Circuits Question: Thevenin Equivalent

Ready2GoXtr · Mar 18, 2010

Homework Statement

Find thevenin equivalent of this circuit with respect to a and b

Circuit schematic with nodes a and b: 100 V source with R1 = 10 Ω in series, R3 = 40 Ω shunt, R4 = 50 Ω carrying current iX, R2 = 20 Ω, a dependent voltage source vS2 = 200 Ω·iX, and a 10 A current source iS.

Homework Equations

Mesh Currents

The Attempt at a Solution

Here I will try to find V(open circuit) = Vth = Vab ((I think this anyways))

I apply mesh currents (any faster methods are welcome if you know them)

Circuit schematic with mesh currents iA, iB, iC and iD marked, nodes a and b, R1 = 10[Ω], R2 = 20[Ω], R3 = 40[Ω], R4 = 50[Ω], v_S1 = 100[V], v_S2 = 200[Ω]iX, dependent voltage source, and current source i_S = 10[A].

iA: -100/V/ + 10/ohm/(iA) + 40/ohm/(iA-iB)=0
iB: 40/ohm/(iB-iA) + 50/ohm/(iB-iC)=0
iC: 50/ohm/(iC-iB) + 20/ohm/(iC) + 200/ohm/(Ix) = 0
iD:-10/A/
iX: iX=iB-Ic

I get the folowing values using solve function on calculator:
iX=-40A/
iA=210/A/
iB=260/A/
iC=300/A/
iD=-10/A/

And using ohms law with parallel resistors having equal voltages..
Vab = 40/ohm/*(iA-iB) = -2000 = Voc = Vth

Now is where I begin to have trouble finding Isc...

I draw the short circuit between a and b (which I believe causes R3 and R4 to have no current through them thus making Ix = 0 and vs2 = 0 as well):

Circuit schematic with nodes a and b across R3 and R4, a short-circuit current Isc marked by a red line; labels R1=10 ohm, R2=20 ohm, R3=40 ohm, R4=50 ohm, vS1=100 V, vS2=200 ohm times iX, iS=10 A.

Simplifying it you gain ((if my previous assumptions are correct reguarding the short circuit)):

Circuit schematic with a 100[V] voltage source in the left branch, R1 = 10[Ω] on top, R2 = 20[Ω] on the top right, a 10[A] current source on the right, and nodes a and b with a red short-circuit current Isc between them.

Now from here I am actually unsure what I should do. I do want to do mesh currents but I don't know if I will receive a correct answer. I also wondered if I could use a closed surface... something like this perhaps:

Circuit schematic with a 100 V voltage source and resistors R1 = 10 Ω and R2 = 20 Ω on the top branch, a 10 A current source on the right, nodes a and b marked, a red short-circuit line between a and b labelled Isc, and a dashed loop drawn around part of the circuit.

If I used that I would get an equation like -100/V/ / 10/Ohms/ + Isc = 0

But then again it just doesn't seem quiet right to me. And i have no way to check my answer.

The Electrician · Mar 18, 2010

You could get rid of the 10 amp source (Is) right from the beginning; it does nothing to the circuit to the left of Vs2. It just adds 10 amps to the current in Vs2, which has no effect on Vs2's voltage.

So, Is contributes nothing to the current in the short you've placed across a-b because Vs2 absorbs the entire 10 amps from Is, and the current in the a-b short is just 10 amps.

Circuits Question: Thevenin Equivalent

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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