LCR Circuit Resonance

Also called

LCR circuit · series LCR circuit · resonance · resonant frequency · phasor diagram · phasors · inductive reactance · capacitive reactance · impedance · current lags voltage · current leads voltage · phase difference · radio tuning · sharpness of resonance · quality factor · alternating current · प्रत्यावर्ती धारा · अनुनाद · कला · प्रेरकत्व

Topics

• In a pure resistor the alternating current is in phase with the voltage across it: both peak together.
• In an inductor the current lags the voltage by 90°; its reactance X_L = ωL grows with frequency.
• In a capacitor the current leads the voltage by 90°; its reactance X_C = 1/ωC falls with frequency.
• A phasor is a rotating arrow whose projection gives the instantaneous value…
• In a series LCR circuit V_L and V_C point opposite ways, so the source voltage is the phasor sum of V_R and (V_L − V_C).
• The impedance is Z = √(R² + (X_L − X_C)²) and the current amplitude is V/Z.
• At resonance X_L = X_C, so Z = R, the current is largest and the circuit behaves like a pure resistor.
• The resonant angular frequency is ω₀ = 1/√(LC); a smaller R makes the resonance peak taller and sharper.
• A radio is tuned by changing its capacitor so that ω₀ matches the chosen station's frequency.

About this model

A GLB file of about 562 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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