Help with temporal analysis of RC with current source

Dan4d

Joined Nov 10, 2019
5
Hi Everyone, I'm doing this excersice, I have to find vc(t)

I already could find vc(o) wich is 46V, but I'm having trouble when it connects to the second part of the problem.I tried to read the loop as vc(t)+vR3(t)+vR4(t)=0 but then i can't find a clear path to keep studying this circuit.

Thanks

WBahn

Joined Mar 31, 2012
26,148
You need to define what vR3(t) is. Yes, it's sufficiently obvious that it's the voltage across R3, but there are two possible polarities for it and you need to define which it is. Same for vR4(t).

While your equation might be KCL around the loop that includes those three components, that isn't the only loop that has to be solved for.

Before you go any further, figure out what both the voltage and current are for the capacitor for when the switch is just closed and after it has been closed for a long time.

Dan4d

Joined Nov 10, 2019
5
Before you go any further, figure out what both the voltage and current are for the capacitor for when the switch is just closed and after it has been closed for a long time.
Yes, this was the first thing I stated when I started studying the circuit, the Capacitor has been a long time.

While your equation might be KCL around the loop that includes those three components, that isn't the only loop that has to be solved for.
What do you refer with KCL, english is not my first language, so many abreviatures are strange for me.

Dan4d

Joined Nov 10, 2019
5
Would be a good move to do thevenin with I1 and R4?

WBahn

Joined Mar 31, 2012
26,148
Yes, this was the first thing I stated when I started studying the circuit, the Capacitor has been a long time.
You only gave the capacitor for right after the switch is moved, which is critically important. But you should also determine the capacitor current just after the switch is moved as well as the capacitor voltage and current a long time after the switch is moved. These provide check values that your solution has to agree with.

What do you refer with KCL, english is not my first language, so many abreviatures are strange for me.
This is an English-only forum and you gave no hint that English was your second language. I'm not a mind reader and I don't know what your native language is or what abbreviations you are and aren't familiar with. You English seems just fine.

KCL is Kirchhoff's Current Law

WBahn

Joined Mar 31, 2012
26,148
Would be a good move to do thevenin with I1 and R4?
Certainly not required, but a very reasonable thing to do.

RBR1317

Joined Nov 13, 2010
563
I have to find vc(t)
Whenever you have a switched circuit with a *single* energy storage element (L or C) and no impulsive currents or voltages, there are a few things to realize that can simplify the solution:

1. The current through an inductance (L) and the voltage across a capacitance (C) will be exactly the same after the switching event as it was just prior to the switching event. This is true even for multiple switching events.

2. The current through an inductance (L) and the voltage across a capacitance (C) will follow an exponential curve as it changes from its initial value (at the switching event) to its final stasis value (after many time constants).

3. Use the initial value and the final stasis value along with the circuit time constant to construct the equation for a rising or falling exponential curve that describes the behavior of the single energy storage element.

4. When finding the final stasis value, an inductance (L) is replaced by a short circuit while a capacitance (C) is replaced by an open circuit.

5. If there are multiple switching events, calculate the final stasis value for each event separately.

My introductory circuits textbook had an entire chapter on this, but it didn't say much more than these five points.

WBahn

Joined Mar 31, 2012
26,148
The TS may or may not have gotten to time constants yet. Some texts have them slug through the differential equation for a few circuits before using that as the basis for introducing the concept of a time constant and then showing how, for first-order circuits, the time-constant can be extracted without messing with differential equations. Not only does this establish the fundamentals of what time constants are and where they come from, but by having had to do a couple of non-trivial circuits using differential equations, the student is well motivated to learn any technique that will let them avoid that in the future.

MrAl

Joined Jun 17, 2014
7,811
Hi Everyone, I'm doing this excersice, I have to find vc(t)

View attachment 218060
I already could find vc(o) wich is 46V, but I'm having trouble when it connects to the second part of the problem.I tried to read the loop as vc(t)+vR3(t)+vR4(t)=0 but then i can't find a clear path to keep studying this circuit.

Thanks
Hi,

The real key to solving these kinds of circuits is to understand how to deal with initial conditions. Basically you analyze the circuit the same as you always do except each storage component has some value for its initial condition such as 3 volts or 3 amps. There are various ways to handle this depending on what math you are using to analyze the circuit. When the circuit has to switch states such as this one does you get the initial conditions of the next state from the final conditions of the previous state and apply them the same way you do with any circuit that has initial conditions.
When you have a circuit with energy storage elements the initial conditions play a big role in the solution(s) but really you could say that all circuits with energy storage elements always have initial conditions it is just that for simpler problems the initial conditions are often all zero. For switching circuits like this however they are usually only zero at the very start of the problem and after that there is almost always some remnant energy stored in one or more energy storage elements.
This all makes the circuit a little harder to analyze, but it also makes it more interesting because it means your analysis techniques extend to circuits that have internal energy stored at the start of the problem or even sometime after that.

You may wish to state how you have learned to handle initial conditions in the past and that will help people guide you using the method(s) you already understand.

WBahn

Joined Mar 31, 2012
26,148
He gave the relevant initial condition in the initial condition (and it's contained in the material you quoted). The initial voltage on the capacitor, just after the switch is thrown, is 46 V. He has also given a loop equation for one of the two essential loops, though whether or not it is correct depends on the assigned polarities of the voltages across the resistors, which had not been given. He needs another equation, which can either be due to KVL around an independent loop or KCL at an independent and non-trivial junction.

He's also asked about doing a source-transformation on part of the circuit, which is a very reasonable thing to do, but has been quiet since. Has the due date passed?

MrAl

Joined Jun 17, 2014
7,811
He gave the relevant initial condition in the initial condition (and it's contained in the material you quoted). The initial voltage on the capacitor, just after the switch is thrown, is 46 V. He has also given a loop equation for one of the two essential loops, though whether or not it is correct depends on the assigned polarities of the voltages across the resistors, which had not been given. He needs another equation, which can either be due to KVL around an independent loop or KCL at an independent and non-trivial junction.

He's also asked about doing a source-transformation on part of the circuit, which is a very reasonable thing to do, but has been quiet since. Has the due date passed?
Well perhaps my previous post was a tad redundant then.

I think the source transformation idea is good too that makes it a little simpler. Of course i wont mention which source(s) yet though.