LC Resonance circuits

The LC cicuit

Design a parallel LC resonant circuit with a resonant frequency between 50-200 kHz. use [math]\displaystyle{ L }[/math] = 10 - 100 [math]\displaystyle{ \mu H }[/math].
Construct the LC circuit using a non-polar capacitor
Measure the Gain [math]\displaystyle{ \equiv \frac{V_{out}}{V_{in}} }[/math] as a function of frequency. (10 pnts)
Measure the Gain when an external resistance approximately equals to the inherent resistance of the rf choke [math]\displaystyle{ R_{L} }[/math]. (10 pnts)
Compare the measured and theoretical values from the resonance frequency ([math]\displaystyle{ \omega_{L} }[/math]) and the Quality factor [math]\displaystyle{ Q \equiv 2 \pi \frac{W_S}{W_L} = 2 \pi \frac{\mbox{Energy Stored}}{\mbox{Energy Lost}} }[/math] value for each case; [math]\displaystyle{ W = \frac{1}{2}Li^2 }[/math]. (10 pnts)

Questions

If r=0, show that [math]\displaystyle{ Q = \frac{1}{\omega_0 R_L C} }[/math]. (10 pnts)
Show that at resonance[math]\displaystyle{ Z_{AB} \approx Q \omega_0 L }[/math]. (10 pnts)