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Unformatted text preview: Lecture 20 Lecture 201 LC Oscillations 2 2 1 , , 2 2 E B Q dQ U U LI I C dt = = = No Resistance = No dissipation 2 2 2 1 1 dQ Q dt LC LC f ω ω π + =⇒ = = Lecture 20 Lecture 202 Mechanical Analogy 2 2 1 1 , , 2 2 dx U kx K mv v dt = = = max 0, U K K = = max , U U K = = max , U U K = = . E constU K = = + harmonic oscillator with k m ω = No friction = No dissipation 2 2 dx k k x dt m m ω + =⇒ = /2 f ω π = Lecture 20 Lecture 203 More on LC Oscillations Energy stored in capacitor: 2 2 1 () cos 2 E peak U t Q t C ω = t E U t B U Energy stored in inductor: 2 2 2 1 () sin 2 B peak U t L Q t ω ω = 1 LC ω = where 2 2 1 () sin 2 B peak Ut Q t C ω = 2 () () 2 peak E B Q UtUt C + = so sin peak dQ I Q t dt ω ω = =− Charge and current: cos peak Q Q t ω = (with δ =0) Period is half that of Q(t) Lecture 20 Lecture 204 Series RLC Circuits The resistance R may be a separate component in the circuit, or the resistance inherent in the inductor (or other parts of the circuit) may be represented by R . Finite R Energy dissipation...
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This note was uploaded on 04/07/2008 for the course PHYS 241 taught by Professor Wei during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Wei
 Resistance, Friction

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