H11P1: LC Tank

Parallel resonant "tank" circuits are common in radio equipment. But unfortunately there is always resistance that prevents them from being perfect: in every real inductor, the wire that makes up the inductance has some resistance, and there may be leakage in the capacitor that can be modeled as a resistance. Also, the Norton resistance of the system connected to the tank circut looks like a leakage through the capacitor. So a realistic model for a tank circuit is the following:
In the space provided below write an algebraic expression in terms of the device parameters for t

Question

H11P1: LC Tank

Parallel resonant "tank" circuits are common in radio equipment. But unfortunately there is always resistance that prevents them from being perfect: in every real inductor, the wire that makes up the inductance has some resistance, and there may be leakage in the capacitor that can be modeled as a resistance. Also, the Norton resistance of the system connected to the tank circut looks like a leakage through the capacitor. So a realistic model for a tank circuit is the following:
In the space provided below write an algebraic expression in terms of the device parameters for t

anonymous · Answer

first
z=((RcSL+RcRl)/RcCL)/(s^2+s((L+RcRlC)/RcCL))+((Rc+Rl)/(RcCL))
so,
DeltaW=((L+RcRlC)/RcCL))
simp...... DeltaW = (1/RcC)+(Rl/L)
and
wo^2=((Rc+Rl)/(RlCL))

remember that:
wo=2pif

good luck..