AC Circuit Analysis: LCR & Resonance

[DTskkaii]

Hi, I am currently struggling with this AC question that is required for my first year electrical engineering coursework. I know sort of how to go about it all, but am having a really difficult time implementing the correct calculations. Any help would be appreciated!

Context
You are given a simple AC LCR circuit (setup in that order, in series, depicted graphically as a square). The AC Voltage source in the circuit replicates the input energy from the sound waves hitting the glass. The inductor and capacitor replicate the resonance characteristics of the glass, and the resistor replicates the energy being converted by the glass as it vibrates. When the energy converted in the resistor is over 200J/s the glass can no longer support vibration and shatters.

Given Values
Vs = ?
L = 4H
C = 3 x 10^(-10)F
R = 50Ohms

Questions
(1) Find the resonant frequency (rad/sec and Hz) of the sheet of glass.
(2)Find the magnitude of the voltage across the resistor in the equivalent circuit, required to break the glass, at the resonant frequency.
(3) Find the magnitude of the voltage source in the equivalent circuit, required to break the glass at resonant frequency. Compare the last two values found.
(4) Using the voltages found above, find the gain (in dB, gain = 20log(Vout/Vin), where Vout is across the resistor) vs the frequency for the following points: 0.01 x w0, 0.1 x w0, w0, 10 x w0, 100 x w0 (where w0 is the resonant frequency.
(5) The clients plan to use that is only accurate to within +-20% of the desired frequency.
- How much sound power do they need to be sure to break the glass?
- At the worst case scenario (20% away from resonant frequency ) find the voltage magnitude and phase shift across each component; source, inductor, capacitor and resistor.

Comments
Sorry for the wall of text, but I just wanted to get it all out so there wasn't any confusion or misinformation. Again, it would be greatly appreciated if anyone can offer guidance on this question in any degree of haste. To note, I do really want to learn the methodology, so please include some small descripts of the steps youre taking, if its necessary :)

 

[DTskkaii]

Just fyi, I've done the first question, and am struggling to figure out my next step.

My answer for Q1 was 28,867.513 rad/s or 4,594.407Hz.

Just to show I'm not trying to get answers without trying :)

 

[technician]

I agree with your resonant frequency.
Do you know the relationship of VL, Vc and the supply voltage Vs at resonance?

 

[DTskkaii]

Thankyou for the fast response.

Sorry if I'm a little slow on the theory, we were only taught the content last week.

I believe this is the point where angular frequencies come into play.?

 

[technician]

At resonance VL = Vc (you could say that they 'cancel' out) so the supply voltage is the voltage across the resistance R

 

[DTskkaii]

Ooh okay.
So in the instance of Q2 and Q3, specifically the 'compare' the two figures, they must be equal. Cool :)

Can you allude at all to the Q2 calculations please?
I'm trying to find what the next step is, and it seem I should be saying that angular frequency = 200w/s, and finding Zr, Zc, Zl; Zt, then using I=Vs/Vt, and then Vr=IZr to get the potential across the resistor. However, I am not given the Vs. (obviously, this would make the question void in the first place). I can't find where I have been taught another way to approach this.

 

[technician]

You calculate the frequency from the fact that XL = Xc at resonance.
You should have equations for calculating XL and Xc that include frequency...

 

[gneill]

Ooh okay.
So in the instance of Q2 and Q3, specifically the 'compare' the two figures, they must be equal. Cool :)

Can you allude at all to the Q2 calculations please?
I'm trying to find what the next step is, and it seem I should be saying that angular frequency = 200w/s, and finding Zr, Zc, Zl; Zt, then using I=Vs/Vt, and then Vr=IZr to get the potential across the resistor. However, I am not given the Vs. (obviously, this would make the question void in the first place). I can't find where I have been taught another way to approach this.

Under what condition will the glass break? What is the energy dissipated in a resistor w.r.t. the voltage across it? Does it depend upon frequency?

 

[DTskkaii]

*removed for revision*

Will post again if I have another question :)

 

[DTskkaii]

*removed for revision