A series LCR circuit has R = 20 Ω, L = 1.6 H and C = 40 μF. It is connected to a variable-frequency AC source. If the inductive reactance at resonance is N ohms, find N.

Question

G1 Physics · Accepted Answer

At resonance, ω₀ = 1 ÷ √(LC). Substitute: L = 1.6 H, C = 40×10⁻⁶ F. Thus, ω₀ = 1 ÷ √(1.6×40×10⁻⁶) = 1 ÷ √(64×10⁻⁶) = 1 ÷ (8×10⁻³) = 125 rad·s⁻¹. The inductive reactance is X(L) = ω₀L = 125×1.6 = 200 Ω. Therefore N = 200.