A inductor (sometimes called a solenoid) is made up of an electric conductor wrapped in loops, which are typically many coils and frequently several layers. In the case of a DC circuit the current I that flows through the coil creates an induction magnetic field B, whose intensity ɸ within it is proportional to current: ɸ=LI. This proportionality coefficient L can be described as the induction coefficient or the inductance for the coil (the measure of inductance is called the henr). It is directly related to the ratio of turn as well as the cross-sectional size of the coil and ininversely proportional to the length of the coil. An increase of multiples on the amount of inductance a particular coil could be achieved by using an ferromagnetic core (e.g. iron). Inductor with a core which forms an enclosed magnetic circuit are even more inductor-friendly. In the ideal case of inductance (zero resistance) in the DC circuit it is evident that the drop in voltage across the coil similar to that of a rectilinear conducting is incredibly small and is a shorter circuit within the circuit. The alternating current that flows through the coil results in changes of the magnetic field surrounding the coil. According to Faraday’s Law, the magnetic field changes cause an electromotive force that is added to counteract the changes in the current flowing through the coil’s circuit. This phenomenon is known as self-induction, also known as self-induction.

Self-induction phenomenon is explained by formula:

Or in differential form:

When operating in AC circuits, capacitance as well as inductance act differently in relation to resistance. In the case of resistance, as per Ohm’s law:

flowing through resistor R is directly proportional to the voltage at its ends:

and the proportionality factor is the resistance:

U = IR

The equation is valid for both instantaneous voltages and currents:

as well as amplitudes:

or effective values.

In the case of capacitance and inductance the current that flows through them is also dependent on voltage, however both of them cause the phase shift φ to shift between current and voltage. The current that flows through a capacitor is ahead of the voltage of the capacitor by π/2. For inductance, the current is delayed in relation to the voltage by π/2.

A quantity characterizing the relationship between current and voltage in alternating current circuits

circuits is called the slope, which can be expressed by the formula:

where X is referred to as the reactance. This number is the resistance exhibited by capacitive and inductive components and inductive elements in the alternating currents of the specific frequency ω.

In order for current to flow within a circuit, the voltage uL that is applied from the outside must be balanced with that of the electromotive force. This implies that the voltage of uL must be identical and opposite to SEM eL all the time. This force is at its highest value when the change rate of the current is highest.

This occurs when the current waveform changes direction (crosses the time axis passing through the zero value). As a result, the voltage uL on the inductor in ac circuit, is shifted in phase with respect to the electromotive force eL by an angle π [rad] = 180, overtaking the current (i) flowing in the circuit by an angle π/2 [rad]= 90.

The angle π/2 is the angle of the phase shift of the voltage uL on the inductor with respect to the current i. The voltage uL at the coil terminals can be expressed by the equation:

The power is able to take into account both negative and positive values and fluctuates with time at twice the rate of the voltage and current. This implies that a perfect inductor pulls electricity from a source over the time period of a specific time and then returns this energy to the source in a different time frame. When the time span during which the instantaneous magnitude of the electrical current is increased it is used to generate magnetic fields (the device stores the energy). In the interval during where the amount of current drops, energetic energy that is stored within the field of magnetic flux released back back to the source. The energy generated by the movement of the current through an ideal inductor in ac circuit is known as reactive inductive power. It is expressed as rms values using the formula

The unit of inductive reactive power is the var [var].

References:

http://www.zspgrot.edu.pl/www_mechatronika/files/technik.mechatronik_311-50-_o1.04_u.pdf

http://fizyka.ur.krakow.pl/cwicz36.pdf