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Show that in the free oscillations of an lc circuit on quora |
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Answer» ircuit, also called a resonant circuit, is an ELECTRIC circuit consisting of an inductor(L) and a capacitor (C), connected together. The electric current and the charge in the capacitor in the circuit UNDERGO electrical LC oscillations when a charged capacitor is connected to an inductor. The electrical energy stored in the capacitor is its initial charge (qm). It is expressed as follows: Ue =1/2( qm)^2/C/.The inductor contains zero energy, and the charge varies sinusoidally with time. When the switch is turned on the current in the circuit starts to increase and the charge in the capacitor keeps decreasing, The current in the circuit induces a magnetic field in the inductor. When the current increases to its maximum level (Im) the magnetic energy in the circuit is represented as: Ub = 1/2*L*(Im)^2.The magnetic field starts decreasing because there is no further change in current in the inductor. Then the current is induced in the circuit as a result of the decreasing magnetic field. With reverse polarization current starts charging the capacitor. The process is repeated again once the capacitor is fully charged, The energy in the WHOLE SYSTEM thus oscillates between the capacitor and the inductor. The charge oscillates with a natural frequency of w(o) = 1/(LC)^1/2.In PRACTICE this process is never achieved at its maximum level due to loss of energy in the form of heat from the resistance and also energy loss due to radiation of electromagnetic waves. |
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