{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

p2s10_lec11_LC_oscillations_RC_RL - q q = = Q Q cos cos ϖ...

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

View Full Document Right Arrow Icon
Physics 2 2009 Lecture 11 RC and RL circuits LC circuit oscillations circuit equations energy transfer and storage RLC circuit oscillations
Background image of page 1

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

View Full Document Right Arrow Icon
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 - + = = - =
Background image of page 2
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 - = =
Background image of page 3

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

View Full Document Right Arrow Icon
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.
Background image of page 4
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 + =
Background image of page 5

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

View Full Document Right Arrow Icon
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:
Background image of page 6
Background image of page 7

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

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

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

View Full Document Right Arrow Icon
Background image of page 10
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( ϖ t t + + φ ) ) and q is the charge on the capacitor. and q is the charge on the capacitor. where ω LC 1 = Energy in LC circuits 2 2 2 cos ( ) 2 2 E q Q U t C C ϖ φ = = + 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 τ ϖ φ-= + 2 L R τ= 2 1 1 ' LC =-with: and RLC Circuit...
View Full Document

{[ snackBarMessage ]}