Define the following terms in the series RLC resonance circuit (i) Resonance Frequency, (ii) Resonance curve, (iii) Half-power frequencies or Cut-off frequencies, (iv) Bandwidth, (v) Quality factor

(i) Resonance frequency f_r: the frequency at which X_L = X_C, so the circuit impedance is purely resistive (Z = R, minimum), current is maximum and in phase with voltage: \( f_r = \dfrac{1}{2\pi\sqrt{LC}} \).

(ii) Resonance curve: the graph of circuit current (or power) versus supply frequency at constant voltage. It peaks at I_max = V/R at f_r and falls on either side; a smaller R gives a sharper curve.

   I
 I_max |       /\
0.707Im|------/--\------
       |     /    \
       |  __/      \__
       +----f1--fr--f2----> f
            |<-BW->|

(iii) Half-power (cut-off) frequencies f₁, f₂: the frequencies below and above f_r at which the current falls to \( I_{max}/\sqrt2 \) (0.707 I_max), so the power is half of the maximum power. \( f_1 \approx f_r - \dfrac{R}{4\pi L} \), \( f_2 \approx f_r + \dfrac{R}{4\pi L} \).

(iv) Bandwidth: the range of frequencies between the half-power points: \( BW = f_2 - f_1 = \dfrac{R}{2\pi L} \) Hz (= f_r/Q).

(v) Quality factor Q: the voltage magnification at resonance, \( Q = \dfrac{V_L}{V} = \dfrac{V_C}{V} = \dfrac{\omega_rL}{R} = \dfrac{1}{\omega_rCR} = \dfrac{1}{R}\sqrt{\dfrac{L}{C}} \); also Q = f_r/BW. It measures the selectivity (sharpness) of the resonance curve: higher Q, narrower bandwidth.