Reactance

In electronics and electrical engineering, reactance is the opposition offered to the passage of alternating current through inductors (coils) and capacitors, it is measured in ohms and its symbol is Ω. Together with the electrical resistance, they determine the total impedance of a component or circuit, in such a way that the reactance (X) is the imaginary part of the impedance (Z) and the resistance (R) is the real part, according to the equality:

${displaystyle Z=R+jX,}$

The reactance is used to calculate the amplitude and phase changes of the sinusoidal alternating current that passes through an element of the circuit. Like resistance, the reactance is measured in ohm, with positive values that indicate reagent inductive and negatives indicating reactive capacitive. It denotes with the symbol ${displaystyle X}$. An ideal resistance has zero reaction, while ideal inducers and capacitors have zero resistance. As the frequency increases, inductive reactance increases and capacitive decreases.

Comparison with resistance

Reactance is similar to resistance in that higher reactance leads to smaller currents for the same applied voltage. Furthermore, a circuit made entirely of elements that have only reactance (and no resistance) can be treated in the same way as a circuit made entirely of resistors. These same techniques can be used to combine reactance elements with resistance elements, but complex numbers are usually required. This is covered later in the impedance section.

However, there are several important differences between reactance and resistance. First, the reactance shifts the phase so that the current through the element is shifted by a quarter cycle with respect to the phase of the applied voltage across the element. Second, energy is not dissipated in a purely reactive element, it is stored. Third, the reactances can be negative so that they "cancel out" each other. Finally, major circuit elements that have reactance (capacitors and inductors) have a reactance that is dependent on frequency, unlike resistors that have the same resistance for all frequencies, at least in the ideal case.

The term reactance was first suggested by the French engineer M. Hospitalier in L'Industrie Electrique on May 10, 1893. It was officially adopted by the American Institute of Electrical Engineers in May 1894.

Types of ballasts

When alternating current flows through one of the two elements that have a reactance, the energy is alternately stored and released in the form of a magnetic field, in the case of coils, or an electric field, in the case of capacitors. This produces a lead or lag between the current wave and the voltage wave. This phase shift decreases the power delivered to a resistive load connected after the reactance without consuming energy.

If a vector representation of the inductive and capacitive reactance is performed, these vectors should be drawn in the opposite direction and on the imaginary axis, since the impedances are calculated as ${displaystyle {j}X_{L},!}$ and ${displaystyle {-j}X_{C},!}$ respectively.

However, real coils and capacitors have an associated resistance, which in the case of coils is considered in series with the element, and in the case of capacitors in parallel. In those cases, as already indicated above, the total impedance (Z) is the vector sum of resistance (R) and reactance (X).

In formulas:

${displaystyle {tilde {Z}}=R+jX,}$

where

${displaystyle j}$ is the imaginary unit

${displaystyle {X}=(X_{L}-X_{C})}$ It's the reaction in ohms.

ω is the angular velocity to which the element is subjected, L and C are the values of inductance and capacity respectively.

Depending on the value of the energy and the reactance, it is said that the circuit presents:

• Yeah. ${displaystyle scriptstyle {X/2005}}$, reactance inductive ${displaystyle (X_{L}schoolX_{C})}$.
• Yeah. ${displaystyle scriptstyle {X=0}}$, there is no reactance and impedance is purely resistive ${displaystyle (X_{L}=X_{C}}}}$.
• Yeah. ${displaystyle scriptstyle {X discount}}$, reactance capacitive ${displaystyle (X_{C}{C})}$.

Capacitive reactance

La capacitive reagent represented by ${displaystyle X_{C},!}$ and its value is given by the formula:

${displaystyle X_{C}={frac {1}{omega C}}}={frac {1}{2pi fC}}{,!}$

in which:

${displaystyle X_{C},!}$ = capacitive effectiveness in ohmos.
${displaystyle C,!}$ = Electric capacity in lighthouses.
${displaystyle f,!}$ = Frequency in hertz.

${displaystyle omega !}$ = Angular velocity.

