Explain the term inductive reactance.

Inductive Reactance
Inductive reactance, denoted by XLX_L, is the opposition to the flow of alternating current (AC) provided by an inductor in an AC circuit. It is analogous to resistance in a direct current (DC) circuit, but while resistance opposes the current uniformly, inductive reactance opposes the current based on the frequency of the alternating current.
Explanation:
When an alternating current flows through an inductor, the current creates a changing magnetic field. According to Faraday's Law of Induction, any change in the magnetic field will induce a voltage (also known as electromotive force or emf) in the inductor that opposes the change in current. This opposition to the change in current is what causes the inductive reactance.
The inductor resists the change in the current rather than the flow of current itself, and this resistance increases with the frequency of the AC. Hence, the inductive reactance depends on both the frequency of the AC signal and the inductance of the coil.
Formula for Inductive Reactance:
The inductive reactance is given by:
XL=2πfLX_L = 2 \pi f L
Where:
• XLX_L is the inductive reactance in ohms (Ω\Omega),
• ff is the frequency of the AC in hertz (Hz),
• LL is the inductance of the inductor in henries (H).
Key Points:
• Frequency Dependence: The inductive reactance increases with the frequency of the AC. That is, higher frequency currents encounter more opposition from an inductor.
• Inductor Behavior: Inductors behave like resistors in an AC circuit, but the opposition they provide is frequency-dependent.
• Phase Difference: The current in an inductor lags the voltage by 90∘90^\circ. This means the voltage and current are not in phase, and this phase difference is one of the distinguishing features of inductive reactance.
Physical Interpretation:
• At low frequencies, the inductive reactance is low, meaning the inductor provides less opposition to the current.
• At high frequencies, the inductive reactance increases, meaning the inductor opposes the flow of current more strongly.
Example:
If an inductor with an inductance of 0.1 H is connected to an AC circuit operating at 50 Hz, the inductive reactance XLX_L would be:
XL=2π×50×0.1=31.4 ΩX_L = 2 \pi \times 50 \times 0.1 = 31.4 \, \Omega
Thus, the inductor will provide 31.4 ohms of opposition to the AC current at this frequency.
Conclusion:
Inductive reactance is a crucial concept in AC circuits that describes the opposition an inductor provides to the current. It increases with both the frequency of the alternating current and the inductance of the inductor.