Each coil shows a varying resistance in alternating current circuits in direct proportion to the frequency. This resistance is called inductive recess. Inductive reactance Indicated by XL, its unit is Ohm (Ω).
The inductive reassurance of a coil depends on the frequency of the voltage applied, since the reassurance is directly proportional to the frequency.
So far we have looked at the behavior of inductors connected to DC sources, and so far we know that when a DC voltage is applied to an inductor, the growth of the current is not instantaneous, but is determined by the self-induced inductors.
We also found that the inductor current continued to rise after five time constants until it reached its maximum stable state. The maximum current flowing from an inductive coil is limited only to the resistant part of the coil windings in the gen of Ohm, and as we know from the Ohm law, this is determined by the ratio of voltage to current, V/R.
When ac voltage is applied to an inductor, the flow of the current behaves very differently from the dc voltage applied. The effect of a sinusoidal feed produces a phase difference between voltage and current waveforms. Now in an AC circuit, the contrast to the current flow through the coil windings depends not only on the inducing of the coil, but also on the frequency of the AC waveform.
Resistance to current flowing from a coil in an AC circuit is determined by the AC resistance of the circuit, more commonly known as Impedance (Z). But resistance is always associated with DC circuits, so the term Reacktans is often used to distinguish DC resistance from AC resistance.
Just like resistance, the value of the reassurance is measured in Ohm, but the X symbol is given to distinguish it from a fully resistant value.
Since the component we are interested in is an inductor, the colorance of an inductor is therefore called "Inductive Reactance". In other words, when used in an AC circuit, the electrical resistance of an inductor is called Inductive Colorance.
Inductive Reaccountance, given the XL symbol, is a feature in an AC circuit that opposes the change in current. In our training on Capacitors in AC Circuits, we have seenthat the current ICin a fully capacitive circuit advances the voltage by 90 o. The opposite is true in a fully inductive AC circuit, current ILdelays the applied voltage by 90o or (π/2 rads)
In the fully inductive circuit above, the inductor is directly connected to the AC supply voltage. As the supply voltage increases and decreases with the frequency, the self-induced backend in the coil increases and decreases due to this change.
We know that this self-induced emk is directly proportional to the rate of change of the current passingthrough the coil, and that the feed voltage is greatest when it switches from positive half-cycle to negative half-cycle or vice versa.
As a result, the minimum voltage change rate occurs when the AC sine wave intersects at the maximum or minimum peak voltage level. At these positions in the loop, maximum or minimum currents flow through the inductor circuit.
These voltage and current waveforms indicate that the current is 90os behind the voltage for a completely inductive circuit. Likewise, we can say that the voltage flows 90o'o. In both cases, the general expression is the delay of the current, as shown in the vector diagram. Here the current vector and voltage vector are shown as 90o displaced. The current lags behind the tension.
We can also write this expression as VL = 0o and I L = -90 o accordingto the VL voltage. If the voltage waveform is classified as a sinus wave, the current can be classified as IL negative cosine and at any given time we can define the value of the current as follows:
Where: ω is in radians per second and t is in seconds.
Since the current is always 90osci behind the voltage in a completely inductive circuit, we can knowing the phase of the voltage and find the phase of the current, or vice versa. So if we know the value of VL,ILhas to delay90 o. Similarly, if we know the value of IL,then VL should therefore be 90o ahead. Then, in an inductive circuit, the ratio of this voltage to the current will produce an equation that defines the Inductive Rectal of the coil, XL.
For inductive recess we can rewrite the equation above in a more familiar format that uses the normal frequency of the feed instead of the angular frequency in radians, ω, and this is given as follows:
Where: ε Is frequency and L is inductive of coil and 2ππ = ω.
If any of the above inductive rectance equation, Frequency or Inductanc is increased, it can be seen that the overall inductive reassurance value will also increase. As the frequency approaches forever, the coloring of the inductors will increase forever, acting as an open circuit.
