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# lec14 - LC Circuits Consider the LC and RC series circuits...

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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

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10/16/11 2 LC Circuit Oscillations Kirchoff’s loop rule L C + + - - I Q
10/16/11 3 0 I 1 Q 0 0 2 4 6 1 t 0 Δ I Δ t 1 0 V C 0 2 4 6 1 V t 0 L 1 LC Circuit Oscillations

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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 ω 0 = 1 LC
10/16/11 5 U E t 0 0 2 4 6 U B 0 t 0 2 4 6 Energy in Capacitor Energy in Inductor Therefore, Energy Check: in LC circuit U E ( t ) = 1 2 C Q 0 2 cos 2 ( ω 0 t + φ ) U B ( t ) = 1 2 L ω 0 2 Q 0 2 sin 2 ( ω 0 t + φ ) ω 0 = 1 LC U B ( t ) = 1 2 C Q 0 2 sin 2 ( ω 0 t + φ ) U E ( t ) + U B ( t ) = Q 0 2 2 C

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10/16/11 6 U B versus U E in LC curcuit:
Rates and Frequencies: RC, LR and LC Circuits 10/16/11 7 ω 0 = 1 LC 1/ τ RC = 1/ RC 1/ τ LR = R / L RC Circuit: Charging Rate LR Circuit: Decay Rate LC Circuit: Oscillation Freq.

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lec14 - LC Circuits Consider the LC and RC series circuits...

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