The switch in the following circuit has been opened for a very long time and then closes at t=0 (a) Calculate Vc(t) for t>0. (b) Calculate i(t) for t>0.

Here is my attempt of the problem. I have not dealt with a problem that has two voltage sources before. Also, I have not dealt with a problem that does not become source free after the switch is either opened or closed. I am not sure if I am on the right track, I have getting Vc for t<0 to be 24V, however, Vc for t>0 is 36V?... I thought the Vc for both t>0 and t<0 stays the same. Any tips and help is greatly appreciated

 

What do you mean "source free after switch movement"?

Are you to provide voltage and current at all nodes, or at only a few points? You may want to label each node for easy reference when discussing it.

 

What I mean is that after the switch is changed, the new circuit ends up not having a voltage/current source because of either the open circuit or short circuit.

This time, even after the switch is triggered, the 36V voltage source is present.

 

You've may have missed the point that the presence of the capacitor means that there will be a frst order transient response following the change in switch condition.

You therefore will need to develop the transient response equation and plug in the initial and final steady state conditions to derive the complete time based response for both Vc(t) and i(t).

 

I apologize for my lack of knowledge, I hope my questions do not sound very elementary.

For both t<0 and t>0 the capacitor is to be treated as an open circuit because of the presence of the voltage source, is that correct?

I was attempting to find the Vc(0) for t<0 at first which I assumed to be 24V since it is parallel with the 24V voltage source. After the switch at t>0 the 36V is parallel which makes the Vc(0) for t>0 to be 36V. I thought Vc(0-) and Vc(0+) was to be equal?

 

For both t<0 and t>0 the capacitor is to be treated as an open circuit because of the presence of the voltage source, is that correct?

No that's not correct. You can certainly consider the capacitor as an open circuit for the puposes of finding Vc(t) for t<0 and t=∞. These are are the initial and final steady-state values of the capacitor voltage. But not true for the case of t>0 and t<∞. The capacitor voltage begins to change from t>0 (after switch closure) onwards. That's why a transient solution is required.

Have you ever done this type of analysis in class?

 

I do not believe we have done an example in class such as this in class. At least not that I am ware of. Most of the examples in class or from the text book are simpler than this problem. As I stated previously, most of the homework problems or examples in the book end up as a source free circuit after the switch is thrown.

I have examined the problems at the end of the chapter to find something similar to this problem, but again the problems that have two voltage or current sources end up being source free after the switch is thrown.

I am trying to understand step by step what needs to be done, but it is very confusing.

 

I'm not an expert or anything but we are going through this subject right now. I think it would be easier to find thevenin equivavelent circuit using superposition and than find asked Vc. Not sure if I'm correct though

 

You've correctly calculated the current i(t) for t<0 as 0.002A [2mA].

With 2mA flowing, the 2k resistor will have 4V drop across it. So Vc(0-) will be (36V-4V) or 32V.

 

You've correctly calculated the current i(t) for t<0 as 0.002A [2mA].

With 2mA flowing, the 2k resistor will have 4V drop across it. So Vc(0-) will be (36V-4V) or 32V.

Yep, your i(t) calculation was correct. And the post above was correct about the Vc(0-). If you still don't get why, just think that Vc is parallel to (6k+4k+12V).

Then on t=0+, the 12 V source and 4k resistor will give no effect to the remaining circuit, and the Vc voltage still remains 32 V. However at this state i(t) will surely change (try to figure it out).

Then at t>0, the 36 V source is still present, which means you must use Complete Response analysis, that Vc(t) on t>0 will have a forced response value plus natural response value.