I am working on a RL circuit problem and am having some trouble. I will list the steps I have gone through and see if you can help me out. This is how our professor should us how to solve these problems using the step by step method. http://imagizer.imageshack.us/v2/640x480q90/534/fokx.png Step 1: k1+k2e^(-t/tau) Step 2: First solve for Vo(0-) To do this I short circuited the inductor and used three loop equation to solve for I1, I2 and I3 respectively 7I1 + 3I3 = 12 2I2 = 12 3I1 + 9I3 = 0 so respectively we have I2 = 6A and we can solve for I1 and I3 to find I1 = 2A and I3 = -2/3A and we can use that to find Il(t) will equal 20/3 since Il(t) = (I2 - I3) we can also solve for V(0-) and that would be 2I1 = 4V Step 3: Solve for Vc(0+) This is where I start running into problems I believe. Now we can replace the short circuit with the current for Il(t) since Il(0-) = Il(0+) and since the switch closes we have a new circuit. Now I came up with 4 different equation using loop analysis and got 4I1 + 4I2 = 0 4I1 + 7I2 + 3I4 = 12 2I3 = 12 3I2 + 9I4 = 0 now when I solve for the currents I get I1 = -6A I2 = 6A I3 = 6A I4 = -2A now this does not seem right one because (I2 - I3) should equal 20/3 and because when you use these values to calculate Vo(0+) our value comes out to 0V but i am not sure where I went wrong. Any help would be appreciated. Thank you.
One issue for forum members in looking at your solution is that we aren't given the current annotations you use in your equations in relation to the schematic. You need to show these (including assumed directions) on your schematic. vo(0-) is certainly 4V as you have indicated. An important question to ask in relation to the conditions at t=0+ is how one takes into account the 2H inductor given its known state at that instant - e.g. current flow. Further questions: Are you able to predict the final post transient value of vo(∞)? How will you determine the circuit time constant?
I was thinking about it and once I get to Vo(0+) I will now have a two current source. The 2A source and 20/3A source that inductor generates and the voltage source and would the easiest way to solve it using superposition and solve for Vo(0+) and then I could use superposition to find the steady state value and have one current source and one voltage source and do the same thing find Vo(0+). And for the second part I would just find Rth and tau = L/Rth and I understand how to do that part. I was just getting caught up on solving the circuit.