Series Resonance, Quality Factor, and Bandwidth
The resonant angular frequency is 1/sqrt(LC). For a series RLC circuit, Q measures sharpness and bandwidth in angular frequency is R/L.
Why this shows up in the exam
Radio station selection · Frequency filters · Resonant sensors
Learn the idea
At series resonance, XL equals XC and current is maximum. The inductor and capacitor exchange energy while their opposite reactances cancel at one frequency. The source then sees only resistance.
🧠 Memory hook: At resonance: reactances cancel, resistance remains.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- omega₀ = 1/sqrt(LC) — resonant angular frequency
- Z_res = R — series impedance at resonance
- Q = omega₀ L/R — series-circuit quality factor
- Delta omega = R/L — half-power angular-frequency bandwidth
How to approach it
- 1Set XL = XC
- 2Find omega0
- 3At resonance use Z=R before calculating current
Common slip-ups that cost marks
- •Saying impedance is zero when R is present
- •Assuming VL and VC are individually zero
- •Mixing angular-frequency and ordinary-frequency bandwidth
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A conducting rod of length 2 m moves at 3 m/s perpendicular to a 4 T magnetic field. Find the motional emf.
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