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reactance

Reactance, denoted X, is a form of opposition that electronic components exhibit to the passage of alternating current (alternating current) because of capacitance or inductance.  In some respects, reactance is like an AC counterpart of DC (direct current) resistance.  But the two phenomena are different in important ways, and they can vary independently of each other.  Resistance and reactance combine to form impedance, which is defined in terms of two-dimensional quantities known as complex number.

When alternating current passes through a component that contains reactance, energy is alternately stored in, and released from, a magnetic field or an electric field.  In the case of a magnetic field, the reactance is inductive.  In the case of an electric field, the reactance is capacitive.  Inductive reactance is assigned positive imaginary number values.  Capacitive reactance is assigned negative imaginary-number values.

As the inductance of a component increases, its inductive reactance becomes larger in imaginary terms, assuming the frequency is held constant.  As the frequency increases for a given value of inductance, the inductive reactance increases in imaginary terms.  If L is the inductance in henries (H) and f is the frequency in hertz (Hz), then the inductive reactance +jXL, in imaginary-number ohms, is given by:

+jXL = +j(6.2832fL)

where 6.2832 is approximately equal to 2 times pi, a constant representing the number of radians in a full AC cycle, and j represents the unit imaginary number (the positive square root of -1).  The formula also holds for inductance in microhenries (?H) and frequency in MHz (MHz).

As a real-world example of inductive reactance, consider a coil with an inductance of 10.000 ?H at a frequency of 2.0000 MHz.   Using the above formula, +jXL is found to be +j125.66 ohms.  If the frequency is doubled to 4.000 MHz, then +jXL is doubled, to +j251.33 ohms.  If the frequency is halved to 1.000 MHz, then +jXL is cut in half, to +j62.832 ohms.

As the capacitance of a component increases, its capacitive reactance becomes smaller negatively (closer to zero) in imaginary terms, assuming the frequency is held constant.  As the frequency increases for a given value of capacitance, the capacitive reactance becomes smaller negatively (closer to zero) in imaginary terms.  If C is the capacitance in farads (F) and f is the frequency in Hz, then the capacitive reactance -jXC, in imaginary-number ohms, is given by:

-jXC = -j (6.2832fC)-1

This formula also holds for capacitance in microfarads (?F) and frequency in megahertz (MHz).

As a real-world example of capacitive reactance, consider a capacitor with a value of 0.0010000 ?F at a frequency of 2.0000 MHz.  Using the above formula, -jXC is found to be -j79.577 ohms.  If the frequency is doubled to 4.0000 MHz, then -jXC is cut in half, to -j39.789 ohms.  If the frequency is cut in half to 1.0000 MHz, then -jXC is doubled, to -j159.15 ohms.

This was last updated in September 2005

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