Transients(L)

gneill

Okay! So you have the Thevenin equivalent for the network that's driving the inductor. To put numbers to them, R_TH = 21.6 and V_TH = 53.76. Correct?

Now, the Norton equivalent circuit has the same resistor value as the Thevenin equivalent, and the voltage source is replaced with a current source of V_TH/R_TH. The resistor is in parallel with the current source.

Do the same work for the case after the switch is closed. Note that all the switch does is put R1 in parallel with R2. What numbers do you get for the Norton equivalent in this case?

builder_user

But when switch is closed there is the inductive element.It resistance add too?




This circuit after commutation?

Attached Thumbnails

 

gneill

We're treating the inductor as the load being driven by a Norton equivalent of the source network. It plays no part in finding the equivalent circuit for the source network.

So no, there is no inductor added to the source network by the switch. It only adds R1 in parallel with R2 to the circuit we just analyzed. We will deal with the inductor after we have the equivalent circuits for the sources.

What we want to end up with is two Norton equivalent circuits, one for each state of the switch. These two equivalent circuits replace the current source and resistor networks of the original circuit. These equivalent circuits will be "driving" the inductor. They will make it easy to analyze what happens when the switch is closed.

builder_user

After replacing there will be diff. equatations?



So this scheme?
and
R=R1*R2/(R1+R2)
U=J*R

Attached Thumbnails

 

gneill

I'll show you how to analyze the circuit without differential equations to begin with. That way you'll know what result you're looking for!

Yes, the figure you provided is the circuit of the source network after commutation of the switch. You want to find its Norton equivalent, just like you did for when the switch was open. What's its Norton resistance and current?

builder_user

But I must find U as time function...like this
U=900/375*e^375t+C


The problem is....I must use differential equatations.But they only need at the moment of commutation.With Laplace and without it(especially for LC).It's the task.

builder_user

Strange but currents are the same.

gneill

The equivalent circuits will allow you to write the differential equations very easily. In fact, you will probably already have done so for circuits in this basic form!

I will show you how to write the desired U(t) function by inspection, so that you can check your differential equation result. Will that work for you?

gneill

I think you may have forgotten about R3 and R4...

builder_user

I found U.
U/R3=J3
U/R4=J4?

builder_user

I need equations like this

from example
moment of commutation
UL=Ldi/dt

i2+i3=i1
i1*R1+i2*R3=E
-i2*R3+i3*R4+Ldi3/Dt=0

-E-i3*R1/(R1+R3)*R3+i3*R4+Ldi3/dt=0
i3=2.4+c*e^-375t

i(0)=1.7(before commut.)
2.4+c*e^0=1.7
c=-0.7

i3(t)=2.4-0.7*e^-375t

gneill

What are J3 and J4?

If you are looking at the Thevenin equivalent of your circuit, there is no current through R3 or R4. The Thevenin voltage is produced by the current flowing through the parallel combination of R1 and R2. The Thevenin resistance is the sum of R3 and R4 and the parallel combination of R1 and R2.

The Norton resistance, R_N, is the same as the Thevenin resistance. The Norton current is V_TH/R_TH.

builder_user

I see.


Operator method it seems to similar
find i before and after commutation
replace inductor with operator resistor
p=j*w - operator.

gneill

The equations will be easy to write from the equivalent circuits. You will have only to deal with one current source, one resistor, and one inductor. Your textbook probably has this form as an example!

builder_user

so, for L i'll just need to use U=Ldi/dt?

gneill

Yes. Certainly.

What I've been trying to do is reduce the before and after commutation circuits to their very simplest forms so that it will be very easy to apply any method of circuit analysis you wish to use. They will be so basic that your textbook should already provide a solved example.

builder_user

Ok.So I just need to make system of equatations and only to solve it?