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Impedance of an Inductor
An inductor's impedance is purely imaginary and increases linearly with angular frequency.
Interpretation
Impedance of an inductor is Z_L = jωL, where ω = 2πf. It increases linearly with frequency.
Inductors oppose changes in current, so their impedance is higher at higher frequencies.
Example: L=10mH, f=50Hz (ω≈314) → Z_L = j314 × 0.01 = j3.14Ω.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| ZL | Inductive impedance | Ω |
| j | Imaginary unit (√−1) | — |
| ω | Angular frequency (2πf) | rad/s |
| L | Inductance | H |
What it means
The impedance of an inductor is Z_L = jωL, where ω = 2πf is the angular frequency, and L is the inductance. The impedance is purely imaginary, indicating a 90° phase shift where the voltage leads the current. The magnitude |Z_L| = ωL increases linearly with frequency. At DC (ω=0), an inductor behaves as a short circuit (Z=0). At high frequencies, it behaves as an open circuit. This frequency‑dependence is used in filters (low‑pass, high‑pass) and in chokes to block AC while passing DC. Inductors are also used in tuned circuits and transformers. Example: An inductor L=10mH at f=50Hz (ω≈314 rad/s) has Z_L = j314*0.01 = j3.14Ω. At 1kHz (ω=6283), Z_L = j62.83Ω, indicating a larger opposition to current.
Worked example
Impedance of an Inductor – Practical Example
Real‑World| Parameter | Value |
|---|---|
| L | 10 mH = 0.01 H |
| f | 1 kHz = 1000 Hz |
| Formula | ZL = j·ω·L, ω = 2πf |
Common mistakes
- ω: Angular frequency (rad/s) – not frequency in Hz.
- Phase shift: Voltage leads current by 90° (inductor).
- Magnitude: |Z_L| = ωL – increases with frequency.
- Units: Ohms.
- Ideal: Assumes no resistance in the inductor.
Applications
The impedance of an inductor is Z_L = jωL, increasing linearly with frequency. Inductors oppose changes in current, so they appear as high impedance at high frequencies and are used in filters and choke coils. Engineers use this formula to design low‑pass filters, to block high‑frequency noise, and to tune resonant circuits. In power electronics, inductor impedance determines the current ripple in converters. By understanding the frequency dependence, professionals can design circuits that exploit inductive behaviour for signal conditioning and power supply regulation. This impedance is also used in matching networks for RF circuits.
- Filter design (low‑pass, high‑pass, band‑stop)
- Power supply ripple rejection (inductive filtering)
- RF tuning circuits (oscillators, matching networks)
- Choke coils for EMI suppression
- Educational understanding of inductive reactance
Frequently Asked Questions
The impedance of an inductor is Z_L = jωL, purely imaginary and proportional to frequency.
+90° (voltage leads current by 90°).
Z_L increases with frequency (Z_L ∝ f). At DC (f=0), Z_L = 0 (short).
|Z_L| = ωL = 2πfL.
Q = I² ωL = V² / (ωL) (VAR).
Series: L_total = L₁ + L₂; Parallel: 1/L_total = 1/L₁ + 1/L₂.
I = V / (jωL), lagging voltage by 90°.
Filters, chokes, transformers, and tuned circuits.
Real inductors have series resistance, parasitic capacitance, and core losses.
Common errors include: 1) forgetting the j term, 2) using the wrong frequency, 3) applying to DC (where it's zero), 4) combining with other impedances incorrectly, and 5) using the wrong units.