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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.
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
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 ).
The constitutive equation describes the behavior of an ideal inductor with inductance , and without resistance, capacitance, or energy dissipation. In practice, inductors do not follow this theoretical model; real inductors have a measurable resistance due to the resistance of the wire and energy losses in the core, and parasitic capacitance ...
An interesting point to note is the fact that the measured self-inductance of the coil does not change even on taking dielectric loss within the capacitor into account. Another advantage of using this modified bridge is that unlike the variable capacitor used in Maxwell bridge , it makes use of a fixed capacitor which is relatively quite cheaper.
Toroidal transformer - the core is in the shape of a toroid. This is a commonly used shape as it decreases the leakage flux, resulting in less electromagnetic interference. Induction coil or trembler coil - an early transformer which uses a vibrating interrupter mechanism to break the primary current so it can operate off of DC current.
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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.