Is there any simple circuit with Single RLC components which has resonant frequency not equal to (LC)^-1/2?
Can someone please help with such examples?

 

Is this related to a school assignment?

 

Is there any simple circuit with Single RLC components which has resonant frequency not equal to (LC)^-1/2?
Can someone please help with such examples?

Hello,

There are three definitions of resonant frequency. If we choose one that defines the resonant peak response as the response due to the resonant frequency, then for one example if you put the capacitor in series with the inductor and then place the resistor across the inductor, the resonant frequency is not 1/sqrt(L*C).

You should try other configurations doing the analysis and perhaps with a circuit simulator too. See if you can calculate one of the resonant frequencies for each combination.

Also, if you include frequencies that are not really resonant, you can combine the RLC in such as way that the response has no peak. That is, no resonate frequency, simply because it is overdamped, and overdamped RLC circuits do not resonate in any sense of the word because their response does not include a sinusoidal part.

With just three components the analysis should not be too difficult, but if you need help you should show your best attempt at answering this first.

 

Is there any simple circuit with Single RLC components which has resonant frequency not equal to (LC)^-1/2?
Can someone please help with such examples?

What definition of resonant frequency are you using?

How many different ways are there to connect and R, an L, and a C?

Do the analysis for each and see if 1/sqrt(LC) satisfies your definition.

 

frequency not equal to (LC)^-1/2?
Can someone please help with such examples?

This is the pulsation or angular velocity, omega.
For the frequency, it is the Thomson formula and it has 2Pi in the denominator

The oscillation frequency basically depends on L and C
R is set as the real coil has resistance,
Then at the radio receivers, a resistor is placed in parallel with parallel LCs to reduce their quality factor.

Basically, a small quality factor gives a smaller bandwidth, basically the radio receiver becomes more selective.

Likewise, there are many LC combinations that give the same result but have a different quality factor.

The Thomson formula is easily obtained by setting the capacitive reactance XC=XL equal to the inductive reactance.

 

This is the pulsation or angular velocity, omega.
For the frequency, it is the Thomson formula and it has 2Pi in the denominator
View attachment 339141
The oscillation frequency basically depends on L and C
R is set as the real coil has resistance,
Then at the radio receivers, a resistor is placed in parallel with parallel LCs to reduce their quality factor.

Basically, a small quality factor gives a smaller bandwidth, basically the radio receiver becomes more selective.

Likewise, there are many LC combinations that give the same result but have a different quality factor.

The Thomson formula is easily obtained by setting the capacitive reactance XC=XL equal to the inductive reactance.

Hi,

The question was about when you CANNOT use that formula

 

Is there any simple circuit with Single RLC components which has resonant frequency not equal to (LC)^-1/2?
Can someone please help with such examples?

Based on the commonly accepted Definition (imaginary pat of the circuits impedance equal to zero) the resonant frequency of the parallel combination (1/jwC) and (R+jwL) is not equal to SQRT(1/LC).
Rather, it is
wo=SQRT[(1/LC)+(R/L)²]