# RLC circuit

The instructions are the following.

Connect a function generator (squarewave!!),
large inductor and small capacitor in series, with the cap. grounded.
Watch cap. voltage on o'scope-> exponentially-decaying sinewave.
Measure half life (thl) to find time constant (tau=thl/ln2). Measure
oscillation period (Td) to find damped resonant frequency (Wd) Ask
question: Does 1/tau^2 + w(omega)d^2=1/(LC)??

Is there some way to get the half life time and oscillation period of this circuit if
I know the values of the RLC? I need to compare the experiments with some real
results just to make sure I did this correctly? Also the R here is from the function generator
Asked:
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Commented:
To get the decay constant theoretically requires a value for R. What is it?
Commented:
At series resonance (which is what you have here) the reactance of the C is the same magnitude as the reactance of the L
reactance of L = 2 pi f L
reactance of C = 1/(2 pi f C)
Commented:
"1/tau^2 + w(omega)d^2=1/(LC)"

you will have measured tau, you know L and C, the above info will allow you to calculate wd, so if tau checks out you will probably be doing things correctly.
Author Commented:
R is 470 ohm, and what is reactance? I believe f here is the frequency produced by the squarewave function generator? correct?
Commented:
"what is reactance"   I gave you the equations for reactance in my second response.
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f is not the sig gen frequency but it the frequency of the exponentially decaying sine wave as measured by the oscilloscope in the instructions.
Author Commented:
I know but what does reactance mean?
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reactance is sort of ac resistance as distinct from dc resistance. (It is actually a vector 90 degrees from the dc resistance.
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Continuing that thought...

Reactance is either capacitive or inductive except at the resonance frequency in which case the reactance is neither capacitive nor inductive, but just simple dc resistance; theoretically zero ohms at resonance with just an inductor and capacitor in the curcuit.
However in actuality, the resistance at resonance is at least slightly above zero ohms: It's the internal dc resistance of the wires, connectors and physical imperfections of the circuit components plus the effect of any actual resistor-like elements in the circuit.

(resonance in a circuit requires there to be both a capacitive (C) and a inductive (L) components)

Commented:

The R is the internal resistance that is presented by the function generator when it is connected in the circuit.  Being a (serial) component in the circuit and a real physical device (rather than a theoretical one) it presents some resistance of its own  -- can't get around it.
Author Commented:
and how is reactance useful here?
Commented:
"and how is reactance useful here?"
It is used to calculate the resonate frequency of the circuit. (In your case the wd)
It is the ac equivalent of resistance. It is used in the ac ohms law. You cannot do ac circuits without it.
Author Commented:
so after getting the reactance how do I get the resonate frequency?
Commented:
I told you in my second post.
It is the frequency f at which the reactance of L and C have the same magnitude.
I assume that you know the values of L and C. and that you know what 2 and pi are. That leaves you to calculate the f.
Author Commented:
and I don't know what tHL is....
Commented:
"I know the values of the RLC?"
But you said that you knew what the L an C were.
If you do not know what L and C are, there is no way you can calcaulat the resonated frequency.
Author Commented:
in your third post. "you will have measured tau", I haven't know this
Commented:
quote from your lab instructions
"Measure half life (thl) to find time constant (tau=thl/ln2)"
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You do not have to measure tau to calculate f
Author Commented:
Yes but I haven't done that...
Commented:
do it, we can't
Author Commented:
ok.. guess I am stuck until I can do that in lab.. is there a way I can get this value computational?
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Per the equation that aburr reminded you about, if you know eithe tau or thl then you can calculate the other (assuming you know ln2, of course)
Commented:
"is there a way I can get this value computational"
To get the resonant frequency - yes - see above

To get tau - not without more difficulty that you want to undertake. But that calculation is not important. If your oscilloscope shows something near to the frequency you calculated, you are doing something right. If you can see the oscillations decaying, you can be quite sure that your tau will be acceptable.

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Author Commented:
I don't know either tau or thl so therefore I will need to do this in lab, unless someone has a way to figure out this thl..
Commented:
You have a series circuit:   Z  =  R  +  jwL  +  1/jwC

You should certainly be able to solve for the natural frequencies.
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Commented:

Remember R is any restance you have in the series circuit including the internal restance of the generator.
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