Questions and Answers
What are the two laws that form the basis of operation of electrical machines?
What is the instantaneous emf according to Faraday’s law given?
e = 960π cos(120πt)
What is the average voltage induced in the coil given a flux change from 5 mWb to 2 mWb?
60 V
The flux linkage can only change when the flux varies in magnitude with time.
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The voltage when induced in a machine winding, gives rise to __________ power conversion.
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What is the formula to calculate the emf in a single conductor moving in a magnetic field?
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What is the direction of force on a current-carrying conductor placed in a magnetic field determined by?
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What are the two main laws forming the basis of operation of electrical machines?
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What is the formula for the instantaneous emf according to Faraday’s law?
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In Example 1, what is the expression for variable flux?
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Calculate the average voltage induced in the coil from Example 2.
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The induced voltage in a machine winding is called pulsational or transformer emf.
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What does Fleming’s left hand rule help to determine?
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The emf in a moving conductor cutting across a magnetic field is given by the formula e = _____ volts.
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What primarily causes the change of flux linkage in electrical machines?
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What equation is referred to as the flux cutting rule?
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In Example 4, what is the length of the conductors moved across the magnetic field?
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What is the flux density in the magnetic field used in Example 4?
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Study Notes
Basic Laws of Electrical Machines
- Two fundamental laws govern the operation of electrical machines: Faraday’s law of electromagnetic induction and the law of interaction.
- Electrical machines convert electrical energy to mechanical energy or vice versa.
- Faraday's law states that a changing flux linkage induces an electromotive force (emf) in a coil.
Faraday's Law and Flux Linkage
- Defined variables: N = number of turns in coil, Φ = total magnetic flux linking the coil.
- Flux linkage (λ) is expressed as λ = NΦ.
- A change in flux linkage over time induces an emf.
- Instantaneous emf can be calculated from the rate of change of flux linkage.
Examples of Induced Voltage
- Example 1: For a coil with 4000 turns linked by a variable flux, the induced voltage is e = 960π cos(120πt).
- Example 2: When a permanent magnet causes the flux in a 2000-turn coil to drop from 5 mWb to 2 mWb in 0.1 seconds, the average induced voltage is 60 V.
Change of Flux Linkage
- Can occur due to:
- Variance in flux magnitude over time.
- Relative motion between the coil and flux.
- Flux linkage can be expressed in terms of position (θ) and time (t).
- Voltage types:
- Motional or rotational emf, which results from mechanical motion.
- Pulsational or transformer emf, enabling electrical energy transfer between windings, such as in transformers.
Force on Current-Carrying Conductor
- A conductor of length l in a magnetic field (density B) experiences a force proportional to the current (i).
- Force can be determined using Fleming’s left-hand rule.
Voltage Induction in Moving Conductors
- An emf is induced in a conductor of length l moving through a magnetic field density B at speed u: e = Blu volts.
- This is known as the flux cutting rule and represents a motional emf.
- Direction of the induced voltage is determined by Fleming’s right-hand rule.
Application to Rotating Electrical Machines
- In rotating machines, induced voltage is often calculated using the flux cutting rule due to complex flux linkage in coils.
- Example 4: For a generator with conductors of length 2 m moving at 100 m/s in a magnetic field of flux density 0.6 Wb/m², the induced emf can be calculated using the flux cutting rule.
Basic Laws of Electrical Machines
- Two fundamental laws govern the operation of electrical machines: Faraday’s law of electromagnetic induction and the law of interaction.
- Electrical machines convert electrical energy to mechanical energy or vice versa.
- Faraday's law states that a changing flux linkage induces an electromotive force (emf) in a coil.
Faraday's Law and Flux Linkage
- Defined variables: N = number of turns in coil, Φ = total magnetic flux linking the coil.
- Flux linkage (λ) is expressed as λ = NΦ.
- A change in flux linkage over time induces an emf.
- Instantaneous emf can be calculated from the rate of change of flux linkage.
Examples of Induced Voltage
- Example 1: For a coil with 4000 turns linked by a variable flux, the induced voltage is e = 960π cos(120πt).
- Example 2: When a permanent magnet causes the flux in a 2000-turn coil to drop from 5 mWb to 2 mWb in 0.1 seconds, the average induced voltage is 60 V.
Change of Flux Linkage
- Can occur due to:
- Variance in flux magnitude over time.
- Relative motion between the coil and flux.
- Flux linkage can be expressed in terms of position (θ) and time (t).
- Voltage types:
- Motional or rotational emf, which results from mechanical motion.
- Pulsational or transformer emf, enabling electrical energy transfer between windings, such as in transformers.
Force on Current-Carrying Conductor
- A conductor of length l in a magnetic field (density B) experiences a force proportional to the current (i).
- Force can be determined using Fleming’s left-hand rule.
Voltage Induction in Moving Conductors
- An emf is induced in a conductor of length l moving through a magnetic field density B at speed u: e = Blu volts.
- This is known as the flux cutting rule and represents a motional emf.
- Direction of the induced voltage is determined by Fleming’s right-hand rule.
Application to Rotating Electrical Machines
- In rotating machines, induced voltage is often calculated using the flux cutting rule due to complex flux linkage in coils.
- Example 4: For a generator with conductors of length 2 m moving at 100 m/s in a magnetic field of flux density 0.6 Wb/m², the induced emf can be calculated using the flux cutting rule.
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Description
This quiz covers the fundamental laws of electrical machines, including Faraday's law of electromagnetic induction and the operation of D.C. machines, transformers, and induction machines. It is designed for students enrolled in EE 172 and aims to reinforce key concepts in electrical engineering.
