Transient circuit analysis problem with a dependent source

In summary, the conversation revolved around solving a circuit problem involving a switch, inductor, and voltage controlled current source. The goal was to find the value of L/R(equal), using the equations iL(t) = iL(∞) + ( iL(0-) - iL(∞) )* ( e^(-(t/τ) ) ) and VL(t) = L * [ ∂iL(t) / ∂t ], and the hint that voltage across an inductor can change instantaneously but current through the inductor can't change instantaneously. The conversation also addressed potential contradictions and confusion in the circuit, but ultimately concluded that the only possible answer is I = 4 * e ^
  • #1
Michael_0039
59
7
Homework Statement
Find the Vo of the Transient circuit
Relevant Equations
nil
Hi all,

I tried to solve this, but I can't find the R(equal). I use the following method.

The circuit:
22.PNG

For t<0 the switch is closed so the iL(0-)=4 A

For t>0 it opens and the iL(∞)=0 A

Now, I want to find the value τ=L/R(equal)

Then I will use the: iL(t) = iL(∞) + ( iL(0-) - iL(∞) )* ( e^(-(t/τ) ) )

And finally VL(t) = L * [ ∂iL(t) / ∂t ] which is the Vo

What do you suggest ?Thanks.
 
Last edited:
Physics news on Phys.org
  • #2
Been a long time since I've used a simulator but I'm assuming the device in parallel with the inductor is a Voltage Controlled Current Source (VCCS) with 4Vo being its transfer function.

If that is the case, what resistance value would yield a current of 4 times the applied voltage?
 
  • #3
Thanks for your answer!

I think I solved it¨, this is my try:

New Doc 2019-09-30 10.37.17_1.jpg

New Doc 2019-09-30 10.37.17_2.jpg
 
  • #4
There seems to be contradiction, I am confused.

On the one hand, the inductor current should maintain 4A at the moment the switch is turned off.

However, on the other hand, if the voltage of the inductor is initially zero, the VCCS should force the inductor current to zero immediately after the switch is turned off.

Where is my inference wrong?
 
  • #5
alan123hk said:
However, on the other hand, if the voltage of the inductor is initially zero, the VCCS should force the inductor current to zero immediately after the switch is turned off.
Hint: Voltage across an inductor can change instantaneously but current through the inductor can't change instantaneoulsy.
 
  • Like
Likes berkeman and scottdave
  • #6
After the switch is opened, the current throughout the right-hand loop is all the same. Use this fact to set up the differential equation, and integrate to solve for I(t).

The expression will be an exponential, so the exponent will tell you what the time constant is.
 
  • #7
@scottdave Thanks for your answer.

What about my post #3 is that a correct process? For this kind of problems I use those steps in post #3. I never tried something else.
 
  • #8
cnh1995 said:
Hint: Voltage across an inductor can change instantaneously but current through the inductor can't change instantaneoulsy.

Thanks for your hint, it is true that the voltage across inductor can change instantaneously, but current flowing through inductor cannot change instantaneously.

I am only worried that there may be ambiguous situation in this particular circuit.

I mean that I = Io * e ^(-t /(4L))= 4 * e ^(-50t) may be just a possible answer, and there may be another possible answer.

Since the voltage across the inductor is zero, the current source should be zero when the switch is opened, so why can't the voltage across the inductor become infinite because the current source can be considered as infinite resistance?

It also means that the current flowing through the inductor disappears in an extremely short period of time in this situation.
 
  • #9
alan123hk said:
Since the voltage across the inductor is zero,
What is the voltage across the inductor the moment you open the switch?
 
  • Like
Likes alan123hk
  • #10
cnh1995 said:
What is the voltage across the inductor the moment you open the switch?

Thank you for your valuable reply. :smile:
After re-study the circuit, I agree that I = 4 * e ^(-50t) is the only answer.
 
Last edited:
  • Like
Likes scottdave
  • #11
alan123hk said:
Thank you for your valuable reply. :smile:
After re-study the circuit, I agree that I = 4 * e ^(-50t) is the only answer.
I haven't verified the calculations, but there is no contradiction in this circuit. The moment you open the switch, the inductor voltage instantaneously increases to whatever is required to maintain the 4A current.
 
  • #12
Note which direction I is flowing through the inductor. How will it flow through the dependent source? What will the polarity of Vo be?
 
  • Like
Likes Michael_0039

FAQ: Transient circuit analysis problem with a dependent source

1. What is a transient circuit analysis problem with a dependent source?

A transient circuit analysis problem with a dependent source refers to a type of circuit analysis that involves analyzing an electrical circuit with a dependent source, which is a component whose voltage or current depends on the voltage or current of another component in the circuit.

2. How is a transient circuit analysis problem with a dependent source different from a regular transient circuit analysis?

A transient circuit analysis problem with a dependent source is different from a regular transient circuit analysis because it involves taking into account the effects of the dependent source on the rest of the circuit. This means that the equations used to solve the circuit will include variables related to the dependent source.

3. What types of dependent sources can be present in a transient circuit analysis problem?

The most common types of dependent sources that can be present in a transient circuit analysis problem are voltage-controlled voltage sources (VCVS), current-controlled voltage sources (CCVS), voltage-controlled current sources (VCCS), and current-controlled current sources (CCCS).

4. How do you solve a transient circuit analysis problem with a dependent source?

To solve a transient circuit analysis problem with a dependent source, you will need to use a combination of Kirchhoff's laws, Ohm's law, and the equations for the specific type of dependent source present in the circuit. This will allow you to set up a system of equations that can be solved to determine the voltage and/or current at each point in the circuit.

5. What are some common applications of transient circuit analysis problems with dependent sources?

Transient circuit analysis problems with dependent sources are commonly used in the design and analysis of electronic circuits, such as filters, amplifiers, and oscillators. They are also used in the study of electrical systems, such as power grids and communication systems, to predict and analyze the behavior of the system under different conditions.

Similar threads

Replies
8
Views
3K
Replies
3
Views
3K
Replies
3
Views
1K
Replies
2
Views
991
Replies
2
Views
1K
Replies
7
Views
5K
Replies
1
Views
11K
Replies
2
Views
2K
Back
Top