rlc_problem3 - We then find S1 =-400 rad/s S2 =-1600 rad/s...

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Sample Problem Topic: RLC Circuits/Response Statement of Problem: Given the circuit shown in the figure below Assume the switch in this circuit has been open a long time. At time t=0, the switch closes. There is no stored energy in the capacitor Find v 0 for t 0. Solution Since the circuit isn’t strictly in a parallel or series configuration, make the following source transform to begin analyzing the circuit: Find the resonant frequency with the equation: 𝜔 0 = 1 𝐿𝐶 = 1 1.25 1.25 10 6 = 800 Find the attenuation with the equation: = 1 2 𝑅𝐶 = 1 2 400 1.25 10 6 = 1000 The next step is to find the poles of the equation. We simply use the quadratic equation. 𝑠 = −∝ ± 2 − 𝜔 0 2 = 1000 ± 1000 2 800 2 = 1000 ± 600
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Unformatted text preview: We then find: S1 = -400 rad/s S2 = -1600 rad/s Note that the question states that the switch has been open for a long time. This implies that the inductor is acting like a short circuit. The question also states that no energy is stored in the capacitor. Once the switch closes, the capacitor is still “bypassed” using the short assumption of the inductor. No charge accumulates in the capacitor, and the 30mA will circulate through the inductor and the current source. The circuit reaches steady state when the switch is closed. (Of course, this wouldn’t be the case in a “real life” circuit, but in this ideal situation, no current reaches the capacitor)....
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