Inductive & Capacitive Reactance — A/L Physics

What must I remember about Inductive & Capacitive Reactance?

• Inductive Reactance (X_L): Opposition offered by an ideal inductor to AC current: X_L = ω L = 2π f L (units Ohm Ω); Current LAGS voltage by phase angle of π/2 radians (90°); Inductor blocks high frequencies, passes DC (X_L = 0 for f = 0).
• Capacitive Reactance (X_C): Opposition offered by an ideal capacitor to AC current: X_C = 1 / (ω C) = 1 / (2π f C) (units Ohm Ω); Current LEADS voltage by phase angle of π/2 radians (90°); Capacitor blocks DC (X_C = ∞ for f = 0), passes high frequencies.
• Series LCR Circuit Impedance (Z): Total opposition to current in series LCR circuit: Impedance Z = √[ R² + (X_L - X_C)² ]; Phase angle tan φ = (X_L - X_C) / R; Current amplitude I0 = V0 / Z.
• Power Factor (cos φ): Average power dissipated in AC circuit: P_avg = V_rms * I_rms * cos φ, where Power Factor cos φ = R / Z; for pure L or pure C, φ = 90° so cos φ = 0 (Wattless Current, zero net power dissipation).

Test yourself (1 minute)

1. Series Resonance Condition

   Occurs when inductive reactance equals capacitive reactance: X_L = X_C => ω0 L = 1 / (ω0 C); Resonant frequency f0 = 1 / [ 2π √(L C) ].

2. Characteristics at Series Resonance

   1) Minimum impedance Z_min = R (purely resistive); 2) Maximum current I_max = V / R; 3) Phase angle φ = 0 (power factor cos φ = 1, in-phase); 4) Voltage magnification across L and C (Q-factor times source voltage).

3. Quality Factor (Q-Factor)

   Measure of circuit sharpness/selectivity at resonance: Q = (ω0 L) / R = (1 / (ω0 C R)) = (1 / R) √(L / C) = f0 / Bandwidth.

Practise Inductive & Capacitive Reactance questions today

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 8: AC Theory

What should I study first?

What comes next?

Next in the syllabus

Where does Inductive & Capacitive Reactance fit in the syllabus?

Unit 8.5 · Year 2 · Term 1