a. For the series resonant circuit in Fig. 21.21, find $I, V_R, V_L, and V_C$ at resonance.
b. What is the $Q_s$ of the circuit?
c. If the resonant frequency is 5000 Hz, find the bandwidth.
d. What is the power dissipated in the circuit at the half-power frequencies?

Question

a. For the series resonant circuit in Fig. 21.21, find [latex]I, V_R, V_L, and V_C[/latex] at resonance.
b. What is the [latex]Q_s[/latex] of the circuit?
c. If the resonant frequency is 5000 Hz, find the bandwidth.
d. What is the power dissipated in the circuit at the half-power frequencies?

Accepted Answer

a. [latex]Z_{T_s}=R = 2 Ω\[0.5cm] I=\frac{E}{Z_{T_s}}=\frac{10 V ∠0°}{2 Ω ∠0°}=5 A \angle 0° \[0.5cm] V_R=E = 10 V \angle 0°\[0.5cm] V_L=(I ∠0°)(X_L ∠90°) = (5 A ∠0°)(10 Ω ∠90°)=50 V \angle 90°\[0.5cm] V_C=(I ∠0°)(X_C ∠-90°) = (5 A ∠0°)(10 Ω ∠-90°)=50 V \angle −90°[/latex]

b. [latex]Q_s=\frac{X_L}{R}=\frac{10 Ω}{2 Ω}=5 [/latex]

c. [latex]BW=f_2-f_1=\frac{f_s}{Q_s}=\frac{5000 Hz}{5}=1000 Hz [/latex]

d. [latex]P_{HPF}=\frac{1}{2}P_{max}=\frac{1}{2}I^{2}_{max}R =\left(\frac{1}{2} \right)(5A)^2 (2\Omega)=25W [/latex]

Question 21.1: a. For the series resonant circuit in Fig. 21.21, find I, VR...

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