L14 first.pptx

Inductor current can not change instantaneously il l

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Unformatted text preview: l voltage vc(at t=0) Initial energy stored within inductor is defined in terms of initial current iL(at t=0) R t=o Vs R t=o Vs L C RL circuit Switch is closed at t=0 t=0 − just before ac;on t=o t = 0+ R just aXer ac;on Vs Note! Inductor current can not change instantaneously iL L iL (0 − ) = io iL (0 − ) = iL (0 + ) 5 3/12/14 t = 0 − t = 0 + R t=o R vR iL Vs L vL iL Vs L iL (0 − ) = io For iL (0 + ) = io t ≥ 0 + R vR KVL: Vs = iR R + vL Vs = vR + vL L iL (0 + ) = io ⎛ di ⎞ Vs = iL R + L ⎜ L ⎟ ⎝ dt ⎠ diL R V + iL = s dt L L vL iL Vs diL 1 V + iL = s dt τ L τ= L R First order non- homogeneous D.E. 6 3/12/14 First order non- homogeneous D.E. diL 1 V + iL = s dt τ L D.E. τ= L R Solu;on: Note: For non homogeneous D.E the solu;on has two components! in : Natural response iL (t ) = in + iss iss : steady state in: due to energy stored within the circuit iss: due to sources in the...
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