Mutual Inductance: Homework Questions & Answers

In summary, mutual inductance is a property that describes the relationship between changing currents in two physically close circuits. It is represented by the equation E=-M\frac{di}{dt} and is an important concept in electromagnetism. If you're struggling with this topic, don't hesitate to ask for help and keep practicing until you understand it.
  • #1
exitwound
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1

Homework Statement



Capture.JPG


Homework Equations



[tex]E=-M\frac{di}{dt}[/tex]

The Attempt at a Solution



Can anyone even tell me what the heck this problem is asking? This chapter has been a nightmare and I don't understand any of it. The book is terrible and barely explains what 'mutual inductance' even is. The sample problems are ridiculous too.
 
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  • #2


Hi there,

I'm sorry to hear that you're struggling with this chapter. Mutual inductance can be a difficult concept to grasp at first, but I'm here to help.

Mutual inductance is a property of two circuits that are physically close to each other. It describes the relationship between the changing current in one circuit and the resulting induced voltage in the other circuit. The equation you provided, E=-M\frac{di}{dt}, represents Faraday's law of induction, where E is the induced voltage, M is the mutual inductance, and di/dt is the rate of change of current in the first circuit.

To solve problems involving mutual inductance, you will need to use this equation along with other equations related to circuits, such as Ohm's law and Kirchhoff's laws. It's also helpful to draw circuit diagrams to visualize the relationships between different components.

I recommend going back to the chapter and reviewing the definitions and examples provided. If you still have trouble understanding, don't hesitate to ask for clarification or seek additional resources, such as online tutorials or practice problems. Understanding mutual inductance is an important foundation for understanding more complex topics in electromagnetism, so don't give up! Keep practicing and seeking help, and you'll get there.
 
  • #3


I understand your frustration with the homework questions and answers on mutual inductance. It can be a difficult concept to grasp, but it is an important one in the study of electromagnetism. Mutual inductance refers to the interaction between two circuits or coils, where a change in the current in one circuit can induce a current in the other circuit. This is described by the equation E=-M\frac{di}{dt}, where E is the induced electromotive force, M is the mutual inductance, and di/dt is the rate of change of current.

To better understand this concept, it may be helpful to think of mutual inductance as a form of electromagnetic coupling, similar to how two magnets can attract or repel each other based on their magnetic fields. In the case of mutual inductance, the changing magnetic fields of the two circuits or coils interact with each other, causing an induced current in the other circuit.

To solve problems involving mutual inductance, you will need to use the equation E=-M\frac{di}{dt} and also consider the values of the inductances and currents in each circuit. Practice problems and examples may be helpful in solidifying your understanding of this concept. Remember, as with any complex topic, it takes time and effort to fully grasp it. Keep practicing and seeking help when needed, and you will eventually master mutual inductance.
 

1. What is mutual inductance?

Mutual inductance is the property of an electrical circuit where a changing current in one circuit induces a voltage in another circuit that is placed close to it.

2. How is mutual inductance calculated?

Mutual inductance can be calculated using the following formula: M = N1*N2*Φ / I1, where N1 and N2 are the number of turns in the two coils, Φ is the magnetic flux through the coils, and I1 is the current in the first coil.

3. What is the unit of measurement for mutual inductance?

The unit of measurement for mutual inductance is the henry (H). It is named after the American scientist Joseph Henry and is equivalent to one volt-second per ampere (V-s/A).

4. How does mutual inductance affect circuit behavior?

Mutual inductance can have both positive and negative effects on circuit behavior. It can help in reducing interference between two circuits and can also be used to create transformers and other devices. However, it can also cause unwanted voltage spikes and can make circuit analysis more complex.

5. What are some real-world applications of mutual inductance?

Mutual inductance has various real-world applications, including transformer circuits, electric motors, generators, and wireless power transfer systems. It is also used in radio frequency identification (RFID) technology and inductive charging for smartphones and other electronic devices.

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