Question

With the proper figures, describe the following terms in the context of Series R-L-C circuit

(i) Resonance Frequency (f0)

(ii) Power factor for f = f0,

(iii) Half-Power Bandwidth

(iv) Selectivity (Quality Factor) 

Answer 1

RLC circuit

(1) resonance frequency

$X_L=X_C$

$wL=\frac{1}{wc}$

$w=\frac{1}{\sqrt{LC}}$

$f=\frac{1}{2\pi\sqrt{LC}}$

(B)

Power factor

$Cos\theta=\frac{R}{Z}$

$Z=\sqrt{R^2+(X_L-X_C)^2}$

$(c)$

Band width

$BW=f_2-f_1=\frac{R}{2\pi L}$

(D)

Quality factor

$Q=\frac{w_rL}{R}=\frac{1}{w_rCR}$