Solving RLC Circuit with Step-by-Step Guide | Circuit Diagram Included

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The discussion focuses on solving an RLC circuit problem where the switch has been closed for an extended period before opening at t = 0. Key calculations include determining the total resistance of 12 ohms and the damping factor, alpha, calculated as 4 Neper. Participants emphasize the importance of establishing initial conditions for the inductor current and capacitor voltage before the switch opens, and they recommend writing the mesh equation to derive a second-order differential equation for the circuit analysis.

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1. The switch in the circuit shown in Figure has been closed for a long time
before t = 0 but opened at t = 0. Solve for i(t) for t ≥ 0.

*Hereby I attached the circuit diagram for the question above.

And this is where I got so far.
(6ohm+6ohm)=12ohm
alpha=R/2L
= 4 Neper.
But then I don't know how to solve for the rest.
 

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We don't do homework for you. You must show some effort in order to get some help.
What were the current in the inductor and the voltage at the capacitor before the opening of the key. These are the initial conditions for your circuit.
Write the mesh equation for the circuit after the opening. You will have a second order differential equation.
Solve the differential equation and substitute the initial conditions.
 

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