Problem 4: RLC circuits (20 pts) 10 Hiz(t) Vince) t=0 + 100mV DC tic(t) tir(t) R$ v(t) 1F 1H a The initial energy stored

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Problem 4 Rlc Circuits 20 Pts 10 Hiz T Vince T 0 100mv Dc Tic T Tir T R V T 1f 1h A The Initial Energy Stored 1 (43.62 KiB) Viewed 42 times

Problem 4 Rlc Circuits 20 Pts 10 Hiz T Vince T 0 100mv Dc Tic T Tir T R V T 1f 1h A The Initial Energy Stored 2 (47.49 KiB) Viewed 42 times

Problem 4 Rlc Circuits 20 Pts 10 Hiz T Vince T 0 100mv Dc Tic T Tir T R V T 1f 1h A The Initial Energy Stored 3 (21.29 KiB) Viewed 42 times

Problem 4: RLC circuits (20 pts) 10 Hiz(t) Vince) t=0 + 100mV DC tic(t) tir(t) R$ v(t) 1F 1H a The initial energy stored in the inductor and capacitor is zero. Att = 0, a 100mV DC source is attached to the RLC circuit through a 12 resistor. We know the equation and parameters for t20 at critical damped condition: dv(0*) = D. - aDz; v(t) = D, te-at + Dze-at, v(0+) = Dz. dt ZRC and for parallel RLC circuit, a = 2,90 = te a) Find the R value for critical damping (6 pts) (hint: you may convert the 100mV DC and 19 to current source-based equivalent circuit first using source transformation) b) What will be initial current of i(0*), ic(0*) and ir(0*). (9 pts)

EE 201: Electric Circuits c) If R is larger than the value calculated in a), the circuit will be in (Circle the correct answer): (3 pts): A. Under-damped condition: B. Over-damped condition; C. Critical-damped condition. d) If R is larger than the value calculated in a),(Circle the correct answer) (2 pts): A. Ringing will happen; B. The response will still be smooth but will settle slower, without ringing. D. The response will still be smooth but will settle faster, without ringing. Problem 5: Frequency Domain Circuit Analysis (15 pts) 2mH -000 12 w ZTH w оа Vs(t) VTH (1) 1mF ob Original Thevenin Equivalent In the above circuits, vs(t) = 2cos1000t. a) Convert the inductor and capacitor into impedance (2. and Ze). (2 pts) b) Find the Thevenin Equivalent voltage VTH in both frequency and time domain. (6 pts)

EE 201: Electric Circuits c) Find the Thevenin Equivalent impedance Ztr. (4 pts) d) In order to extract the maximum average power from the source, find the loading impedance should be attached between "a" and "b".(3 pts)