Parallel circuit with resonant branch

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Discussion Overview

The discussion revolves around analyzing a parallel circuit with a resonant branch consisting of a resistor, inductor, and capacitor. Participants explore the calculation of the resonant frequency, impedance, and current drawn from the circuit at a specified frequency. The scope includes theoretical calculations and practical implications in circuit analysis.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant calculates the resonant frequency of the RLC branch to be 2054.7 Hz using a specific method.
  • Another participant challenges this calculation, suggesting that the resonant frequency should be around 65 kHz based on the formula 1/sqrt(LC) with given values for L and C.
  • A third participant agrees with the 65 kHz frequency and provides impedance calculations for the capacitor at that frequency.
  • There is a clarification regarding the formula for resonance, with some participants discussing the need for the factor of 2π to convert to Hz.
  • One participant acknowledges an error in component values and seeks further clarification on the circuit analysis.
  • Another participant provides impedance calculations for the branches and discusses the phase angle of the circuit.
  • There is a mention of the need to calculate the modulus of the impedance and the current drawn from the circuit, with some confusion about the "rms" terminology.

Areas of Agreement / Disagreement

Participants express differing views on the correct resonant frequency, with some supporting the initial calculation and others advocating for a higher frequency. The discussion remains unresolved regarding the correct approach to calculating the resonant frequency and the subsequent implications for the circuit analysis.

Contextual Notes

Participants reference different formulas and methods for calculating resonance and impedance, indicating potential misunderstandings or variations in approach. The discussion includes corrections and clarifications that highlight the complexity of the calculations involved.

Who May Find This Useful

This discussion may be useful for individuals interested in circuit analysis, particularly those studying resonant circuits and impedance calculations in electrical engineering or physics contexts.

SimpleJack
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Here's a question my mate asked me to help out with, but I'm a bit stuck, any help would be good. Apologies for not being able to show the circuit (don't know how) so I'll explain it.

A parallel circuit has a supply of 1 Vrms and has 2 branches. The first branch has a single capacitor of 2.2 microFarads. The second branch has a resistor of 5 Ohms, and inductor of 0.2 milliHenrys and a capacitor of 30 nanoFarads.

The first part was to work out the sesonant frequency of the branch with the 3 components, we both got 2054.7 Hz.

The second part was to find the magnitude the magnitude and the phase angle of the current drawn for the entire of the circuit at the frequency of part a (i.e 2054.7Hz). So we worked out that the impedance of the lone capacitor was 35.2 Ohms.

From this point we are at a bit confused. Are we right up to this point and where do we go from here?

Cheers.
 
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How did you get the resonant frequency of the 3 component branch?
The equation for resonance, if I'm not mistaken is 1/sqrt(LC)

So given C = 30nF and L = .2mH, resonant frequency should be 408 krads, or about 65 kHz.

Your approach is correct for the capacitor impedance. Remember that a capacitor is purely reactive.

Resonance implies that the L and C cancels out at that frequency, so on the second branch, you only have the resistor left. So you're left with a simple RC parallel circuit connected to a voltage source.
 
I get about 65 kHz as well.

The impedance of the 2.2 uF is about 1.1 Ohms at that frequency.



http://ourworld.compuserve.com/homepages/Bill_Bowden/XLC.htm
 
Last edited by a moderator:
Am I wrong in thinking the formula for resonance was 1 over 2 x pi x sqrt(LC)
 
2pi if you need the freq in Hz.

If you did that, you still should get around 64.974 kHz
 
OK sorry, I got the figures wrong. The RLC branch is made of a 5 Ohm resistor, a 30nF capacitor and a 0.2H inductor. My bad,

Can anyone shed any more light on this now...?


Thanks.
 
2055 Hz Then.

Impedance of the 2.2uF is 35.2 Ohms at 2055 Hz.



http://ourworld.compuserve.com/homepages/Bill_Bowden/XLC.htm
 
Last edited by a moderator:
Right got that, so a parallel circuit, the resonant branch impedance is 5 Ohm at angle 0, the lone capacitor branch is 35.2 angle -90 deg.

Thats product/sum = 4.9 at angle -8.1 or 4.9+j0.7.

With a source of 1Vrms, how do you work out the current drawn, what is with the "rms" part?

Cheers, almost there.
 
Z = 4.9 - j0.7 Still capacitive.. so minus.


Phase angle is about 8.1 deg. tan-1 0.7/4.9 Xc/R

You have to work out the modulus of the impedance . Sq rt of the sums of the squares of R and Xc and then I = V/Z
 

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