rlc_problem6 - ? ? = + ? 1 ? 50 ? + ? 2 50 ? The final...

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Sample Problem Topic: RLC Circuits/Response Statement of Problem: Given the circuit shown in the figure below Assume the circuit has been operating for a long time. At time t=0, the 200V source suddenly drops to 100V. Find v 0 (t) for t 0. Solution Find the resonant frequency with the equation: ° 0 = 1 ±? = 1 40 10 3 10 10 3 = 50 Find the attenuation with the equation: = ² 2 ± = 4 2 40 10 3 = 50 Note that ω 0 and α are equal, this means that the system is “critically damped.” The V 0 formula takes on the form:
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Unformatted text preview: ? ? = + ? 1 ? 50 ? + ? 2 50 ? The final voltage across the capacitor will be equal to the voltage source, V f = 100V ? = 100 + ? 2 = 200, ? ? 2 = 100 Differentiating: ? ? = 50 ? 2 + ? 1 = 0 D 1 = 50 D 2 Thus, D 1 = 5000V/s Finally, we arrive at the final equation: ? = 100 + 5000 ? 50 ? + 100 50 ? , ? ?...
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