Series LCR Impedance and Phasors
The impedance magnitude is the hypotenuse formed by R and XL-XC. The phase angle follows tan(phi) = (XL-XC)/R.
Why this shows up in the exam
Radio tuning · Band-pass filters · AC circuit design
Learn the idea
In series LCR, resistance and net reactance combine at right angles. A phasor diagram separates the in-phase resistive voltage from the opposing inductive and capacitive voltages. Their vector combination determines the source voltage.
🧠 Memory hook: Subtract reactances first, then use Pythagoras with R.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Z = sqrt(R² + (X_L - X_C)²) — series LCR impedance
- I_rms = V_rms/Z — series current
- tan(phi) = (X_L - X_C)/R — voltage-current phase angle
How to approach it
- 1Calculate XL and XC
- 2Find net reactance
- 3Build Z, current, and phase
Common slip-ups that cost marks
- •Adding XL and XC
- •Adding component voltage magnitudes arithmetically
- •Using a parallel-circuit rule for a series circuit
🌟 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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