The circuit in the Fig. 1 is initially relaxed and is excited at t = 0 by a sinusoidal source. Determine the voltage (in t) across the capacitor for t > 0 using Laplace techniques.
1.1. What is the response form of this circuit? (5p) 1.2. Equation (in t) for circuit’s current (10p) 1.3. Equation (in t) for voltage across capacitor (5p) 1.4. Redesign and draw the circuit such that the response form is different (anything other than the one from 1.1) (show your work) (10p)
2. (15p) The 100 mH inductor in the below Fig.2 is initially relaxed. At t = 0, a 100 V source is connected. Determine and sketch the expressions for i(t) (current in the circuit) and vL(t)(voltage across the inductor) for t > 0. Note: Do not use Laplace transform
3. (25p) The inductor in the Fig. 2 (see Question #2) is initially relaxed and is excited at t = 0 by a 100 V source. 3.1. Determine the expressions for i(t) (current in the circuit) and vL(t)(voltage across the inductor) for t > 0 using Laplace techniques. (15p) 3.2. Does your expressions from second question match? (5p) 3.3. What is your conclusion regarding the two methods? (5p)
4. (30p) For the of the circuit in the Fig. 4: 4.1. Determine the transfer function if the input is v1(t) and output is v2(t). (10p) 4.2. Determine the total poles and zeros, also construct an s-plane plot of the finite poles and zeros. (5p) 4.3. Classify the stability of the system. (5p) 4.4. Determine the response of the above system if the input is excited at t = 0 by v1(t) = 15 V (10p)
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