Exam_1_ans - EEL3112 Spring 2014 Exam#1 1 Linear Circuit...

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EEL3112 – Spring 2014 – Exam #1 1. Linear Circuit Problem Consider the circuit shown on the Figure Page with the switch initially in the “A” position, position “B” for t 0, L=1, R=2, C=1, V1=V 1 , V2=V 2 , V 1 and V 2 real constants. 1.a: What is the initial inductor current and capacitor voltage as a function of V 1 and V 2 ? [5] With the switch in the “A” position C is fully charged and becomes an open circuit. Therefore, i L (0 - )=0, and v C (0 - )=V 1 1.b: Using the impedance method, what is I(s) as a function of V 1 and V 2 ? [20] V1/s V2/s L(s)=s C(s)=1/s R=2 S V1/s=(IC) Figure 1: With the switch in the “B” position. KVL (B position): , ; ) ( ) ( ) ( ) ( ) ( ) ( 1 2 2 2 2 2 2 2 1 2 1 2 1 2 V V V s s V s I s V s I s s s s V s V s I s s s V where (s 2 +2s+1) is called the characteristic equation. 1.c: Classify the circuit as being under, critically, and over damped. [5] The characteristic equation s 2 +2s+1 = (s+1) 2 has repeated real roots {ans. critically damped}
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  • Fall '07
  • Harris
  • Electrical impedance, characteristic equation

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