FAQ
TL;DR: A 1 mH air-core coil shows only 0.314 Ω reactance at 50 Hz, so “L = √(Z² − R²)/(2πf)” [Elektroda, rystor, post #523144] is reliable only when Z ≫ R. Pick ≥10 kHz test signals or use geometry formulas to stay within ±5 % error.
Why it matters: These quick checks help hobbyists and RF designers size coils without an expensive LCR meter.
Quick Facts
• µ₀ (vacuum permeability) = 4π × 10⁻⁷ H/m [Elektroda, konstruktor, post #522305]
• Single-layer air coil: L(mH)=0.08·d²·n² / (3d+9l), d & l in cm [Elektroda, stasiekm, post #523047]
• Xₗ of 1 mH: 0.314 Ω at 50 Hz, 6.28 Ω at 1 kHz, 62.8 Ω at 10 kHz (calculated)
• Handheld LCR meters start ≈ US$30, 0.5 % typical accuracy [OWON datasheet, 2023]
• Error >50 % if R > 0.7 Z in impedance method (derived from formula)
How do I calculate inductance when I know turns, diameter and length?
Use the single-layer air-core formula: L(mH)=0.08·d²·n² / (3d+9l) with d and l in cm. For multi-layer coils add 10a (winding thickness) to the denominator [Elektroda, stasiekm, post #523047] Doubling turns increases L fourfold—a useful design shortcut.
Can I measure inductance without knowing the coil’s geometry?
Yes. 1 Measure DC resistance R. 2 Apply AC, note RMS voltage U and current I; Z = U/I. 3 Compute L = √(Z²–R²)/(2πf). This “technical method” needs Z ≫ R for accuracy [Elektroda, rystor, post #523144]
Why does the square-root term become negative in my calculation?
A negative value means R ≥ Z, so the reactive part is buried under resistance. Increase test frequency or lower wire resistance until Z > 1.4 R (≥50 % margin) [Elektroda, krakeen, post #523413]
Is 50 Hz mains suitable for the impedance method?
Rarely. A 1 mH coil has only 0.314 Ω reactance at 50 Hz, comparable to wire resistance, causing >30 % error [Elektroda, konstruktor, post #524521] Use audio-range signals (>1 kHz) or a signal generator.
How does adding a series resistor help?
It limits current and allows voltage-divider math: L = [(R1+R_L)·U_L – R_L·U_in]/[2πf·(U_in–U_L)] [Elektroda, konstruktor, post #524851] Choose R1 ≈ (2–5)·X_L for stable readings.
Quick 3-step: measure L with a series resistor and two voltmeters
- Wire R1 in series with the unknown coil.
- Feed a sine wave (≥1 kHz); record U_in and U_L.
- Insert values into the divider formula above to solve for L. Average three runs for <5 % spread.
What’s an LC-oscillator trick for coils?
Build a Colpitts or Hartley oscillator with a known capacitor C. Measure oscillation frequency f with a counter; compute L = 1/(4π²f²C) [Elektroda, lechoo, post #986710] This method gives ±2 % if C’s tolerance is known.
How thick should the winding wire be?
Keep current density ≤4 A/mm² for power coils; RF coils often use 0.5–1 mm enamel wire to reduce skin effect above 10 MHz [RS Handbook, 2021]. “The top wire thickness is out of the question” noted one user [Elektroda, jarek92, post #3806035]
What edge cases make these formulas fail?
Edge failures include: very short coils (l<0.3·d) where end effects dominate, ferrite near the coil altering µ, and high-frequency skin effect reducing effective turns. Always validate with an LCR meter if precision <1 % is needed.
Are there low-cost tools to automate these tests?
Yes. USB LCR-T4 testers under US$30 cover 20 Hz–300 kHz with 0.5 % spec [OWON datasheet, 2023]. Smartphone-scope combos plus a small signal generator also work for hobby labs.
How does frequency affect measured inductance?
True inductance is constant, but parasitic capacitance causes self-resonance. Above f_sr, apparent L falls and can even go negative (capacitive). Keep test frequency below 0.3·f_sr for valid results [Agilent AppNote E4980, 2012].
What if I only have a multimeter and DC supply?
You can’t measure L directly. However, by charging a known capacitor with the coil in series and timing the transient, you can back-solve L, but accuracy is poor (±20 %). Better borrow an LCR bridge, as krakeen concluded [Elektroda, krakeen, post #527983]
