E il vs r l r dil 1 v il s dt l soluon

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: ( 0 ) = iL (t ) = Vs + A = io R A = io − Vs R Vs ⎛ V ⎞ −t + ⎜ io − s ⎟ e τ R⎝ R⎠ R vR vL iL Vs iL (0 + ) = io L D.E. Solu;on: diL 1 V + iL = s dt τ L where τ= L R iL (t ) = Vs ⎛ V ⎞ −t + ⎜ io − s ⎟ e τ R⎝ R⎠ iL ( 0 + ) = Vs ⎛ V⎞ + ⎜ io − s ⎟ = io R⎝ R⎠ (ini;al value) iL ( ∞ ) = Vs ⎛ V⎞ V + ⎜ io − s ⎟ ( 0 ) = s R⎝ R⎠ R (final value) t ≥ 0+ Check: t = 0 + t = ∞ 9 3/12/14 R iL (0 + ) = io vR vL iL Vs τ= L D.E. iL ( ∞ ) = Vs R L R diL 1 V + iL = s dt τ L Solu;on: iL (t ) = Vs ⎛ V ⎞ −t + ⎜ io − s ⎟ e τ R⎝ R⎠ t ≥ 0+ − t ≥ 0+ t iL (t ) = ( final ) + ( initial − final ) e τ RC circuit Switch is closed at t=0 t=0 − t = 0+ just before ac;on t=o R just aXer ac;on Vs Note! Capacitor voltage can not change instantaneously vc C vc (0 − ) = vo vc (0 − ) = vc (0 + ) 10 3/12/14 t ≥ 0 + t = 0 − t=o R R ic C vc Vs vc Vs vc (0 + ) = vo vc (0 − ) = vo t ≥ 0 + For Vs = vR + vc KVL: C ⎛ dv ⎞ Vs = C ⎜ c ⎟ R + vc ⎝ dt ⎠ Vs = ic R + vc dvc 1 V + vc = s dt RC RC dvc 1 V + vc = s dt τ τ τ = RC First order non- homogeneous D.E. R vc (0 + ) = vo ic Vs vc vc (∞ ) = Vs C τ = RC D.E. Solu;on: dvc 1 V + vc = s dt τ τ t...
View Full Document

This document was uploaded on 03/16/2014 for the course EEL 3004C at University of Central Florida.

Ask a homework question - tutors are online