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Unformatted text preview: 1 Lecture16 Oscillation in LC circuit without resistor We have In absence of any resistor in circuit, charge ( q ) initially stored in C drives current ( i ) in circuit and, later, the current charges capacitor; this process repeats over time. Energy in circuit oscillates from electrical energy to magnetic energy indefinitely. Signs of charge in C and current in L alternate between + and . Time C q U E 2 2 2 2 1 Li U B Electric energy in Capacitor: Magnetic energy in Inductor: 2 t t t 2 2 3 2 V R I V C I V L I ) ( 1 1 , sin dt dI L dt dI L V Idt C Q C V I R V t I I For L t C R LC circuit with, and without resistor When resistor is added, energy loss by Ohmic heating damps out current (i.e., U B ) as well as charge (i.e., U E ), as shown above. Phase Relations among V R , V C , V L and I Potential drops across resistor, inductor and capacitor scale differently with current: When AC current is established in R, C, or L, potential drop over it is uniquely related to current I because of above mathematical relationships. With resistor Without resistor 3 Temporal Response of Potential Drop Resistor: V  R I = 0 I = I o sin d t V R = I o R sin d t =I R sin( d t+0) Capacitor: I = I o sin d t Inductor: I = I o sin d t Idt C V C Q V 1 dt dI L V ) 2 sin( cos t L I t L I V d d d d L ) 2 sin( cos t C I t C I V d d d d C d d d V R is in phase with I....
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 Spring '08
 Hickman
 Physics, Charge, Current, Energy

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