p240_ct22_f07 - Physics 240 Fall 2007 Lecture #22 No...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 240 Fall 2007 Lecture #22 Dr. Dave Winn 2405 Randall Lab winn@umich.edu No discussion tomorrow (11/21)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Essential ideas from last time Electrical oscillations in LC circuits Frequency of oscillation ω = 1/ LC Total energy is constant Energy is traded between E (in capacitor) and B (in inductor) fields Charge on C and current in L both oscillate: Q(t) = Q 0 cos( ω t+ ϕ ) I(t) = - ω Q 0 sin( ω t+ ϕ ) These oscillations are “out of phase”: when charge is large, current is small, when charge is small, current is large.
Background image of page 2
Real oscillators Real oscillators don’t run forever. They gradually lose energy In mechanical oscillators, friction drains energy In electrical oscillators, resistance drains energy Time it takes things to stop depends on what keeps it going (inertia and L) compared to what stops it (friction and R). Timescale for mechanical damping: ~inertia / friction Timescale for electrical damping: inductance / res. (~L/R) Just like a normal RL circuit!
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Mechanical Example Mass on a spring is the oscillator, friction provides the damping If damping is weak, many oscillations before dying away, if strong, no oscillations will occur Oscillation frequency is shifted, it oscillates more slowly The equations: () 2 2 2 2 0 2 2 2 2 ) cos( 0 m b m k m b t e X t x kx dt dx b dt x d m ma bv kx ma F m bt = = + = = + + = = ω ωω φω
Background image of page 4
The Electrical Example Oscillator is the LC circuit, damping from resistance If damping is weak, many oscillations before dying away, if strong, no oscillations will occur Oscillation frequency is shifted lower The equations: () 2 2 2 2 2 2 2 1 2 ) cos( 0 0 L R LC L R t Qe t q C q dt dq R dt q d L dt di L iR C q L Rt = = + = = + + = + + ω ωω φω
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 2 1 < L R LC 2 2 1 > L R LC 2 2 1 = L R LC
Background image of page 6
What happens to the energy? Energy is gradually drained away… It is lost as Ohmic i 2 R losses in the resistor The timescale for loss is the damping time L/R () L Rt B E L Rt E L Rt E e C Q U U t e C Q U t e Q t q C q U = + + = + = = 2 ) ( cos 2 ) cos( 2 2 0 2 2 0 2 0 2 φω
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/04/2008 for the course PHYSICS 240 taught by Professor Davewinn during the Fall '08 term at University of Michigan.

Page1 / 27

p240_ct22_f07 - Physics 240 Fall 2007 Lecture #22 No...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online