24 Questions
What is the purpose of placing a dot in the circuit at one end of each magnetically coupled coil?
To indicate the direction of the magnetic flux
What is the reference polarity of the mutual voltage dependent on?
The reference direction of the inducing current and the dots on the coupled coils
In Fig. 5(a), what is the sign of the mutual voltage v2?
- M di1/dt
What is the total inductance of the coils in Fig. 6(a)?
L1 + L2 + 2M
What is the significance of the dot convention in coupled coils?
It determines the polarity of the mutual voltage
What is the relationship between the direction of the inducing current and the polarity of the mutual voltage?
The direction of the inducing current determines the polarity of the mutual voltage
What is the application of the dot convention in Fig. 5?
To determine the polarity of the mutual voltage
What is the purpose of the dot convention in mutual inductance?
To determine the polarity of the mutual voltage
What is the unit of measurement for mutual inductance?
Henrys (H)
What is the condition for mutual coupling to exist?
The inductors are in close proximity and the circuits are driven by time-varying sources
What is the polarity of the mutual voltage M di/dt?
May be negative or positive
What is the purpose of the dot convention in circuit analysis?
To determine the polarity of the mutual voltage
What is the effect of a time-varying current in another circuit on a coil?
It induces a voltage in the coil
What is the relationship between M12 and M21?
M12 = M21
Why is it difficult to determine the polarity of the mutual voltage M di/dt?
Because four terminals are involved
What is the effect of mutual inductance on the behavior of inductors?
It produces a voltage in reaction to a time-varying current
What is the term for the inductance of an inductor due to the current flowing through it?
Self-inductance
When two coils are in close proximity, what is the result of the magnetic flux emanating from one coil?
Magnetic coupling between the coils
What is the term for the inductance of one coil with respect to another coil?
Mutual inductance
According to Faraday's law of induction, what is the cause of the voltage induced in a coil?
A changing magnetic field
What is the component of the magnetic flux that links both coils?
Ø12
What is the voltage induced in coil 2 due to the current flowing in coil 1?
M12 di1/dt
What is the relationship between the magnetic flux and the current flowing through a coil?
The magnetic flux is proportional to the current
What is the direction of the induced voltage in a coil due to a changing magnetic flux?
In the opposite direction to the changing magnetic flux
Study Notes
Mutual Inductance
- Mutual inductance (M) is the property of an inductor to produce a voltage in reaction to a time-varying current in another inductor near it.
- Mutual inductance is measured in henrys (H) and is always a positive quantity.
- The mutual voltage (M di/dt) can be negative or positive, depending on the orientation of the coils and the direction of the current.
Mutual Inductance Between Two Coils
- The mutual inductance of coil 1 with respect to coil 2 is denoted as M12.
- The mutual inductance of coil 2 with respect to coil 1 is denoted as M21.
- M12 and M21 are equal, and the mutual inductance between the two coils is referred to as M.
Dot Convention
- The dot convention is used to determine the polarity of the mutual voltage.
- A dot is placed in the circuit at one end of each of the two magnetically coupled coils to indicate the direction of the magnetic flux.
- The dot convention is used in conjunction with Lenz's law and the right-hand rule to determine the polarity of the mutual voltage.
Application of Dot Convention
- The dot convention is used to determine the polarity of the mutual voltage in coupled coils.
- The polarity of the mutual voltage depends on the reference direction of the inducing current and the dots on the coupled coils.
- Examples of the application of the dot convention are illustrated in Fig. 5.
Coupled Coils in Series
- The dot convention can be used to determine the total inductance of coupled coils in series.
- The total inductance is given by Eq. (18) and Eq. (19) for series-aiding and series-opposing connections, respectively.
Analysis of Circuits Involving Mutual Inductance
- The dot convention is used to determine the polarity of the mutual voltage in circuits involving mutual inductance.
- Examples of analyzing circuits involving mutual inductance are illustrated in Fig. 7.
Learn about mutual inductance, its measurement, and its effects on coils. Understand how it produces voltage in response to time-varying current.
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