Lesson RLC and Filters · RLC parallel and resonance
Parallel resonance
Parallel resonance (anti-resonance) occurs when the inductive and capacitive branch currents cancel. Line current falls to a minimum (ideally just the resistive branch), and impedance rises to a maximum. Same fr = 1/(2π√(LC)) idea as series resonance, but the symptoms flip: high Z, low line current.
IL = IC (ideal)
When the reactive currents cancel:
IT ≈ IR Z ≈ R of the resistive branch (maximum relative to off-resonance)
In a pure L∥C “tank” with no R, ideal line current would approach zero at resonance while a circulating current still flows between L and C.
Circulating current
Energy sloshes between magnetic field (L) and electric field (C). Branch currents can be large even when the line clamp reads little. That surprises techs who only clamp the feeder.
Frequency regions
| Region | Effect on parallel tank |
|---|---|
| Below fr | Often more capacitive or inductive depending on configuration — check branch dominance |
| At fr | Max Z, min line current |
| Above fr | Opposite reactive dominance |
Use fr = 1/(2π√(LC)) for the ideal LC pair.
Series vs parallel resonance contrast
| Series resonance | Parallel resonance | |
|---|---|---|
| Z | Minimum (≈R) | Maximum |
| Line current | Maximum | Minimum |
| Danger mode | Overcurrent / high EL,EC | High circulating current in tank; voltage issues in some drives |
| Classic use | Series tuning | Tank circuits, rejection |
Field relevance
- Tuned circuits and filters
- Interactions between PF capacitors and transformer inductance
- Notch behavior when a parallel resonant path rejects a frequency
Practical caution
Do not assume “low line current means nothing is stressed.” Inside a resonant tank, L and C may still run heavy current. Infrared and individual branch measurements matter.
Numbers you should be able to work cold
Same fr formula as series: fr=1/(2π√(LC)). Difference is symptoms: high impedance to the source, low line current, possible large tank current.
If a helper remembers only one sentence, give them:
Series resonance: max line current. Parallel resonance: min line current.
Tank heating
Infrared on L and C during a “quiet” line-current reading catches circulating energy. Shop filters and harmonic traps deserve that check after unexplained heat.
Notch preview
A parallel resonant arm in series with a signal becomes a notch at fr — Unit 26 uses that idea. Parallel resonance is not only a power curiosity; it is a filter building block.
Field case
Situation. A filter circuit shows almost no current from the source at a particular harmonic frequency, yet the inductor is hot.
What happened. Parallel resonance: source current canceled, circulating current between L and C remained high.
Applied lesson. Clamp both line and tank branch when diagnosing resonant filters or unexplained heating.
### Teaching pause — say this out loud
Before you leave this lesson, explain the main idea to an imaginary first-month helper in under one minute. If you need the book open to do it, reread How it works once more. Field diagnosis only helps after the concept is yours.
Also sketch the key diagram from memory (triangle, wye/delta, filter shape, or charge curve — whichever this lesson used). Labels beat artistic skill.
### Why this lesson matters on Monday morning
Parallel resonance is not trivia. You will meet it when a meter reading looks “impossible,” when a replacement part is almost right, or when a helper asks why the book uses √3 or lead/lag. Master the model here so the next call is pattern recognition, not panic.
Common Monday uses: verify a nameplate against clamps, explain a PF or capacitor change to a customer, or catch a miswired series/parallel or wye/delta assumption before energizing.
In the field
Symptom
Low line I at a frequency; hot L or C; odd impedance
Where to look
L∥C tanks, PF cap + transformer L, tuned filters
Likely causes
- Operating at parallel fr
- harmonic hits anti-resonance
What to measure
- Line I vs branch I
- estimate fr
- temperature
What not to do
- Trust only the feeder clamp
Checklist
- I contrast max Z / min I with series resonance
- I explain circulating current in the tank
- I use fr = 1/(2π√(LC))
- I look for heating inside the tank
- I connect this to notch/reject filters
- I avoid mixing series vs parallel symptoms