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rlc_problem1

# rlc_problem1 - Sample Problem Topic RLC Circuits/Response...

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Sample Problem Topic: RLC Circuits/Response Statement of Problem: Given the circuit shown in the figure below Assuming at time t=0, the 15mA DC current source is applied to the circuit. Initial current in the 20H inductor is -30mA. Initial voltage on the capacitor = 60V. Find the expression for i L (t) for t 0 if R = 800 Solution Find the resonant frequency with the equation: 𝜔 0 = 1 𝐿𝐶 = 1 20 5 10 6 = 100 Find the attenuation with the equation: = 1 2 𝑅𝐶 = 1 2 800 5 10 6 = 125 The next step is to find the poles of the equation. We simply use the quadratic equation. ? = −∝ ± 2 − 𝜔 0 2 = 125 ± 125 2 10 4 = 125 ± 75 We then find: S1 = -50 rad/s S2 = -200 rad/s There are three forms the solution for I L can take. Since the above circuit is overdamped ( α 2 > ω 0 2 ), the solution takes on the form:

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