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The table below lists formulas for the self-inductance of various simple shapes made of thin cylindrical conductors (wires). In general these are only accurate if the wire radius a {\displaystyle a} is much smaller than the dimensions of the shape, and if no ferromagnetic materials are nearby (no magnetic core ).
Because the toroid is a closed-loop core, it will have a higher magnetic field and thus higher inductance and Q factor than an inductor of the same mass with a straight core (solenoid coils). This is because most of the magnetic field is contained within the core.
Leakage inductance derives from the electrical property of an imperfectly coupled transformer whereby each winding behaves as a self-inductance in series with the winding's respective ohmic resistance constant. These four winding constants also interact with the transformer's mutual inductance. The winding leakage inductance is due to leakage ...
In electrical terms, this means that the self-inductance of the coil is zero. The bifilar coil (more often called the bifilar winding) is used in modern electrical engineering as a means of constructing wire-wound resistors with negligible parasitic self-inductance. [1] Bifilar wound toroidal transformer, also known as a common-mode choke
In a ferromagnetic core inductor, when the magnetic field approaches the level at which the core saturates, the inductance will begin to change, it will be a function of the current (). Neglecting losses, the energy W {\displaystyle W} stored by an inductor with a current I 0 {\displaystyle I_{0}} passing through it is equal to the amount of ...
is the major radius of the toroid, is its minor radius. This formula assumes the turns are evenly spaced and that these turns are small relative to the radius of the coil itself. The output of the Rogowski coil is proportional to the derivative of the wire current.
Thus, for a typical inductance (a coil of conducting wire), the flux linkage is equivalent to magnetic flux, which is the total magnetic field passing through the surface (i.e., normal to that surface) formed by a closed conducting loop coil and is determined by the number of turns in the coil and the magnetic field, i.e.,
In mathematics, a toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. [ 1 ] For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced.