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I am trying to obtain v(t) (voltage across capacitor) and i(t) (current through inductor) for all t > 0;

schematic

simulate this circuit – Schematic created using CircuitLab

The textbook's solution uses source transformation on the current source in order to analyze the circuit with just 1 type of source for t > 0. I am wondering if it is possible to solve this circuit if I leave the current source as it is (no transformation).

I tried, but failed. At this point I am confused. Shouldn't I be able to solve this circuit without source transformation?

The steps to my approach are here. I am providing them for context. If you want to jump to my question, it's at the end of this post.

  1. Consider the circuit for t < 0. Solve for the current through the inductor and voltaqe across resistor, i(0-), v(0-).

  2. Voltage across capacitor cannot change simultaneously so v(0-) = v(0+). Same idea for the inductor, i(0-) = i(0+).

  3. Next we calculate the Neper frequency. Since this is a series RLC circuit, it is R/(2*L) = 8/(2*5) = 0.8.

  4. Then we calculate the natural response w0 = 1/(sqrt(LC)) = 1.

  5. Since Neper Freq. < w0, we have an underdamped response.

Now here is the issue. We have a step response caused by the sources. The equation for the voltage for underdamped responses is of the form

v(t) = Vss + V(0)

Where Vss is the steady-state voltage of the circuit. HOWEVER, in this circuit we also have a current source. How should I deal with this current source if I don't want to turn it into a Voltage Source?

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  • \$\begingroup\$ This question is similar to this: Someone asks you to move a car, you try as good as you can but fail, because the hand brake is pulled up. You ask "How is it done?", someone tells you the answer and tells you to first pull down the hand brake. you realize it's much easier to first pull down the hand brake and then move the car. You understand that. But still you're annoyed with the fact that you couldn't move the car with the hand brake pulled up, and now you want other people to move the car with the hand brake pulled up. Yes, it can be done, it's not fun, you need to be strong. \$\endgroup\$ – Harry Svensson Oct 24 '17 at 5:47
  • \$\begingroup\$ Yeah I know what you mean. I just want to make sure that I fully understand the concept. In theory, everything should work as long as the logic is sound. I know that it would be harder to solve it in my way. The thing that worries me is not that it would be harder.. rather that I wouldn't know how to solve it, since I don't know how to interpret the current sources influence on the circuit. \$\endgroup\$ – AlwaysLearning Oct 24 '17 at 5:55
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You're not meant to have 2 independent sources working at the same time in the circuit, so the best way to deal with this is to use source transformation which will produce a voltage source making the circuit a combination of 2 voltage sources. I'm not sure it can be solved otherwise. Besides before you solve for neper frequency the RLC circuit has to be either a completely parallel or series circuit. Your circuit above is neither (series-parallel), to find 'alpha' you have to use source transform to make it a completely series circuit.

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