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DTskkaii
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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 :)
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 :)
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