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#AC theory

2 public questions tagged with this topic.

Resonance in LCR Circuit and Q-Factor

In an ideal AC circuit with only a capacitor, what is the relationship between the rates of change of voltage and curren

**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. In a capacitor, I = C (dV/dt) , meaning the current is directly proportional to the rate of change of voltage. Conversely, the rate of change of current relates to the second derivative of voltage, but the primary relationship is that current depends on (dV/dt) . Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L -

Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor

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AC Through Capacitor - Capacitive Reactance

In a purely capacitive AC circuit, the current leads the voltage by what phase angle?

**Capacitive reactance** X_C =1/(ω C)=1/(2π f C) (Ω), C capacitance (F), current leads voltage by 90°, I_rms = V_rms/X_C = V_rms ω C, I_peak = V_peak ω C, impedance Z = X_C for pure C. For 45 μF, 60 Hz, X_C=1/(2π×60×45×10⁻⁶)=58.9 Ω, V_rms=110 V, I_rms=1.867 A, I_peak=2.64 A. For a capacitor, i = i_m sin (ω t + (π/2)) , v = v_m sin ω t . Phase difference: Φ = (π/2) , so current leads voltage by 90° . 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,

Ref: NCERT > Physics Book > Alternating Currents > AC Through Capacitor - Capacitive Reactance

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