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LRC series circuit

Given 10Vmax ac source, LRC series circuit, Imax at resonance frequency Imax=2A; f= 200Hz; Imax = 1.2A;
f=350Hz Imax = 1.5A

What equations are used and how are the values found?

What is the resonant freq and the phase angle at 250Hz?

Solution Preview

Please see the attached files.

We have a series RLC circuit, and we are interested in the current that flows when a given AC voltage is applied, so it doesn't matter in what orderthe three components are connected. The complex impedance at radian frequency ω is . The current is V/Z. The magnitude of the current is at a maximum when the magnitude of the impedance is at a minimum. The magnitude of the impedance is:


It's pretty obvious that this has a minimum at ωL = 1/ωC, but we can take the derivative anyway:


This derivative takes some work, but this is what you get.

Setting d|Z|/dω to zero we see that yes, the maximum current is at the resonant frequency

. When we substitutute this for ω in |Z| we get |Z| = R as we could have seen above. We are told that Imax at resonance is 2 Amperes, so we know R:

R = Z(ω0) = 10V/2A = 5 ...

Solution Summary

LRC sereis circuit is analyzed, such as its maximum current, resonant frequency, and phase angle.