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by: Jonah Leary

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ME 3210 Week 7 Notes ME 3120 - 01

Jonah Leary
WSU
GPA 3.284

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These are the notes I took last week, covering circuits.
COURSE
System Dynamics
PROF.
Ahsan Mian
TYPE
Class Notes
PAGES
3
WORDS
KARMA
25 ?

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This 3 page Class Notes was uploaded by Jonah Leary on Saturday October 15, 2016. The Class Notes belongs to ME 3120 - 01 at Wright State University taught by Ahsan Mian in Fall 2016. Since its upload, it has received 3 views. For similar materials see System Dynamics in Mechanical and Materials Engineering at Wright State University.

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Date Created: 10/15/16
ME 3210 Notes – Week 7 Chapter 6:  Electrical/Electromechanical Systems 2 vs=v=iR P=vi=i R= v Resistor:   R Series:  RovR +1 2 i=constant 1 = 1 + 1 Parallel: R ov R1 R2 v=constant ϕ dϕ Inductance:  L= [Henry H] ϕ=Magnetic Flux Snell’s Law:  v= i dt dϕ di v=iR+ =iR+L Current through coiled wire causes magnetic field:   dt dt C= Q i= dQ =C dv Capacitor:  Store charge between parallel plates: v dt dt dv P=vC dt Prob 6.6a) Output v Input v 0 s V_ 0 v siR +v1+i 0 2 Kirchhoff’s Voltage Law:   i=C dv 0   v = R +R C dv 0+v dt s ( 1 2) dt 0 dv R +R C 0+v =0→ b)  Find free response:   ( 1 2) dt 0 dv −1 −1 0 = dt→ln v ( 0 t+C ¿ v0 (R1+R C2) (R 1R C2) C − 1 t C ¿ ¿ −1 t (R1+2)C v0( )e →C =ln v 0 ( 0( )) (1+R2) v0(t)=e v 0, fr=v (0)e dv 0 c)  Find forced response:   vs(t=V u (s) ( 1R C2) +v 0V u (ts Table 2.3.2: dt x+ax=b→v ´ + 1 v = V u (t) 0 (R +R C ) 0 ( +R C ) s 1 2 1 2 −1 t x t)= +C e ¿ −at→v (t=V+C e ¿ (1+R2C a 0 −1 ¿ ¿ (R1+R2Ct v0(0 =V +C →C =v 0(0)−V →v 0,tt)=V +(v 0(0)−V)e −1 t v t)=V 1−e (R1+R2C ) v 0, ss=V 0, f −1 (1+R2Ct   v0,tr(v 0(0)−V)e v siR +v1 0 v 0v +CR 2 Prob 6.12) i=C dv → i dt=dv→v= 1 idt V_ dt C C ∫ 0 1 dv 0 1 di v0= ∫ idt+i R 2 = i+R 2 C dt C dt vs−v 0 dv 0 1 vs−v0 d vs−v0 vs−v 0 R2 dvs dv0 i= = +R 2 = + ( − ) R1 dt C R 1 dt R 1 C R1 R1 dt dt R 2 dv0 1 R2dv s 1 1+ + v0= + vs ( )R 1 dt R1C R1dt R1C R= →V (s)=RI s)→Z s = V s)=R Impedance:   i I( ) 1 1 I(s) V s ) 1 v= ∫ idt→V ()= →Z (s= = C C s I ( ) Cs 1 1V (s) V(s) i= ∫ vds→ I(s= →Z s)= =Ls L L s I( )

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