Short Circuit Current Calculation

[magnifik]

i am trying to find the short circuit current for the following circuit.

the R_L is the thevenin equivalent resistance. i am trying to find the current when R_L is a wire (short circuit).

by KVL, i have
IR₁ + \mu₁(v₂-v₁) + IR₂ + \mu₂(v₃-v₁) + IR₃ = 0

(the above is not formatted correctly. it should be
IR₁ + m₁(v₂-v₁) + IR₂ + m₂(v₃-v₁) + IR₃ = 0 )

what i am having trouble with is trying to simplify it. specifically, i am trying to get rid of v₂ and v₃

can i substitute v₃ = IR₂
and v₂ = IR₁
??

thanks.

 

[jegues]

i am trying to find the short circuit current for the following circuit.
the R_L is the thevenin equivalent resistance. i am trying to find the current when R_L is a wire (short circuit).

Assuming you are placing your ground at the bottom of the circuit, what can be said about v1 and v2?

If you want to simplify it more, express v1 and v3 in terms of the current times their respective resistance(s).

(HINT: Maybe there is a reason I didn't explicity tell you to solve for v2)

 

[magnifik]

Assuming you are placing your ground at the bottom of the circuit, what can be said about v1 and v2?

If you want to simplify it more, express v1 and v3 in terms of the current times their respective resistance(s).

(HINT: Maybe there is a reason I didn't explicity tell you to solve for v2)

Are the following relationships correct...
v₁ = IR₁
v₂ = v1
v₃ = IR₂

 

[jegues]

Are the following relationships correct...
v₁ = IR₁
v₂ = v1
v₃ = IR₂

Give v3 another shot!

Remember it's not simply the voltage across that one resistor, it's the voltage at that node with respect to ground.

 

[magnifik]

Give v3 another shot!

Remember it's not simply the voltage across that one resistor, it's the voltage at that node with respect to ground.

is it correct to solve it in this way
v3 + m1(v2-v1) / R2 = 0
v3 = -m1(v2-v1)

 

[jegues]

You told me in your above post that v1=v2, so your implying that v3=0?

V3 isn't 0.

 

[magnifik]

i got v3 = -m1(v2-v1), not 0

 

[jegues]

You told me v2=v1, thus v2-v1=0.

Which is in your expression for v3, is it not?

 

[magnifik]

oh, i see now. I'm still having trouble trying to figure out v3.

 

[magnifik]

i tried to do source transforms and analyze viz node method and got
v₃ = -v₁m₂R₂/(R₃ - m₂R₂)

 

[jegues]

i tried to do source transforms and analyze viz node method and got
v₃ = -v₁m₂R₂/(R₃ - m₂R₂)

Okay now that we know that the voltage source is effectively 0 volts wouldn't v3 be defined as follows,

V3 = I(R1 + R2) ?

 

[magnifik]

ahh yes, i see that. thanks. were my other assumptions correct?
v₁ = v₂ ?

 

[jegues]

ahh yes, i see that. thanks. were my other assumptions correct?
v₁ = v₂ ?

I'm not trying to be rude, but have you read my replies?

I had told that v2-v1 = 0.

So yes, v2 = v1.