# Electromagnetic inductance -- Mutual inductance

• dipankar.a511
Es = Is Zs + Ip Zm where Zp and Zs are the primary and secondary coil impedance, respectively, and Zm is the mutual impedance. Although, a full understanding of the energy transfer between the primary and secondary coils requires a more complex analysis. So, in summary, the change in current in the primary coil results in an induced emf in the secondary coil, causing a growth in current in the secondary coil and creating a magnetic field. This process continues in a cyclical manner, with energy being transferred between the coils. However, a more detailed analysis is necessary to fully understand the energy transfer.
dipankar.a511
I know that- The change in current of primary coil changes the magnetic flux linked with the secondary coil and this an emf will be induced in secondary coil (which also has an inductor in the circuit) so current grows in secondary coil and the current in secondary coil produces magnetic field.
Q.Is it correct to say that the growing current (inductor in the secondary will resist the change in current) in secondary coil will result in a change in magnetic flux (due to magnetic field of secondary coil) linked with primary coil and an emf will be induced by secondary coil in primary and this will continue so on and so forth like two mirrors opposing each other and making infinite images or will the cycle get over just at secondary coil. Is this reasoning flawed in terms of law of conservation of energy and lenz's law?

It's a continual process, not an X effects Y which then affects X which then affects Y, etc. Neither the current nor the magnetic field flux can increase in strength instantly.

Right, like Drakkith said. To solve it precisely, the trick is to set up the differential equations correctly from the beginning. (In the case of a spice simulation, this happens automatically, assuming you've set up your components correctly.) The differential equations will have terms for both self inductance and mutual inductance of the coils involved. Then a single solution leads to a closed-form answer.

By the way, depending on your level of coursework, you might not be expected to solve the differential equations in this manner. It's not especially critical in certain circumstances anyway, such as when the coupling is weak, or say, when the current through secondary coil isn't that much. So unless your coursework/instructor expects you solve the full differential equations, this may not be that important. Just keep it in mind for later if you study more advanced circuit theory.

On a different yet related note, while most simple transformers might couple symmetrically in either direction, there exist passive components out there such as "duplexers," "circulators," "isolators" and "directional couplers" that tend to couple the signal in one direction only, but not the reverse (or one port to another port, but not the same ports in reverse).

Last edited:
dipankar.a511 said:
I know that- The change in current of primary coil changes the magnetic flux linked with the secondary coil and this an emf will be induced in secondary coil (which also has an inductor in the circuit) so current grows in secondary coil and the current in secondary coil produces magnetic field.
Q.Is it correct to say that the growing current (inductor in the secondary will resist the change in current) in secondary coil will result in a change in magnetic flux (due to magnetic field of secondary coil) linked with primary coil and an emf will be induced by secondary coil in primary and this will continue so on and so forth like two mirrors opposing each other and making infinite images or will the cycle get over just at secondary coil. Is this reasoning flawed in terms of law of conservation of energy and lenz's law?
It is probably easiest to consider the situation under steady state sinusoidal conditions. You don't have to keep going backwards and forwards. Then Ep = Ip Zp + Is Zm

## What is electromagnetic inductance?

Electromagnetic inductance is the phenomenon where an electric current is induced in a conductor when it is placed in a changing magnetic field.

## How is electromagnetic inductance related to mutual inductance?

Electromagnetic inductance and mutual inductance are closely related. Mutual inductance refers to the induction of an electric current in one coil due to the changing magnetic field of a nearby coil. It is a form of electromagnetic inductance.

## What factors affect mutual inductance?

The factors that affect mutual inductance include the number of turns in the coils, the distance between the coils, the orientation of the coils, and the relative permeability of the materials in the coils.

## What is the unit of measurement for mutual inductance?

Mutual inductance is typically measured in henrys (H), which is equivalent to volts per ampere (V/A).

## How is mutual inductance used in practical applications?

Mutual inductance has many practical applications, including in transformers, motors, generators, and wireless charging devices. It is also used in various types of electronic circuits, such as filters and oscillators.

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