What occurs when $$\omega = \omega_r$$
The circuit frequency equals its natural frequency? So what. And why is it important?
Electronic – What happens to RLC circuits at resonance frequency, conceptually
frequency
Related Solutions
There is nothing like dc frequency. We call the signal which is constant and has no changes in it's value as dc signal and it has zero frequency. The bias signal is one type of dc signal. If we take Fourier representation of a sinusoidal signal like sinusoidal signal [\$\sin(\omega t)\$], it contains the odd harmonics of the fundamental frequency. there is no dc bias present in it. If this signal is applied to frequency doubler, it's frequency would be doubled and consequently the odd harmonics are also doubled.
Now consider a signal with dc bias like \$A+B\sin(2\pi ft)\$. If we consider the Fourier representation of the signal, it contains a zero frequency component of amplitude (\$A\$) and two frequency components at (\$f\$ and \$-f\$) with amplitude (\$B\$). when this signal is applied to frequency doubler it doesn't have any effect on the zero frequency but the other two frequency components get translated to \$2f\$ and \$-2f\$.
DC bias is entirely independent of the concept of frequency doubling.
Realization of signal using transforms would help to solve the frequency related questions.Hope this answered your question.
What effect will it have on my resonant frequency
Theoretically it will have no effect on the resonant frequency. The resonant frequency is purely determined by the capacitor having exactly the opposite reactance of the inductor at a particular frequency and the two reactances cancel leaving the series tuned circuit having only resistance at resonance.
However, with lower values of resistance the peak shape of the resonance will change but the centre point of the peak will remain as previous.
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Best Answer
A series RLC circuit has an impedance of: -
\$R + j\omega L +\dfrac{1}{j\omega C}\$
Knowing that "j" in the denominator is the same as "-j" in the numerator means there is a frequency when the inductive and capacitive reactances totally cancel and this means that the only component left is resistance, R.
This occurs when \$j\omega L = -\dfrac{1}{j\omega C}\$
Or \$\omega^2 = \dfrac{1}{LC}\$ or \$\omega = \dfrac{1}{\sqrt{LC}}\$
It's a really big deal when wanting to filter just one small band of frequencies whilst disregarding the rest; in simple terms, at resonance, a series RLC circuit lets through a small band of frequencies and progressively attenuates frequencies that are not in the "pass-band".
It's a big deal for radio receivers and transmitters so it's really very, very important.
If you analyse a parallel RLC circuit it has the same formulas and, depending on the circuit configuration, it can do pretty much the same as a series RLC circuit. The "R" in a parallel circuit is a different way of expressing losses and it functions inversely to the "R" in a series RLC circuit.
Resonance can do bad things too - if not controlled it can produce voltages that cause semiconductor devices to breakdown - voltage regulators is a device that springs to mind.
Have you seen the video of that suspension bridge rocking backwards and forwards and then collapsing - that was uncontrolled resonance and mechanically it has virtually the same formula - it is a second order filter.