Inductive reactance

Inductive reactance is a property exhibited by an inductor, and inductive reactance exists based on the fact that an electric current produces a magnetic field around it. In the context of an alternating current circuit (although this concept applies anytime the current is changing), this magnetic field is constantly changing as a result of the current oscillating back and forth. It is this change in the magnetic field that induces another electric current to flow in the same wire (electromagnetic counter-force), in such a direction that it opposes the flow of the current originally responsible for producing the magnetic field (known as Law of Lenz). Therefore, inductive reactance is an opposition to the change of current through an element.

For an ideal inductor in an alternating current circuit, the inhibitory effect on the change in current flow results in a lag, or phase shift, of the alternating current with respect to the alternating voltage. Specifically, an ideal inductor (without resistance) will cause the current to lag the voltage by a quarter of a cycle, that is, 90°.

In electric power systems, inductive reactance (and capacitive, although inductive is more common) can limit the power capacity of an AC transmission line, because power is not fully transferred when voltage and current are out of phase (detailed above). That is, the current will flow in a phased system, but the real power will not be transferred at certain moments, because there will be points in which the instantaneous current is positive while the instantaneous voltage is negative, or vice versa, which implies a transfer of power negative. Therefore, actual work is not done when the power transfer is 'negative'. However, current continues to flow even when a system is out of phase, causing transmission lines to heat up due to current flow. Consequently, transmission lines can only get so hot (or else they would physically sag too much, due to heat expanding metal transmission lines), so transmission line operators have a "ceiling" in the amount of current that can flow through a given line, and excessive inductive reactance can limit the power capacity of a line. Power providers use capacitors to shift phase to minimize losses, depending on usage patterns.

Inductive reagent ${displaystyle X_{L}}$ is proportional to the sinusoidal signal frequency ${displaystyle f}$ and inductance ${displaystyle L}$which depends on the physical form of the inducer:

${displaystyle X_{L}=omega L=2pi fL}$.

The average current circulating through inductance ${displaystyle L}$ in series with a sinusoidal RMS alternate voltage source ${displaystyle A}$ and frequency ${displaystyle f}$ equals:

${displaystyle I_{L}={frac {A}{omega L}}}={frac {A}{2pi fL}}}} !$

Because a square wave has multiple amplitudes in the sinusoidal harmonics, the average current that flows through a inductance ${displaystyle L}$ in series with an alternating tension source of RMS width ${displaystyle A}$ and frequency ${displaystyle f}$ equals:

${displaystyle I_{L}={Api ^{2} over 8omega L}={Api over 16fL}}}$

so it seems that the inductive reactive to a square wave is approximately 19% smaller ${displaystyle X_{L}={16 over pi }fL}$ that the reactance to the sinusoidal wave of CA.

Any thin-size conductor has inductance; inductance becomes greater by multiple turns in an electromagnetic coil. [ Faraday's law of electromagnetic induction gives the electromagnetic counterforce. ${displaystyle {mathcal {E}}}$ (current pressure) due to a magnetic flow density change rate ${displaystyle scriptstyle {B}}$ through a current loop.

${displaystyle {mathcal {E}}=-{frac {dPhi _{B}{dt}}}}{d}}}}}$

For an inducer formed by a coil ${displaystyle N}$ loops this gives:

${displaystyle {mathcal {E}}=-N{frac {dPhi _{B}}{d}}{d}}}}{d}}}$.

The counter-emf is the source of the opposition to current flow. A constant DC current has zero rate of change, and you see an inductor as a short circuit (usually made of a material with a low resistivity). An alternating current has a time-averaged rate of change that is proportional to frequency, this causes the inductive reactance to increase with frequency.

Inductive reagent is represented by ${displaystyle X_{L}}$ and its value is given by:

${displaystyle X_{L}=omega L=2pi fL}$

in which:

${displaystyle X_{L}}$ = Inductive reaction in ohms.

${displaystyle L}$ = Inductance in hay.

${displaystyle f}$ = Frequency in hertz.

${displaystyle omega }$ = Angular velocity.