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

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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
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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 B L i 2 0 L n lA 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 dt iR 0 i ( t ) i 0 e t / L i 0 V emf / R L di dt iR V emf     // ( ) 1 t L R emf V i t e R  L = L / R Circuit connected to emf Circuit disconnected from emf
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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 “electromagnetic oscillations”, consider a simple LC circuit containing an inductor L and a capacitor C 2 1 2 E q U C 2 1 2 B U 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 Now let’s follow the evolution with time of the current, charge, magnetic energy, and electric energy in the circuit
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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
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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 EB U U U  2 2 11 22 q U U U Li C
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November 2, 2010 University Physics, Chapter 30 11 LC Oscillations (2) Because we have assumed that there is no resistance and
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This note was uploaded on 11/28/2010 for the course PHY 222 taught by Professor Yu during the Spring '10 term at Beaufort County Community College.

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

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