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⚛️ Physics  ·  Alternating Current  ·  NEET & JEE

An LCR circuit has L = 10 mH, C = 10 μF, R = 10 Ω. If V = 100 V at resonance, what is V<sub>L</sub> (voltage across inductor)?

Answer: Q × 100 V = 10 × 100 = 1000 V.

  • A Q × 100 V = 10 × 100 = 1000 V
  • B 100 V, equal to the source voltage with little quality-factor amplification
  • C 0 V, as if the inductor carried no voltage drop at resonance whatsoever
  • D 50 V, half of the applied source voltage with little resonance factor included

Correct answer: A. Q × 100 V = 10 × 100 = 1000 V

Explanation: f<sub>0</sub> = 1/(2π√(0.01×10⁻⁵)) = 1/(2π×10⁻³ · √10) ≈ 503 Hz. ω_0 ≈ 3162 rad/s. Q = ω_0 L/R = 3162 × 0.01/10 ≈ 3.16. V<sub>L</sub> = Q × V<sub>source</sub> = 3.16 × 100 ≈ 316 V.

V and I Phase Relationships in AC CircuitsPure Inductor: I lags V by 90°VIPure Capacitor: I leads V by 90°VIMemory aid "ELI the ICE man": in an inductor (L) E(V) leads I; in a capacitor (C) I leads E(V)For a pure resistor, V and I stay perfectly in phase (no lag or lead at all)

In a pure inductor the current lags the voltage by 90° (energy is briefly stored in the magnetic field before current responds); in a pure capacitor the current leads the voltage by 90° (current must flow to build up charge before voltage rises) - the mnemonic "ELI the ICE man" keeps these straight.

Concept context

AC circuits, impedance, LCR series circuit, resonance, transformers, and power factor.

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