Resonance frequency in an LCR circuit

[Boxcutter]

Hello everyone!

I've been trying to derive the expression

w = sqrt( (1/(LC)) - (R_l^2 / L^2) )

where w is the resonace frequency, L is the inductance of the inductor, R_l is the resistance in the inductor, R is the resistance of the resistor and C is the capacitance of the capacitator.

for this circuit:

http://web.telia.com/~u18412273/lcr.JPG

I'm not sure how to attack the problem and I can't find any good texts about it.
I know how to do it in series circuits. I've been trying to do it in a correspondning way for this one but I can't quite do it.

Any help is appreciated
/Daniel

 

[Curious3141]

Hello everyone!

I've been trying to derive the expression

w = sqrt( (1/(LC)) - (R_l^2 / L^2) )

where w is the resonace frequency, L is the inductance of the inductor, R_l is the resistance in the inductor, R is the resistance of the resistor and C is the capacitance of the capacitator.

for this circuit:

http://web.telia.com/~u18412273/lcr.JPG

I'm not sure how to attack the problem and I can't find any good texts about it.
I know how to do it in series circuits. I've been trying to do it in a correspondning way for this one but I can't quite do it.

Any help is appreciated
/Daniel

Set up an expression for the complex impedance of the circuit (you can forget about the R since it doesn't affect the analysis). Find the omega for which the impedance of the capacitor in parallel with (series inductance + resistance) becomes a pure real number. At this point the reactive component disappears, the load is purely resistive and resonance is achieved.