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I understand that in a Frequency Response experiment dealing with an RLC circuit, the graph of Current against Frequency is supposed to be symmetrical about the resonant frequency theoretically.

However, experimentally it is not the case.

Could anyone explain why this happens?

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    $\begingroup$ Since frequency $f\geq 0$ is a non-negative quantity, and under the plausable assumption that the theoretical current $I(f)> 0$ is non-vanishing for all $f>0$, why would you expect the theoretical graph $f\mapsto I(f)$ to be a symmetric function $I(f)\stackrel{?}{=}I(2f_0-f)$ around the resonance frequency $f_0$ in the first place? $\endgroup$
    – Qmechanic
    May 11, 2013 at 12:21
  • $\begingroup$ @Qmechanic: Does $I(f/f_0) = I(f_0/f)$ seem more plausible? $\endgroup$
    – Art Brown
    Aug 9, 2013 at 16:02
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    $\begingroup$ @ArtBrown: Right. Technically, that's logarithmically symmetric $I(\ln(f))=I(2\ln(f_0)-\ln(f))$. $\endgroup$
    – Qmechanic
    Aug 9, 2013 at 16:20
  • $\begingroup$ Thanks, @Qmechanic, this terminology is v useful! With your permission, I would like to add it to my answer, with attribution of course. $\endgroup$
    – Art Brown
    Aug 9, 2013 at 17:41
  • $\begingroup$ Study the filter characteristic by plotting bode asymptotic (Frequency response) $\endgroup$
    – user38344
    Jan 27, 2014 at 15:33

2 Answers 2

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For a series LRC circuit, the magnitude of the current is indeed symmetrical about the resonant frequency, if you plot the frequency on a logarithmic scale. $$\left| Z \right| = \sqrt{R^2 +\frac{L}{C} \left[ \frac{\omega}{\omega_0}-\frac{\omega_0}{\omega}\right]^2}$$ where the resonant angular frequency $\omega_0$ is just $$\omega_0 = \frac{1}{\sqrt{L C}} $$ so $$ \left|Z \left(\frac{\omega}{\omega_0} \right) \right|=\left|Z \left(\frac{\omega_0}{\omega} \right) \right| $$ Since the magnitude of the current is the applied voltage divided by $|Z|$, for a constant applied voltage (e.g. magnitude of voltage frequency-independent), the result follows.

The phase is anti-symmetric, in the same sense.

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For every RLC circuit there is an total impedence in the circuit which will lead to loss of current in the form of heat due to resistance . the total impedence is equal to square root of sum of squares of resistance in resistor and total reactance in the circuit(i.e. difference between the reactance of capacitor and inductor) hence in experiment the is always an change in value of current which will be always less then that of theoritical value

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