L14 first.pptx

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

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

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