Physics II - Lecture 7 (RC RL LC RLC Circuits)

Physics II - Lecture 7 (RC RL LC RLC Circuits) - Physics 2...

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1 Physics 2 S 2011 Lecture 07 RC, RL, LC and RLC circuits Harmonic signals AC devices
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3 Capacitors and inductors in circuits 2 2 1 L R C C di d q Emf L L dt dt dq Emf iR R dt q Emf idt CC      Write Emf loop equations and/or junction equations using current or charge as convenient. Solve differential equation for current or charge.
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4 P2F09 4 RC circuit analysis + - i ; 0 Write the loop law: C CR RC q dq V V R C dt E V V dq q E dt RC R   / Include initial conditions in solution: Discharging: 0 1 () t RC C dq q dt RC dq dt q RC V t Ee 
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5 P2F09 5 RL circuit ; 0 0 LR RC E i R di V L V iR dt VV di L iR dt      Then switch to position b Initial condition: Start circuit with switch in “a” position so that current E/R flows through inductor. 0 R t L di R dt iL i i e
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6 iClicker question 7.01 Consider the circuit below with an ideal inductor and an ideal capacitor. The capacitor is initially charged. What will happen to the charge on the capacitor when the switch is closed to allow the capacitor to discharge through the inductor? A) It will decay slowly. B) It will decay quickly. C) It will oscillate. D) It remains constant. Let’s do the demo.
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7 LC circuit oscillations Inductor energy – proportional to i 2 . Capacitor energy – proportional to q 2 . Last semester, we saw how a mass on a spring oscillated. We also saw how one form of energy (kinetic) was exchanged for another (potential). In an inductor/capacitor circuit energy stored in the electric field of the capacitor can be alternated with energy stored in the magnetic field of the inductor.
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8 LC circuit Loop rule: 0 circuit di q VL dt C      Substitute, dq i dt 2 2 0 1 dq q dt LC 
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9 Comparing equations 2 2 2 2 1 Mass on spring Inductor/Capacitor d x k x dt m dq q dt LC  Solution to the LC circuit: q = Q cos( w t + f ) and q is the charge on the capacitor. where ω LC
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10 Energy in LC circuits 22 2 cos ( ) E qQ Ut CC wf 2 2 2 11 sin ( ) B U Li LI t constant BE U U U max max EB Q LI UU C
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11 Energy oscillation in LC circuit Energy vs time when the current is a maximum at t=0.
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This note was uploaded on 03/21/2011 for the course PHYS 1200 taught by Professor Stoler during the Spring '06 term at Rensselaer Polytechnic Institute.

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Physics II - Lecture 7 (RC RL LC RLC Circuits) - Physics 2...

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