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Exam level10 past questions

AC Circuit Analysis and LCR Circuits

AC circuits with resistors, capacitors, and inductors (LCR circuits) exhibit impedance, resonance, phase relationships, and power factor, all crucial for understanding circuit behavior.

Why this shows up in the exam

NEET frequently tests calculations involving impedance, resonance, phase, and power in LCR circuits.

How NEET tests this

Numerical · 9 QsDirect recall · 4 QsStatement analysis · 2 Qs

Learn the idea

In an AC LCR circuit the total opposition is impedance, a vector sum of resistance and reactance, and the relative size of inductive and capacitive reactance decides whether current leads, lags, or is in phase with voltage.

🧠 Memory hook: Think of L and C as opposite twins: when they are equal they cancel (resonance), otherwise the bigger twin pulls the current either forward (C) or backward (L).

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • Impedance Z = √(R²+(X_L‑X_C)²)
  • Inductive reactance X_L = ωL
  • Capacitive reactance X_C = 1/(ωC)
  • Resonance angular frequency ω₀ = 1/√(LC) (or f₀ = 1/(2π√(LC)))
  • Phase angle φ = tan⁻¹((X_L‑X_C)/R) – current leads voltage if φ is negative, lags if positive
  • Power factor = cos φ

How to approach it

  1. 11. Write down given R, L, C and frequency (or f).
  2. 22. Compute X_L = 2πf L and X_C = 1/(2πf C).
  3. 33. Form net reactance X = X_L‑X_C and then Z = √(R²+X²).
  4. 44. Find phase angle φ = tan⁻¹(X/R); sign of X tells lead (X<0) or lag (X>0). For resonance set X=0 → f₀ = 1/(2π√LC).

Worked example — watch it click

In an AC circuit the current:

  • A)Always leads the voltage
  • B)Always lags behind the voltage
  • C)Is always in phase with the voltage
  • ✅May lead or lag behind or be in phase with the voltage

The concept behind this problem

The example asks which phase relation is possible; it checks that you know current can lead, lag, or be in phase depending on the net reactance of the circuit.

Step by step

  1. 1In AC circuits: purely resistive (current in phase), purely inductive (current lags by 90°), purely capacitive (current leads by 90°), or combinations (any phase difference).
  2. 2Thus current may lead, lag, or be in phase depending on circuit elements.

Watch out

Assuming the current always leads (or always lags) without considering the pure‑resistive case where it is exactly in phase.

Common slip-ups that cost marks

  • •Using ω = 2πf but forgetting the 2π factor;
  • •Treating X_C as zero for DC – it is actually infinite, giving open circuit;
  • •Mixing up sign of φ – a negative φ means current leads, not lags.

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 10

Assertion (A): A capacitor is connected to a direct current source. Its reactance is infinite. Reason (R): Reactance of a capacitor is given by X = 1/ωC.

Push further

More challenging

5 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 5

A capacitor is connected to an AC source. If the frequency of the AC source is doubled, how does the capacitive reactance change?

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