Help Finding Amplitude of Voltage Across Capacitor At Resonant Frequency

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SUMMARY

The discussion focuses on calculating the amplitude of voltage across a capacitor (Vc) at the resonant frequency in an RLC circuit with a current (I) of 1A. The user derived the equations for impedance (Zeq) and resonant frequency (ω) using the formulas Zeq = (jωL + R) / (jωRC - ω²LC + 1) and ω = √[(L - R²C) / (L²C)]. The solution involves multiplying both the numerator and denominator of the impedance by the complex conjugate of the denominator to eliminate the imaginary component, thereby simplifying the calculation of real impedance conditions.

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mmmboh
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Hi, here is the question:
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For part b) I have to find the amplitude of Vc at the resonant frequency with I=1A, I have found Zeq and well here are my equations:

\frac{jwL+R}{\ jwRC-w^2LC+1} and I have the equation for w at the resonance:w= \sqrt[2]{\frac{L-R^2C}{\L^2C}}

I know at the resonant the impedance is real..but I don't know what to do with my equations, can someone help please.
 
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Multiply both the numerator and the denominator of the impedance by the complex conjugate of the denominator. That makes the denominator real. Then it is easy to find the condition for real impedance: when the imaginary part of the numerator is zero.

ehild
 
Oh I figured it out...thanks!
 
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