Examples of Series Resonance Circuits

Example 1:
a. For the series resonant circuit of Fig. 1, 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?

Example 2: The bandwidth of a series resonant circuit is $400 Hz$.
a. If the resonant frequency is $4000 Hz$, what is the value of $Qs$?
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.

Example 3: A series $RLC$ circuit is designed to resonant at $w_s=10^5 rad/s$, have a bandwidth of $0.15f_s$, and draw $16 W$ from a $120V$ source at resonance.
a. Determine the value of $R$.
b. Find the bandwidth in hertz.
c. Find the nameplate values of $L$ and $C$.
d. Determine the $Qs$ of the circuit.
e. Determine the fractional bandwidth.