However, as the frequency approaches zero or DC, the coloring of the inductors will decrease to zero, acting as a short circuit. This means that inductive reactance is "proportional" to the frequency.
In other words, inductive reassurance increases with frequency, resulting in XL being small at low frequencies and XL high at high frequencies, and this is shown in the following graph:
The inclination indicates that the "Inductive Reactance" of an inductor increases as the feeding frequency on it increases.
Therefore, Inductive Reactance is proportional to frequency: ( XL α ε )
In DC we can see that an inductor has zero recess (short circuit), a high frequency inductor has infinite colorance (open circuit).
Inductive Reactance Sample 1
A 100V, 50Hz feed is connected to a 150mH induced and zero-resistant coil. Calculate the inductive coloract of the coil and the current passing through it.
Serial LR Circuit in AC Circuits
Until now we have considered a completely inductive coil, but it is impossible to have a pure inductive rather than a pure inductive, since all coils, relays or solenoids will have a certain amount of resistance, no matter how small the coil turns of the wire used. Then we can think of our simple coil as a series of induced resistance.
In an AC circuit that contains both inducing, L and resistance, voltage, V, two component voltages, VR and VLwill be the phaser sum. This means that the current flowing from the coil will still lag behind the voltage, but will be less than 90o,depending on the VR and VL values.
The new phase angle between voltage and current is known as the phase angle of the circuit and is indicated by the Greek symbol phi, Φ.
A reference or common component must be present to create a vector diagram of the relationship between voltage and current. In a serially connected R-L circuit, the current is common because the same current passes through each component. The vector for this reference quantity is usually drawn horizontally from left to right.
From our tutorials on resistors and capacitors, we know that the current and voltage in a resistant AC circuit are both "in-phase" and the vector is drawn on top of each other to scale on vr's current or reference line.
We also know from above that in a completely inductive circuit, the current "outperforms" the voltage, and therefore the vector, VL, can be drawn 90os ahead of the current reference and on the same scale as the VR.
In the vector diagram above, it can be seen that the OB line represents the existing reference line, the OA line is the voltage of the resistant component and is in the same phase as the current. The OC line indicates the inductive voltage 90 o in front of the current, soit can be seen that the current is 90 o behindthe voltage. Line OD gives us the voltage obtained or supplied throughout the circuit. The tension triangle is derived from the Pythagorean theorem and given as follows:
In a DC circuit, the ratio of voltage to current is called resistance. However, in an AC circuit, this ratio is known as Impedance, Z, and the units are still in Ohm. Impedance is the total resistance to current flow in an "AC circuit" containing both resistance and inductive reactas.
If we divide the edges of the above voltage triangle into the current, another triangle is obtained, the edges representing the resistance, reactance and impedance of the coil. This new triangle is called the "Impedance Triangle".
Inductive Reactance Sample 2
The resistance of a solenoid coil is 30 Ohm and its inducing is 0.5H. If the current passing through the coil is 4 amps:
a) If the frequency is 50Hz, what is the supply voltage?
b) What is the phase angle between voltage and current?
POWER Triangle of AC Inductor
There is another type of triangular configuration that we can use for one inductive circuit, and that is the "Power Triangle". Power in an inductive circuit is known as the Var symbol, measured in reactive power or volt-amp reagent, volt-amp. In an RL series AC circuit, the current is as far behind the feed voltage as the Φangle.
In a fully inductive AC circuit, the current will have a phase difference of exactly 90 tothe supply voltage. Therefore, the total reactive power consumed by the coil will be equal to zero, since any power consumed by the self-induced emf power produced is canceled. In other words, the net power in watts consumed by a pure inductor at the end of a full cycle is zero, since the energy is both taken from the source and returned to it.
The Reactive Power of a coil, ( Q ) can be given as follows: I2 x XL (similar to I2R in a DC circuit). Next, the three sides of a power triangle in an AC circuit are represented by the power (S), actual power (P) and reactive power (Q), which appear as shown.
Keep in mind that a real inductor or coil will consume power in watts due to the resistance of windings that form an impedance, Z.