Reactance and Impedance: Components, Formula & Examples

Reactance

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Reactance (X) is defined as opposition to current flow in a circuit due to capacitance, inductance, or both. It is expressed in ohms. Reactance has both magnitude and phase values, and it has two components- inductive and capacitive.

Inductive Reactance

• Inductive reactance (XL) is part of total reactance that is contributed by coils, chokes, etc.
• Any device in whose wire is circularly wounded is an inductor, and inductors tend to oppose any change in current over time.
• This opposition is because the current flowing through an inductor creates a magnetic field. 
• In a DC circuit, the intensity and direction of the magnetic field is constant. Thus, current flows easily through the inductor since it is simply related to the length of wire. 
• In an AC circuit the magnetic field changes constantly with change in magnitude and direction of current flow.
• Inductor passes lower frequencies more readily than higher frequencies.

The opposition to change in current flow is called inductive reactance and is defined by the formula: XL = 2πfL

where,

XL = Inductive reactance in ohms

π = 3.14159(…)

F = Frequency in hertz

L = Inductance in henry.

Capacitive Reactance

• Capacitive reactance (XC) is that part of total circuit reactance due to capacitance.
• Capacitance results in a circuit when two conducting surfaces are held parallel to each other and are separated by a small distance with a non-conducting substance (dielectric). For example: Capacitor. Capacitors, which are voltage limiting devices, tend to oppose voltage change. 
• When a DC current is applied to a capacitor, the capacitor draws a current and charges up to the value of the applied voltage.
• In an AC circuit, current of lower frequency takes more time to charge the capacitor before the voltage reverses polarity and the capacitor begins to discharge.
• Since the capacitor takes more time to charge, less current passes through and thus resulting in more reactance at low frequencies.
• When the frequency is increased, the capacitor discharges faster, allowing more current to flow and thus lower reactance. 

Capacitive reactance thus decreases as frequency increases. The actual value of XC is inversely proportional to that of capacitance. The formula: XC = 1/2\(\pi\)FC

Here,

XC = capacitive reactance (in ohms)
\(\pi\) = 3.14159(…)

F = frequency (in hertz) 

C = capacitance (in farads)

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Impedance

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• Impedance (Z) in an AC circuit is the total opposition to current flow due to resistance and reactance.
• When a circuit is purely inductive (no resistance), XL would represent the total opposition to current flow.
• Here, impedance (Z) and inductive reactance (XL) are same, and are represented by values of the same magnitude with a -90° (minus 90 degree) phase angle (\(\theta\) or theta).
• When a circuit is purely capacitive, the magnitude remains same, except \(\theta\) shifts to +90° (plus 90 degree). 
• The phase of the current is always expressed relative to its voltage (leading or lagging).
• Generally, AC circuits contain elements of resistance, inductance and capacitance.
• Therefore, the impedance is a complex value with magnitude and phase (a vector).

The magnitude portion of impedance in a circuit can be calculated by following formulas.

In a series, circuit impedance is calculated by:

\(Z =\sqrt{R^2 + X^2_T}\)

where X_T = X_L – X_C (X_T is combined circuit reactance).

In a parallel circuit, impedance is expressed by

\(Z =\frac{RX_T}{\sqrt{R^2 + X^2_T}}\)

Here,

\(X_T = \frac{X_L X_C}{X_L -X_C}\)

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Important Questions

1. When hydrogen atom is in its first excited level, its radius, is….
2. When an electron does transition from n=4 to n=2 , then emitted line spectrum will be….​..
3. α -particle consists of….
4. An electron of a stationary hydrogen atom passes from the fifth energy level….
5. Complete the equation for the following fission process…. [NEET 1998]
6. using non-relativistic approach, the speed of electron in this orbit will be…. [NEET 2015]

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Things to Remember

• Phase shift: the current and voltage are out of step with each other
• In a purely inductive or capacitive circuit, when no power is dissipated even though a current is flowing, the current is called a wattless current
• RLC circuits exhibit resonance, i.e., the amplitude of the current is maximum at the resonant frequency.
• In an AC circuit with pure capacitances and pure inductances, there is no power loss. Only resistance dissipates energy in an AC circuit.
• The power rating of components used in ac circuits is its average power rating.

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