lec14(2x2)

lec14(2x2) - LC Circuits ! Consider the LC and RC series...

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10/16/11 1 Consider the LC and RC series circuits shown: Suppose that at t =0 the capacitor is charged to a value of Q . Is there is a qualitative difference in the time development of the currents produced in these two cases. Why?? L C C R ++++ - - - - ++++ - - - - LC Circuits 10/16/11 2 LC Circuit Oscillations Kirchoff’s loop rule L C + + - - I Q 10/16/11 3 0 I 1 Q 0 1 t 0 ! I t 1 0 V C V t 0 L 1 LC Circuit Oscillations 10/16/11 4 • The other unknowns are found from the initial conditions. Question: Does this solution conserve energy? • Oscillation frequency has been found from the loop equation. LC Oscillations: Energy Check 0 = 1 LC
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10/16/11 5 U E t 0 U B 0 t Energy in Capacitor Energy in Inductor Therefore, Energy Check: in LC circuit U E ( t ) = 1 2 C Q 0 2 cos 2 ( ! 0 t + " ) U B ( t ) = 1 2 L 0 2 Q 0 2 sin 2 ( 0 t + ) 0 = 1 LC U B ( t ) = 1 2 C Q 0 2 sin 2 ( 0 t + ) U E ( t ) + U B ( t ) = Q 0 2 2 C 10/16/11 6 U B versus U E in LC curcuit: Rates and Frequencies: RC, LR and LC Circuits
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lec14(2x2) - LC Circuits ! Consider the LC and RC series...

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