13.6 Electric Generators and Back Emf
3 min read•june 24, 2024
Electric generators convert mechanical energy into electrical energy using . They consist of an rotating in a , producing . The induced emf varies sinusoidally with time, depending on factors like magnetic field strength and rotational speed.
in motors opposes the input voltage, arising from the armature's rotation in a magnetic field. It's crucial for motor operation, limiting current and allowing steady-state speed. The net emf across the motor is the difference between input and back emf.
Electric Generators
Principles of electric generators
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- of electromagnetic induction states that a changing magnetic flux through a loop induces an in the loop, which is proportional to the rate of change of magnetic flux
- Electric generators consist of an armature (a loop or coil of wire that rotates in a magnetic field), (metal rings attached to the ends of the armature, allowing connection to an external circuit), (conductive contacts that press against the slip rings, providing a connection to the external circuit), and a magnetic field usually provided by permanent magnets or electromagnets
- As the armature rotates, the induced emf alternates sinusoidally, generating ###Alternating_current_()_0### with a frequency that depends on the rotational speed and the number of magnetic pole pairs (electric motors, power plants)
- The rotation of the armature is driven by an external , which overcomes the magnetic forces opposing the motion
Calculation of induced emf
- The induced emf in a rotating loop is given by the equation , where represents the number of turns in the loop, is the magnetic field strength, is the area of the loop, is the angular velocity of the loop, and is time
- The maximum emf occurs when the loop is perpendicular to the magnetic field and can be calculated using , while the emf is zero when the loop is parallel to the magnetic field
- The induced emf varies sinusoidally with time as the loop rotates, resulting in a sinusoidal output voltage (AC power, oscilloscope waveforms)
Generator components and operation
- : The rotating part of the generator, typically containing the armature windings
- : The stationary part of the generator, usually housing the magnetic field
- : A device used in DC generators to reverse the direction of current flow in the external circuit, converting AC to DC
- The interaction between the rotor and stator creates the changing magnetic field necessary for inducing emf
Back Emf in Motors
Back emf in motors
- Back emf () is an induced emf that opposes the input emf in a motor, arising from the armature coils experiencing a changing magnetic flux as the motor rotates, which induces an emf (back emf) in the coils according to Faraday's law
- The back emf opposes the input emf, reducing the net emf across the motor, which is the difference between the input emf and the back emf: , and increases with the motor's rotational speed
- The presence of back emf is essential for motor operation as it limits the current drawn by the motor, preventing damage, and allows the motor to reach a steady-state speed when the back emf equals the input emf (electric vehicles, power tools)
- The relationship between the input emf, back emf, and motor current is given by the equation , where represents the motor current and is the motor resistance
- The direction of the back emf is determined by , which states that the induced current will create a magnetic field that opposes the change causing it
Key Terms to Review (23)
$ ext{mathcal{E}} = ext{NBA} ext{omega} ext{sin}( ext{omega} ext{t})$: $ ext{mathcal{E}} = ext{NBA} ext{omega} ext{sin}( ext{omega} ext{t})$ is a key equation that describes the induced electromotive force (emf) or back emf generated in an electric generator or motor. It represents the voltage that opposes the applied voltage, which is a fundamental principle in the operation of these devices.
$ ext{mathcal{E}}_{input} = ext{mathcal{E}}_{back} + IR$: $ ext{mathcal{E}}_{input}$ is the input voltage or the voltage applied to an electric generator, which is equal to the sum of the back electromotive force ($ ext{mathcal{E}}_{back}$) and the voltage drop across the internal resistance (IR) of the generator. This relationship is a fundamental principle in understanding the operation of electric generators.
$ ext{mathcal{E}}_{max} = NBA ext{omega}$: $ ext{mathcal{E}}_{max}$ represents the maximum electromotive force (EMF) or voltage generated in an electric generator. This term is crucial in understanding the operation and performance of electric generators, as well as the concept of back EMF, which opposes the applied voltage in a motor.
$ ext{mathcal{E}}_{net} = ext{mathcal{E}}_{input} - ext{mathcal{E}}_{back}$: The net electromotive force (emf) generated in an electric generator is equal to the input emf minus the back emf. The back emf is the voltage generated by the generator that opposes the input emf, reducing the net output voltage.
