30_Lec-19

# 30_Lec-19 - Physics 241 Lecture 19 Y E Kim November 2 2010...

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November 2, 2010 1 University Physics, Chapter 30 Physics 241 Lecture 19 Y. E. Kim November 2, 2010 Chapter 30, Sections 1, 2, and 4

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November 2, 2010 Physics for Scientists & Engineers, Chapter 30 2 LC Circuits Analysis of LC Oscillations Driven AC Circuits
November 2, 2010 3 ± Inductance L of a solenoid as proportionality constant between the flux linkage N ) B and the current i (in analogy to q = CV ): ± The unit of inductance is the henry (H) ± The inductance of a solenoid of length l and area A with n turns per unit length an is given by Review: Inductance 2 [] 1 Tm 1 H 1 A ) ± 2 0 nlA P N ) B Li University Physics, Chapter 30

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November 2, 2010 University Physics, Chapter 30 4 Review: LR Circuit ± LR circuit L di d t ± iR 0 i ( ) 0 e ² / W 0 V emf / R ± m f ³ ´ ³ ´ // () 1 ² ² = / Circuit connected to emf Circuit disconnected from emf
November 2, 2010 University Physics, Chapter 30 5 Review: Energy in Capacitors and Inductors ± Remember that the energy stored in the electric field of a capacitor with charge q is given by ± Remember that the energy stored in the magnetic field of an inductor carrying current i is given by ± To illustrate ´HOHFWURPDJQHWLF RVFLOODWLRQVµ± consider a simple LC circuit containing an inductor L and a capacitor C 2 1 2 E U 2 1 2 B Li

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November 2, 2010 University Physics, Chapter 30 6 LC Circuit (1) ± The capacitor is initially fully charged and then connected to the circuit ± The energy in the circuit resides solely in the electric field of the capacitor ± The current is zero ± 1RZ OHW·V IROORZ WKH HYROXWLRQ ZLWK WLPH RI WKH FXUUHQW± charge, magnetic energy, and electric energy in the circuit
LC circuits (2) Time Evolution November 2, 2010 Physics for Scientists & Engineers, Chapter 30 7

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November 2, 2010 University Physics, Chapter 30 8 LC Circuits (3) ± The charge on the capacitor varies with time ± Max positive to zero , to max negative , to zero, back to max positive ± The current in the inductor varies with time ± Zero to max positive , to zero , to max negative, back to zero ± The energy in the inductor varies with the square of the current and the energy in the capacitor varies with the square of the charge ± The energies vary between zero and a maximum value
November 2, 2010 University Physics, Chapter 30 9 LC Circuits (4)

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November 2, 2010 University Physics, Chapter 30 10 LC Oscillations (1) Quantitatively: ± We assume a single loop circuit containing a capacitor C and an inductor L and that there is no resistance in the circuit ± We can write the energy in the circuit U as the sum of the electric energy in the capacitor and the magnetic energy in the inductor ± We can re-write the electric and magnetic energies in terms of the charge q and current i E B ± 2 2 11 22 Li ± ±
November 2, 2010 University Physics, Chapter 30 11 LC Oscillations (2) ± Because we have assumed that there is no resistance and the electric field and magnetic field are conservative , the energy in the circuit will be constant ± Thus the derivative of the energy in the circuit with respect to time will be zero ± We can then write ± Remembering that i = dq / d

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30_Lec-19 - Physics 241 Lecture 19 Y E Kim November 2 2010...

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