When an emf is produced in a coil because of the change in current in a coupled coil , the effect is called mutual inductance. The emf is described by Faraday's law and it's direction is always opposed the change in the magnetic field produced in it by the coupled coil (Lenz's law ). The induced emf in coil 1 is due to self inductance L.
As an inductor, we would expect this iron-core coil to oppose the applied voltage with its inductive reactance, limiting current through the coil as predicted by the equations XL = 2πfL and I=E/X (or I=E/Z). For the purposes of this example, though, we need to take a more detailed look at the interactions of voltage, current, and magnetic flux in the device.
The first coil has N1 turns and carries a current I1 which gives rise to a magnetic field 1BG. Since the two coils are close to each other, some of the magnetic field lines through coil 1will also pass through coil 2. Let
21Φ denote the magnetic flux through one turn of coil 2 due to I1. Now, by varying I1 with time, there will be an induced emf associated with the changing magnetic flux in the second coil:
If the secondary coil is attached to a load that allows current to flow, electrical power is transmitted from the primary circuit to the secondary circuit. Ideally, the transformer is perfectly efficient; all the incoming energy is transformed from the primary circuit to the magnetic field and into the secondary circuit. If this condition is met, the incoming electric power must equal the outgoing power:
Few ideal versions of human constructions exist, and the transformer offers no exception. An idealtransformer is based on very simple concepts, and a large number of assumptions. This is thetransformer one learns about in high school.Let us take an iron core with infinite permeability and two coils wound around it (with zeroresistance), one with N 1 and the other with N 2 turns, as shown in figure 3.2. All the magnetic flux is to remain in the iron. We assign dots at one terminal of each coil in the following fashion: if the flux...
Mutual inductance is a mysterious quantity that we learn about when we study transformer models, but how to measure it is rarely discussed in the literature. It's common knowledge that inductance adds in series. For example, if inductor A is 2uH and inductor B is 3uH, if you connect them in series, then the total inductance is 5uH.
In the most general case, inductance can be calculated from Maxwell's equations. Many important cases can be solved using simplifications. Where high frequency currents are considered, with skin effect, the surface current densities and magnetic field may be obtained by solving the Laplace equation. Where the conductors are thin wires, self inductance still depends on the wire radius and the distribution of the current in the wire. This current distribution is approximately constant (on the surface or in the volume of the wire) for a wire radius much smaller than other length scales.
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