AC: AC, or alternating current, is the flow of electric charge that periodically reverses direction, in contrast to direct current (DC) where the flow of electric charge is unidirectional. AC is the standard form of electricity supplied to homes and businesses, powering a wide range of electrical devices and appliances.
Alternating Current: Alternating current (AC) is an electric current that periodically reverses direction, in contrast to direct current (DC) which flows in a constant direction. AC is the standard form of electricity distribution and is used in a wide range of applications, from powering household appliances to generating electricity in power plants.
Alternating current (ac): Alternating current (AC) is an electric current that periodically reverses direction. Unlike direct current (DC), AC voltage and current change their magnitudes continuously with time.
Armature: The armature is the rotating part of an electric generator or motor that carries the windings in which the electric current is induced. It is a crucial component that converts electrical energy into mechanical energy or vice versa, depending on the device's function.
Back emf: Back electromotive force (back emf) is the voltage generated by an electric motor or generator that opposes the applied voltage. It is a consequence of electromagnetic induction and acts to limit the current in the circuit.
Brushes: Brushes are an essential component of electric generators, responsible for maintaining the flow of electric current between the rotating armature and the stationary part of the generator. They act as the interface between the moving and stationary parts, ensuring a continuous and reliable supply of electricity.
Commutator: A commutator is a mechanical device used in electric generators to convert alternating current (AC) generated in the coil into direct current (DC) for external use. It essentially acts as a switch, reversing the connection of the coil to the external circuit as it rotates, ensuring that the current flows in a single direction. This function is critical for the efficient operation of DC generators, allowing them to provide a stable and usable electrical output.
Counter-Electromotive Force: Counter-electromotive force (counter-EMF or back EMF) is an electromotive force that opposes the applied voltage in an electric circuit, typically occurring in devices such as electric motors. It is a voltage that arises due to electromagnetic induction, acting to reduce the current flow and influence the overall behavior of the circuit.
Electromagnetic Induction: Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (EMF) in a conductor, causing an electric current to flow. This phenomenon is fundamental to the operation of many electrical devices and is crucial in understanding the relationship between electricity and magnetism.
Electromotive Force: Electromotive force (EMF) is the voltage or potential difference generated in an electrical circuit, typically by a source of electrical energy such as a battery or generator. It is the driving force that causes electric charge to flow through a circuit, enabling the conversion of other forms of energy into electrical energy.
Electromotive Force (EMF): Electromotive force, or EMF, is the voltage or potential difference generated by a source of electrical energy, such as a battery, generator, or other electrochemical device. It represents the maximum possible voltage that can be delivered by the source, and it drives the flow of electric current through a circuit.
Faraday's law: Faraday's law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in that circuit. This principle is crucial for understanding how magnetic fields interact with electric circuits and lays the foundation for many applications in electromagnetism.
Lenz's Law: Lenz's law is a fundamental principle in electromagnetic induction that describes the direction of the induced current in a conductor. It states that the direction of the induced current will be such that it opposes the change in the magnetic field that caused it, in accordance with Faraday's law of electromagnetic induction.
Magnetic Field: A magnetic field is a region of space where magnetic forces can be detected. It is a fundamental concept in electromagnetism, describing the invisible lines of force that surround and permeate magnetic materials, electric currents, and changing electric fields. The magnetic field plays a crucial role in various topics within the study of college physics.
Michael Faraday: Michael Faraday was a pioneering scientist known for his groundbreaking work in electromagnetism and electrochemistry during the 19th century. His contributions, particularly in discovering electromagnetic induction and formulating Faraday's Law, laid the foundation for modern electrical engineering and technology.
Rotor: The rotor is the rotating part of an electric generator or motor, responsible for generating the magnetic field that interacts with the stationary part, known as the stator, to produce electricity or motion.
Slip Rings: Slip rings, also known as rotary electrical joints, are a type of electrical interface that allows the transfer of electrical signals and power between stationary and rotating parts of a device. They are a critical component in various electromechanical systems, enabling the continuous transmission of electricity while allowing for the rotation of components.
Stator: The stator is the stationary part of an electric generator or electric motor, consisting of a series of electromagnets arranged in a circular pattern around the rotor. It is a critical component that generates the magnetic field necessary for the operation of these electromechanical devices.
Torque: Torque is a measure of the rotational force that causes an object to rotate about an axis, fulcrum, or pivot. It is the product of the force applied and the distance between the line of action of the force and the axis of rotation.