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RLC Question help??

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Sosijdog

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Hi Guys I am havin trouble with a question on my assignment. Totally stumped and have no idea how to start. Here's the Question:

When placed in series a coil and capacitor resonate at a frequency of 2251 Hz and when placed in parallel they resonate at a frequency of 2228 Hz. At parallel resonance it is also found that a current of 5mA flows from the supply when the supply voltage is 25 V r.m.s. Determine the value of the capacitor and the inductance and resistance of the coil.

I know that at res. Freq in series then Xc = Xl. Also in parallel Il = Ic. Just need a hand to get me started.

Thanks in advance.

Stevo.
 
You mention that at resonance, Xc=Xl. That's not quite true. At resonance, Xc=-Xl. Now, using that information, try analyzing the reactances in parallel.
 
Hi Bob,

Not really sure what you mean by this? Inductive reactance increases proportionally to frequency whilst Capacitive Reactance is inversely proportional. By drawing a graph of each on a common axis of rectance against frequency, Xl increases from zero with increase in frequency whereas Xc falls exponentially from infinity at 0 Hz (D.C.). There comes a point where the two graphs cross and that is resonance frequency or Xc = Xl.

I need to know these values of reactance before I can work out the capacitance and inductance and thats what I cant figure out?

Thanks again.
 
You're confused by the graphs. The graphs plot the absolute value of Xl and Xc for convenience only. Resonance is when |Xc| = |Xl|. But due to their sign, at this point Xc + Xl = 0.

This doesn't seem important when there's only one C and one L, but it's essential to keep it straight when a circuit contains many components.
 
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Sosijdog,

Looks like a toughie, doesn't it. What you have are three unknowns. Before going further, let's review resonance. RLC series resonance can have only one frequency. Parallel RLC resonance has three different resonant frequencies. If the Q of the circuit is high, then they are very close to the same value. See Parallel Resonant Circuits . You probably want to chose the third definition, which gives the parallel resonant frequency for the unity power factor. That makes two equations by series and parallel resonance. Next calculate the admittance or impedance of the circuit and combine it with 25 volts and 5 ma for the third equation. Now you should be able to solve for all three unknowns.

Ratch
Hopelessly Pedantic
 
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Ratchet - Thanks very much for that! The link is also very good.

What you say did seem to make some sort of sense so I will have a stab at it again. I just couldn't figure out how to calculate with 3 unknowns... but no doubt I will be back here.

Cheers!
 
Hi,

This is also very interesting to try and solve using a "hunt and peck" method, where you try different values and plug them into the network equation and solve numerically for a min in one circuit and a max in the other circuit. It becomes immediately apparent that the value of C is uniquely linked to the value of L, and that R sets the "channel spacing" between frequencies of the series and parallel. That gives you some organized method to optimize L and doesnt take forever to find by 'hand'.

Analytically, you can use the series resonant frequency to immediately eliminate one variable, either C or L, because of their unique relationship to each other and that constant series resonate point. You can then also solve for R as a function of L, and Fp as a function of L and R, then insert the equation for R into Fp and solve for L as a function of Fp, then insert the constant Fp and that provides for the best numerical value of L, then calculate R, then C.

If you would like to compare your final calculation to the best possible values (to about 14 digits of precision) then post your final values for L, C, and R here later.

In this kind of problem i would bet that the definition of the resonate frequency is the min current for one circuit and the max current for the other circuit.
 
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