Why does the voltage across the inductor in a series LCR circuit equal the voltage across the capacitor at resonance, de
**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. At resonance, X_L = X_C , and since V_L = I X_L and V_C = I X_C with the same current I , their magnitudes are equal. However, they are 180° out of phase, so their vector sum is zero, not their magnitudes. Applying X_L = ωL, X_C = 1/ωC, Z = √(R² + (X_L - X_C)²), I_rms =
Ref: NCERT > Physics Book > Alternating Currents > Resonance in LCR Circuit and Q-Factor