The Circuit

Okay looking at this circuit, I have to main concept questions

1. The inductor in the circuit has no energy stored in its magnetic field at t=0?
How does this compare to when the questions state that the Switches have been open and closed for a very long time (turning the Inductor into a short right before the switches happen)?

2. If the inductor is a short, then wouldnt that short out the voltage source and the resistor, making the problem some resistors and dependent sources, which don't do anything.

 

Every problem I have done with switching, have had switch blah blah has been closed or open for a very long time, so im not understanding how to start working this problem, so hopefully understand the concepts will help

 

PLEASE post your schematics as PNG attachments to your post. The site you put them on attempted to put more than three dozen cookies on my machine and I had to sit there and click NO for each one. If I want to go back and look at the schematic again I will have to do that dance all over and I'm not willing to do that.

By "for a very long time" just means that any transient events that resulted from that last time the switch was changed have had time to die out and things have achieved steady-state operation. For a DC powered circuit, that means that all of the voltages and currents are no longer changing. With that knowledge, you can then determine your initial conditions.

In this case, you are told something different about the state of the circuit at t=0. Instead of knowing that nothing is changing, you are told what the energy in the inductor's field is. This is enough to tell you want about that inductor at t=0? This then let's you determine what about the other components? This then tells you what about the rate at which things are changing in the inductor? Once you have gotten everything analyzed for t=0, you can then walk forward to the time when the switch opens and find the state just prior to it changing (noting that it has NOT reached steady state). Then you use the continuity requirements for an inductor to perform the analysis of the circuit immediately after the switch has opened. Then you can walk things forward to the moment of interest.

At no point in this problem does the inductor look like a short circuit.

 

Okay here is the circuit.

So i did an integral in order to find the current through the circuit. So I have the integral

\(1/.002 \int 12 \)

So this gives me
\( i_L(t)=6000t \) for t>= 0
For 100[ns] I get \( i_L(100[ns])= .0006A

After that i flip the switch for t=100 [ns]

Finding the \( R_{th} \) with a test source I get it equal to
\(1V/-.000019A = -52631.6 Ohms\)
With that I get \(T=-38E-9 \) T=Time Constant

Plugging this into natural response equation i get

\(i_L(t)= .0006e^{((t-(1E-7))/(38E-9))} [A] \) for t>=1E-7

After that I need to find Vx which is Voltage of the Inductor

So I do \( V_x=L(di/dt) \)

So I get \( V_x=(.002)(1136.29e^{((t-(1E-7))/(38E-9))} \)

Which I get \( V_x = 31.58[V] \) when the answer is 403[V]\)

 

And I didn't notice that you can put attachments on the forum but I will start doing that now. So sorry about that.

 

You need to show your work in more detail. Also, use compete and correct equations, track your units (which you are doing hit and miss), and be sure to show/explain your reasoning and how you used the information from one major step to get to the next. For instance, explain how the information given relates to the equation you used to fine the initial conditions. The explain how the results for t=100- ns relates to the conditions at t=100+ ns, and so on.

At least through the equivalent resistance seen by the inductor with the switch open you are close to the right track, but it appears you are making an error somewhere. So show you steps and we will see if we can find your mistake and get you back on track.