E 10 0 what is vct at all times 1030ut 20

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Unformatted text preview: V at t=0 (i.e., = −10 + 0 ( )). What is VC(t) at all times? -10+30u(t) + - 20 Ω 0.1 mF 3/5/2012 + VC - ECE 201-4, Prof. Bermel 0.25 H Solution 20 Ω + - -10+30u(t) 0.1 mF 20 Ω 0.1 mF + VC - + VC - 0.25 H 0.25 H • Use source transformation to recover original parallel RLC circuit problem: −10 + 0 1 = =− + () 20 22 3/5/2012 ECE 201-4, Prof. Bermel Solution 20 Ω 0.1 mF + VC - [-1+3u(t)]/2 0.25 H • From earlier definitions: 1 Γ= = = 1 ∙ 0 ∙ 10 1 0. 5 ∙ 10 • Circuit is overdamped 3/5/2012 ECE 201-4, Prof. Bermel = 50 = 00 Solution 20 Ω 0.1 mF + VC - [-1+3u(t)]/2 0.25 H • For t<0, inductor looks like short and VC(t<0)=0 • For t>0, non-zero voltage temporarily possible; start by solving for IL in overdamped regime: = + + Here, Γ = 250, and Γ= 3/5/2012 Γ− = 250 − 200 = 150 ECE 201-4, Prof. Bermel Solution 20 Ω 0.1 mF + VC - [-1+3u(t)]/2 0.25 H • Given that: ≥0 = = + • Since IL(0)=-1/2, and VC(0)=0: + +1 +1 −= + +1 =− − 0.25 −100 − 400 =0 = −4...
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This note was uploaded on 11/22/2013 for the course ECE 201 taught by Professor All during the Spring '08 term at Purdue University-West Lafayette.

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