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Series Resonance Help

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Trav

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Connect the 50 Ω output from the function generator to the oscilloscope input and establish a sine wave on the oscilloscope with the following characteristics:
a. f = 100 Hz, Vmax = 500 mV
Disconnect the output of the function generator from the oscilloscope and apply it to your circuit. Using a 100 Ω resistor and 2.2 μF capacitor.

Giving me the result:

f(hz) Vr(V) vc(V) vl(V)
100 0.096 0.65 0.06
150 0.13 0.63 0.08

It then asks me to use these results to calculate the following parametersfor 100 and 150hz:

1. I (A)
2. XL (Ω)
3. XC (Ω)
4. Z (Ω)

Would i be right in saying:

1. I v/r 0.0957/100

2. Xl = 2pi x f x l

3. Xc = 1/2pi x f x c

4. Z = √rsquared+(Xc-Xl)squared
 

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Connect the 50 Ω output from the function generator to the oscilloscope input and establish a sine wave on the oscilloscope with the following characteristics:
a. f = 100 Hz, Vmax = 500 mV
Disconnect the output of the function generator from the oscilloscope and apply it to your circuit.

Giving me the result:

f(hz) Vr(V) vc(V) vl(V)
100 0.096 0.65 0.06 I assume that these voltage are measured across the respective components, not wrt gnd.
150 0.13 0.63 0.08

It then asks me to use these results to calculate the following parametersfor 100 and 150hz:

1. I (A)
2. XL (Ω)
3. XC (Ω)
4. Z (Ω)

Would i be right in saying:

1. I v/r 0.0957/100 Correct since R = 100 Ohm.

2. Xl = 2pi x f x l See below

3. Xc = 1/2pi x f x c

4. Z = √rsquared+(Xc-Xl)squared This will give the right answer because of the square, but it should be Xl - Xc

Edit: The part that im really unsure on is actually part 1, so if anybody could just clarify that i will appreciate it, thanks in advance. Also a 100ohm resistor is used and thats were im getting my 100 figure for in Q1.

Vl = I * Xl & Vc = I * Xc

Thus Xl = Vl/I & Xc = Vc/I

You can then cross check your answers by

Including the EMF & source resistance of the function generator in the calculation to see if you obtain the correct value for I
 
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Think im struggling to find the value of the inductance for the xl formula
 
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Think im struggling to find the value of the inductance for the xl formula
Trav,
I have attached my analysis. I believe that there is an error in the original figures since I get different values for L & C when I calculate them at 100 Hz & 150 Hz.

Obviously they should be approximately equal.

I have assumed that the voltages given are those that would be measured across the components, not with respect to Gnd.

I suggest that you check my calculations as I may have made an error.
 

Attachments

  • XL XC Calc.gif
    XL XC Calc.gif
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Hi,

I came to the same conclusion when i looked at this problem. It also appears that the generator voltage is higher than 0.5 volts (might be as high as 0.6 volts).
I used R=100 ohms also.
Some errors in measurement are likely here for one reason or another.
 
I did a simulation & realised that the 100 Hz figures made more sense if the figures specified are peak values rather than RMS.

But it did not work with the 150 Hz figures. So there must be an error somewhere.

I have attached a spread sheet.

My guess is that his lecturer used L = 100 mH & C = 2 uF as his starting point to create the question.
 

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Hi there Len,

I came up with 0.1H and 2.35uf also, but then when i went back to calculate the responses of the whole network i came to the conclusion that we could not get the same numbers with 0.5v peak we'd need something like 0.6v peak as the source input voltage. So there are a number of questions that come up here regarding the measurements. And yeah, the 150Hz numbers dont make sense at all.
 
Hi there Len,

I came up with 0.1H and 2.35uf also, but then when i went back to calculate the responses of the whole network i came to the conclusion that we could not get the same numbers with 0.5v peak we'd need something like 0.6v peak as the source input voltage. So there are a number of questions that come up here regarding the measurements. And yeah, the 150Hz numbers dont make sense at all.
Good morning Mr Al.
Yes something is wrong. It could be a transcription error in the figures. One digit in error could be all it takes to muck up the whole exercise.

I don't intend to waste any more time on it.
 
inductor was in henries, frequency in Hz, resistor in ohms, why not capacitor in farads instead of microfarads.
 
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