Number of turns in the context of "Cycles per second"

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⭐ Core Definition: Number of turns

The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) or to one revolution (symbol rev or r). Common related units of frequency are cycles per second (cps) and revolutions per minute (rpm). The angular unit of the turn is useful in connection with, among other things, electromagnetic coils (e.g., transformers), rotating objects, and the winding number of curves. Divisions of a turn include the half-turn and quarter-turn, spanning a straight angle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.

In the ISQ, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a dimensionless quantity called rotation, defined as the ratio of a given angle and a full turn. It is represented by the symbol N. (See below for the formula.)

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Number of turns in the context of Electromagnetic coil

An electromagnetic coil is an electrical conductor such as a wire in the shape of a coil (spiral or helix). Electromagnetic coils are used in electrical engineering, in applications where electric currents interact with magnetic fields, in devices such as electric motors, generators, inductors, electromagnets, transformers, sensor coils such as in medical MRI imaging machines. Either an electric current is passed through the wire of the coil to generate a magnetic field, or conversely, an external time-varying magnetic field through the interior of the coil generates an EMF (voltage) in the conductor.

A current through any conductor creates a circular magnetic field around the conductor due to Ampere's law. The advantage of using the coil shape is that it increases the strength of the magnetic field produced by a given current. The magnetic fields generated by the separate turns of wire all pass through the center of the coil and add (superpose) to produce a strong field there. The greater the number of turns of wire, the stronger the field produced. Conversely, a changing external magnetic flux induces a voltage in a conductor such as a wire, due to Faraday's law of induction. The induced voltage can be increased by winding the wire into a coil because the field lines intersect the circuit multiple times.

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Number of turns in the context of Winding number

In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that the curve travels counterclockwise around the point, i.e., the curve's number of turns. For certain open plane curves, the number of turns may be a non-integer. The winding number depends on the orientation of the curve, and it is negative if the curve travels around the point clockwise.

Winding numbers are fundamental objects of study in algebraic topology, and they play an important role in vector calculus, complex analysis, geometric topology, differential geometry, and physics (such as in string theory).

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LINKED FROM (PARENTS)
← Electromagnetic coil ← Winding number ← Magnetic coil
LINKS TO (CHILDREN)
Plane angle → Complete angle → Subtended angle → Circle → Pi → Radian → Degree (angle) → Gradian → Angular unit → Frequency → Cycles per second → Revolutions per minute → Electromagnetic coil → Transformer → Winding number → Angle → Right angle → Metric prefixes → International System of Quantities → Dimensionless quantity → Ratio →