Resonant Frequency of AC Circuit with Coil, Capacitor and Resistance

[xswtxoj]

I don't understand when you have an AC Circuit that has a coil, capacitor and resistance. What factor will the resonant frequency change when the frequency is tripled?

 

[Bob S]

The resonant frequency of a circuit is equal to

f_R= w_R/(2 pi) = (1/(2 pi) 1/sqr(L C)

so to triple the resonant frequency, the product of L and C has to be decreased by a factor of 9.

The Q of the resonant circuit is equal to w_RL/R for a series resiistance, or R/(w_RL) for a parallel resistance.

 

[Bob S]

I attach a resonance curve for a 160 microHenry inductance with a 160 picoFarad capacitor.
There is a series resistor of 100 ohms. The resonant frequency is 1 MHz, and sqrt(L/C) = 1000 ohms, so wL/R = Q = 10. The excitation is a swept frequency of a 1-amp current source from 300 kHz to 2 MHz. The dotted line is the phase of the circuit impedance, starting near + 90 degrees, and ending near - 90 degrees.