Question Q1. Figure 3.1 shows an RLC circuit. Assume that the current source of 2A is applied to the circuit. The inductor has an initial current, i(0) = 1 A and the initial capacitor voltage, v(0) = 20 V. + o ij(t) L R vet) C W Figure Q1 (a) Design your circuit to obtain an overdamped, critically damped, and underdamped response. Let the radian frequency, 0 = 1000 rad/s. Use a standard component values in the design. (b) Find the expression of vo(t) and iz(t) for t 2 0s for each of your circuit design in part (a). Show all your calculations. (C) Simulate the circuit designed in (a) and plot all the responses of of v.(t) and iz(t) for t >0 s on a single graph. (d) Analyze the response from part (c) that will give the shortest time on reaching 80% of the final value of v.(t). Give comment and conclusion. Q2 The circuit in Figure 3.2 is operating in the sinusoidal steady state. 522 1092 M ig ia + + Vg 2.5 mH 2092 VO 12.5 UF Figure Q2 (a) If given vg = 25 sin 4000t V, find the steady state currents and voltage: ig, ia and VO (b) Plot the steady state currents and voltage: ig, ia and v, response.

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Transcribed Image Text: Q1. Figure 3.1 shows an RLC circuit. Assume that the current source of 2A is applied to the circuit. The inductor has an initial current, i(0) = 1 A and the initial capacitor voltage, v(0) = 20 V. + o ij(t) L R vet) C W Figure Q1 (a) Design your circuit to obtain an overdamped, critically damped, and underdamped response. Let the radian frequency, 0 = 1000 rad/s. Use a standard component values in the design. (b) Find the expression of vo(t) and iz(t) for t 2 0s for each of your circuit design in part (a). Show all your calculations. (C) Simulate the circuit designed in (a) and plot all the responses of of v.(t) and iz(t) for t >0 s on a single graph. (d) Analyze the response from part (c) that will give the shortest time on reaching 80% of the final value of v.(t). Give comment and conclusion. Q2 The circuit in Figure 3.2 is operating in the sinusoidal steady state. 522 1092 M ig ia + + Vg 2.5 mH 2092 VO 12.5 UF Figure Q2 (a) If given vg = 25 sin 4000t V, find the steady state currents and voltage: ig, ia and VO (b) Plot the steady state currents and voltage: ig, ia and v, response.

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Q21 As per chegg QA Rulei 9 dim answering one question ie. Q2 as below its both parts.(d) For, 'L', X_{L}=\omega L=4000 \times 2.5 \times 10^{-3} \Omegax_{1}=j 10 \OmegaFor ' C^{\prime}, \quad x_{c}=\frac{1}{\omega C}=\frac{10^{6-3}}{12.5 \times 4}=(20)^{1} \Omega(-j)=-20 J^{\circ} \OmegaNow; f or I_{g}, V_{0} and I_{a}, we Prorecd as;For Ig\begin{array}{l}\text { zin }=5+\{j 10\} \|\{(10)+(20) \|(-20 j)\} \\=5+1 \mathrm{Joj} 1(10+10 \mathrm{~J}) \Omega=10 \sqrt{2} \\\end{array}\begin{array}{l} \therefore I_{g_{1}}=\frac{V_{g}}{2 i n}=\frac{25 L 0^{\circ}}{10 \sqrt{2} L 4}=\frac{5}{2 \sqrt{2}} 145^{\circ} \\I_{1}=\frac{j 10}{20-10 j+10 j} \times I_{g}=\frac{5}{2 \sqrt{2}} \mid 45^{\circ} \times 0.5190 \\I_{1}=\frac{5}{4 \sqrt{2}} 4135^{\circ} \Rightarrow I_{a}=\frac{-20 j}{20-20 j} \times I_{1}=\frac{5}{8} 190^{\circ} \mathrm{A} \\\therefore I_{a}=\frac{5}{8} j \mathrm{~J} \\V_{0}=20 \times I_{a}=20 \times \frac{5}{8} j=\frac{25}{2} j\end{array}\therefore We get expreesion for all the parte as\begin{array}{l}I_{g}=1.767 \sin \left(4000 t+45^{\circ}\right) \\I_{a}=0.625 \sin (4000 t+90) \\V_{0}=12.5 \sin \left(4000 t+90^{\circ}\right)\end{array}(b) Plot of the above function will be;(ii) I_{a}=0.625 \sin \left(4000 t+90^{\circ}\right) A \quad \frac{2 \pi}{4000}=T(II) V_{0}=12.5 \sin (4000 t+90)Thankyou. I have answered Q2 as per QA RULE. .Please like theanswer ASAP. ...