What is the role of resonance in the operation of a radio receiver?
**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 radio receiver, resonance in an LCR circuit is used to tune to a specific frequency. By adjusting the capacitance or inductance, the circuit’s resonant frequency matches the desired station’s signal, amplifying it while filtering out others. 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
Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor
