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#series resonance

3 public questions tagged with this topic.

Resonance in LCR Circuit and Q-Factor

In an LCR series circuit, what happens to the circuit’s behavior when the frequency is significantly above the resonant

**At resonance** V_L = I X_L = I X_C = V_C, may be larger than source voltage Q times, Q-factor = ω₀ L/R =1/(ω₀ C R)= V_L/V = V_C/V, measures sharpness, higher Q sharper resonance, bandwidth Δω = R/L = ω₀/Q, resonant frequency independent of R. Above resonance, X_L = ω L becomes much larger than X_C = (1/ω C) , making the net reactance positive. The circuit behaves as predominantly inductive, with the current lagging the voltage. Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p = N_s/N_p, calculation gives

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LCR Series Circuit - Impedance and Phasor Diagram

A series LCR circuit has \( R = 40 \, \Omega \), \( L = 5 \, \text{H} \), \( C = 80 \, \mu\text{F} \). What is the reson

**Impedance behavior at high frequencies** X_L=ωL dominates ∝ f, X_C=1/ωC →0, so Z≈√(R²+X_L²)≈X_L large, current small, circuit inductive, φ→90°, at low frequencies X_C large, Z≈X_C, capacitive, φ→-90°, at intermediate resonance Z minimal =R. ω₀ = (1/√(L C)) . L = 5 H , C = 80 × 10⁻⁶ F . ω₀ = (1/√(5 × 80 × 10⁻⁶)) = (1/√(4 × 10⁻⁴)) = 50 rad/s . f₀ = (50/2 × 3.14) ≈ 7.96 Hz . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p = N_s/N_p, calculation gives 8 Hz, consistent with

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LCR Series Circuit - Impedance and Phasor Diagram

A series LCR circuit has \( L = 3.5 \, \text{H} \), \( C = 8 \, \mu\text{F} \). What is the resonant angular frequency?

**LCR example** R=100 Ω, X_L=130 Ω, X_C=70 Ω, X_L-X_C=60 Ω, Z=√(100²+60²)=116.6 Ω, V_rms=300 V, I_rms=2.573 A, power P= I_rms² R =662 W? Actually P= V_rms I_rms cos φ, cos φ=R/Z=0.857, P=300×2.573×0.857=661.6 W, illustrating power factor. ω₀ = (1/√(L C)) . L = 3.5 H , C = 8 × 10⁻⁶ F . ω₀ = (1/√(3.5 × 8 × 10⁻⁶)) = (1/√(28 × 10⁻⁶)) ≈ 188.98 rad/s . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms = V_rms/Z, P = V_rms I_rms cosφ, V_s/V_p = N_s/N_p, calculation gives 188.98 rad/s, consistent with phasor analysis and resonance condition X_L = X_C.

Ref: NCERT > Physics Book > Alternating Currents > LCR Series Circuit - Impedance and Phasor Diagram

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