p2s10_lec11_LC_oscillations_RC_RL

# p2s10_lec11_LC_oscillations_RC_RL - q q = = Q Q cos( cos( t...

This preview shows pages 1–10. Sign up to view the full content.

Physics 2 2009 Lecture 11 RC and RL circuits LC circuit oscillations circuit equations energy transfer and storage RLC circuit oscillations

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

View Full Document
P2F09 2 RC circuit review + - i ; 0 C C R C R C q dq V V iR R C dt q E V V E iR C dq q E dt RC R = - = - = - + + = - - = + = / Discharging: 0 1 ( ) t RC C dq q dt RC dq dt q RC V t Ee - + = = - =
P2F09 3 RL circuit ; 0 0 L R R C E i R di V L V iR dt V V 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 i L i i e - = =

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

View Full Document
LC circuit oscillations Inductor energy – proportional to i 2 . Capacitor energy – proportional to q 2 . Last class, we saw how a mass on a spring oscillated. In PHYS 100 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.
LC circuit Loop rule: 0 circuit di q V L dt C ∆ = - - = Substitute, dq i dt = 2 2 0 1 d q q dt LC + =

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

View Full Document
Comparing equations 2 2 2 2 1 Mass on spring Inductor/Capacitor d x k x dt m d q q dt LC = - = - Solution to the LC circuit: Solution to the LC circuit:

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: q q = = Q Q cos( cos( t t + + ) ) and q is the charge on the capacitor. and q is the charge on the capacitor. where LC 1 = Energy in LC circuits 2 2 2 cos ( ) 2 2 E q Q U t C C = = + 2 2 2 1 1 2 2 sin ( ) B U Li LI t = = + constant B E U U U + = = 2 2 max max 2 2 E B Q LI U U C = = = Energy oscillation in LC circuit Energy vs time when the current is a maximum at t=0.-0.2 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 Time in Periods Ratio of U E to U B U = U B + U E U B U E t = /8 t T = / 4 t T = 3 /8 t T = 5 / 2 t T = 4 3 2 1 6 5 /8 t T = 3 / 4 t T = 7 /8 t T = 7 8 1 2 3 4 5 6 7 8 Energy oscillation in an LC circuit 1 Writing the loop equation for emf: 2 2 1 d q dq L R q dt dt C + + = This is the equation for the motion of damped harmonic oscillator, with solution: ( 29 / ( ) cos ' t q t Qe t -= + 2 L R = 2 1 1 ' LC =-with: and RLC Circuit...
View Full Document

## p2s10_lec11_LC_oscillations_RC_RL - q q = = Q Q cos( cos( t...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online