraday.
Figure: Construction of an AC Generator with armature coil, permanent magnets, slip rings, and brushes.
Construction of an AC Generator
An AC generator consists of the following primary components:
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Armature (Rotor):
A rectangular coil of insulated copper wire mounted on a rotating shaft. It spins within a magnetic field to induce an electrical current.
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Permanent Magnet (Stator):
The stationary part of the generator consisting of powerful permanent magnets or electromagnets arranged in a cylindrical configuration around the rotor to produce a uniform magnetic field.
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Slip Rings and Brushes:
The ends of the rotor coil are connected to conductive slip rings that rotate synchronously with the rotor. Carbon or graphite brushes press against the slip rings to collect and transfer the generated electrical current to the external circuit.
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Shaft and Bearings:
The rotor is mounted on a mechanical shaft supported by bearings to minimize friction and enable smooth rotation.
Working of an AC Generator
- Rotation of the Armature: The coil is mechanically rotated using an external power source such as a turbine, engine, or motor.
- Changing Magnetic Flux: As the rotor spins within the stator's magnetic field, the magnetic flux linked with the coil changes continuously, inducing an electromotive force (emf) according to Faraday's law.
- Generation of Alternating Current: The induced voltage drives an alternating current through the coil. Because the orientation of the coil relative to the magnetic field reverses every half-turn, the current direction switches periodically, producing an AC output.
- Current Collection: Slip rings and brushes maintain continuous electrical contact with the rotating coil, feeding the alternating current into the external load circuit.
Direction of Induced EMF & Current Alternation
Suppose armature coil $AHCD$ rotates counterclockwise. As it rotates, the magnetic flux linked with it changes, and the direction of the induced current is governed by Fleming's right-hand rule.
When the armature passes the vertical position during the first half-turn, wire $AH$ moves downward while $DC$ moves upward, creating a current path of $DCHA$ inside the coil and flowing along $B_1 R B_2$ in the external circuit. During the second half-revolution, the motion of the sides reverses ($AH$ moves upward, $DC$ moves downward), reversing the internal current path to $AHCD$ and directing external current as $B_2 R B_1$. Thus, the direction of the induced emf and current alternates after every half-revolution.
When the armature passes the vertical position during the first half-turn, wire $AH$ moves downward while $DC$ moves upward, creating a current path of $DCHA$ inside the coil and flowing along $B_1 R B_2$ in the external circuit. During the second half-revolution, the motion of the sides reverses ($AH$ moves upward, $DC$ moves downward), reversing the internal current path to $AHCD$ and directing external current as $B_2 R B_1$. Thus, the direction of the induced emf and current alternates after every half-revolution.
Figure: Working of Generators.
Mathematical Expression for Induced EMF
The total motional emf induced in the two active cutting lengths $L$ of the rotating coil moving with linear velocity $v$ in a magnetic field $B$ with $N$ turns is expressed as:
$\mathcal{E} = 2 v B N L \sin(\theta)$
Since each particle of sides $AH$ and $DC$ rotates in a circle of radius equal to half the width of the coil ($b/2$), the linear velocity $v$ is related to angular velocity $\omega$ by:
$v = r\omega = \left(\frac{b}{2}\right)\omega$
Substituting $v$ into the emf equation, and noting that area $A = L \cdot b$ and angular displacement $\theta = \omega t$:
$\mathcal{E} = 2 \left(\frac{b}{2}\omega\right) B N L \sin(\omega t) = (L \cdot b) N B \omega \sin(\omega t)$
$\mathcal{E} = \mathcal{E}_0 \sin(\omega t)$
Where the peak (maximum) value of the induced emf is:
$\mathcal{E}_0 = A N B \omega$
$\mathcal{E}_0$ represents the maximum or peak value of the induced emf, which depends directly on the cross-sectional area of the coil ($A$), number of turns ($N$), magnetic field intensity ($B$), and angular speed of rotation ($\omega$).
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