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Exercise:
The oscillation of an LC oscillator with capacitance CO is investigated with an oscilloscope. The measured voltage signal is displayed in the figure. center includegraphicswidthtextwidth#image_path:lc-oscillation-graph# center abcliste abc With the help of the measured voltage signal determine the oscillation's period angular frequency frequency and initial amplitude. abc Calculate the inductance of the coil. abc Calculate the total oscillation energy. abc Calculate the maximum current in the circuit. abcliste

Solution:
abcliste abc From the measured signal we can read the initial amplitude V_VO and the period TTO. We find for the angular frequency omega omF fracpiT om approx resultomP and for the frequency f fracomegapi fF fracT f approx resultfP abc The period is given by T fracpiomegapisqrtLC Solving for the inductance leads to L LF fracT^pi^timesC L approx resultLP- abc The total oscillation energy corresponds to the maximum energy in the capacitor: sscEtot sscWel max EF fractimesCtimesV^ E approx resultEP- abc The maximum current is given by I_ omega Q_ omega C V_ IF fracpiTtimesCtimesV I approx resultIP- Alternatively the maximum current can be found using the conservation of energy: sscWel max sscWmag max frac C V_^ frac L I_^ Solving for the maximum current leads to I_ IbF sqrtfracCLtimes V Ib approx resultIbP- This solution is equivalent to the first one since I_ IbF fracsqrtLC C V_ omega C V_ abcliste
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Exercise:
The oscillation of an LC oscillator with capacitance CO is investigated with an oscilloscope. The measured voltage signal is displayed in the figure. center includegraphicswidthtextwidth#image_path:lc-oscillation-graph# center abcliste abc With the help of the measured voltage signal determine the oscillation's period angular frequency frequency and initial amplitude. abc Calculate the inductance of the coil. abc Calculate the total oscillation energy. abc Calculate the maximum current in the circuit. abcliste

Solution:
abcliste abc From the measured signal we can read the initial amplitude V_VO and the period TTO. We find for the angular frequency omega omF fracpiT om approx resultomP and for the frequency f fracomegapi fF fracT f approx resultfP abc The period is given by T fracpiomegapisqrtLC Solving for the inductance leads to L LF fracT^pi^timesC L approx resultLP- abc The total oscillation energy corresponds to the maximum energy in the capacitor: sscEtot sscWel max EF fractimesCtimesV^ E approx resultEP- abc The maximum current is given by I_ omega Q_ omega C V_ IF fracpiTtimesCtimesV I approx resultIP- Alternatively the maximum current can be found using the conservation of energy: sscWel max sscWmag max frac C V_^ frac L I_^ Solving for the maximum current leads to I_ IbF sqrtfracCLtimes V Ib approx resultIbP- This solution is equivalent to the first one since I_ IbF fracsqrtLC C V_ omega C V_ abcliste
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Attributes & Decorations
Branches
Harmonic Oscillations
Tags
angular frequency, capacitance, frequency, inductance, lc oscillator, period
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration