Frequency Dependence of Reactance
XL is directly proportional to frequency; XC is inversely proportional. These opposite trends create filters and resonance.
Why this shows up in the exam
Audio crossovers · High-pass and low-pass filters · Noise suppression
Learn the idea
Higher frequency makes an inductor harder and a capacitor easier for AC. An inductor resists rapid current change, so its reactance rises with frequency. A capacitor gets less time to build opposing voltage, so its reactance falls with frequency.
🧠 Memory hook: Frequency up: L blocks more, C blocks less.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- X_L = 2 pi f L — inductive reactance grows with f
- X_C = 1/(2 pi f C) — capacitive reactance falls with f
How to approach it
- 1Write both reactances
- 2Apply the frequency change as a ratio
- 3Predict current from total Z
Common slip-ups that cost marks
- •Reversing the trends
- •Changing R with frequency in an ideal-resistor model
- •Comparing reactances without common units
🌟 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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