The bandwidth of a series resonant circuit is 400 Hz.
a. If the resonant frequency is 4000 Hz, what is the value of $Q_s$ ?
b. If R = 10 Ω, what is the value of $X_L$ at resonance?
c. Find the inductance L and capacitance C of the circuit.
d. What are the probable commercial values of L and C?

Question

The bandwidth of a series resonant circuit is 400 Hz.
a. If the resonant frequency is 4000 Hz, what is the value of [latex]Q_s[/latex]?
b. If R = 10 Ω, what is the value of [latex]X_L[/latex] at resonance?
c. Find the inductance L and capacitance C of the circuit.
d. What are the probable commercial values of L and C?

Accepted Answer

a. [latex]BW=\frac{f_s}{Q_s}\hspace{30 pt} or\hspace{30 pt} Q_s=\frac{f_s}{BW}=\frac{4000 Hz}{400Hz}=10 [/latex]

b. [latex]Q_s=\frac{X_L}{R}\hspace{30 pt} or\hspace{30 pt} X_L=Q_sR=(10)(10 Ω) = 100 Ω [/latex]

c. [latex]X_L=2\pi f_sL\hspace{30 pt} or\hspace{30 pt} L=\frac{X_L}{2\pi f_s}=\frac{100 Ω}{2\pi(4000 Hz)} =3.98 mH\[0.5cm] X_C=\frac{1}{2\pi f_sC}\hspace{30 pt} or\hspace{30 pt} C=\frac{1}{2\pi f_sX_C} =\frac{1}{2\pi(4000 Hz)(100 Ω)} =397.89 nF[/latex]

d. [latex]L = 3.98 mH ≅ 3.9 mH\[0.5cm] C = 397.89 nF ≅ 390 nF = 0.39 \mu F[/latex]

Question 21.2: The bandwidth of a series resonant circuit is 400 Hz. a. If ...

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