# Resonant frequency of RLC circuit if for two values of omega we have same max amplitude current

Original question:

An alternating current is flowing through a series LCR circuit. It is found that the current reaches a value of 1 mA at both 200 Hz and 800 Hz frequency. What is the Resonance frequency of the circuit?

My method was that according to given conditions for two frequencies w and w' we have $$\\left(\omega L-\frac{1}{\omega c}\right)^{2}=\left(\omega^{\prime} L-\frac{1}{\omega^{\prime} c}\right)^{2}\$$ so from here we get that either $$\\omega+\omega' = 1/\sqrt{LC} = 1000\;\text{Hz}\$$, or $$\\omega-\omega' = 1/\sqrt{LC} = 600\;\text{Hz}\$$, so resonant frequency is either of the two but given is that resonant frequency is $$\\sqrt{\omega\omega'} = 400\;\text{Hz}\$$, why is that so ?

• You're misreading the problem. Neither 200 or 800 Hz is the resonant frequency. It's between them. Apr 16 at 16:15
• I write about it here, for example. It shows you that $\omega_{_\text{L}}\,\omega_{_\text{H}}=\omega_{_0}^{\:2}$ and therefore $f_{_\text{L}}\,f_{_\text{H}}=f_{_0}^{\:2}$.
– jonk
Apr 16 at 19:39

Your equation $$\\left(\omega L-\frac{1}{\omega c}\right)^{2}=\left(\omega^{\prime} L-\frac{1}{\omega^{\prime} c}\right)^{2}\$$ has demolished a part of the information. Your equation is true as a consequence but it does not reversely imply the right solution for LC, it gives 2 possible values and only one of them is the right LC.