How Do You Calculate Thevenin Equivalents in Circuit Analysis?

[dead_devil_66]

Homework Statement

[PLAIN]http://d.imagehost.org/0018/enunciado.png

It's in portuguese but what it's being asked is to find the Rth and Vth, the Thevenin equivalents for that network, in that cut point...

V2 and all resistors values are known.

Homework Equations

The Attempt at a Solution

For Rth, I'm unsure between

( R2 + R5 ) || ( R4 || R5 )

OR

R2 || ( ( R4 || R3 ) + R5)
For Vth, my solution is using nodal analysis. I guess you guys can see the datum with the 'arrow'.

A: -Ir4 + Ir3 + Ir2 = 0
B: -Ir3 - Ir2 + Ir4 = 0

I'm assuming the positive ones as the currents that go out from the node.

Va = V2
Ir4 = (Vb - Va) / R4
Ir3 = (Va - Vb) / R3
Vth = R2*Ir2 <=> Ir2 = Vth/R2

Vth/R2 = ( Vb - V2 ) / R3 + ( V2 - Vb ) / R4

So, now I'm stuck! How can i get the Vb?
Thanks in advance!

 

[Quinzio]

Break the circuit into 2 pieces then apply Thevenin to part1 then draw the simplified circuita and apply T. again.

It's more intuitive and simple.

 

[dead_devil_66]

and what about using Mesh analysis method?

[PLAIN]http://d.imagehost.org/0269/circuito4.png

J1: -V2 + Vr4 + Vr3 = 0
J2: -Vr3 + Vr5 - Vr2 = 0

J1 is the upper mesh current, J2 is the other one.

By solving the system i got:

J1 = -( ( V2 * ( R5 - R2 - R3 ) ) / ( R3 * ( R5 - R2 + R4 ) ) )

J2 = -( V2 / ( R5 - R2 + R4 ) )

Ir2 = J2


i think that

Vth = Ir2 * R2


Right?

 

[dead_devil_66]

Break the circuit into 2 pieces then apply Thevenin to part1 then draw the simplified circuita and apply T. again.

It's more intuitive and simple.

so, should i sum R2 and R5 and make that sum resistor the load resistor?

 

[DeeNos]

I would first commend you on your attempt at solving this exercise using nodal analysis. Your approach is correct, but you seem to be stuck on how to get Vb. To solve for Vb, you can use the fact that the current going through R5 is equal to the current going through R4 (since they are in parallel). This means that you can use Ohm's Law to express Vb in terms of the known values of V2, R2, R3, and R4. Once you have Vb, you can then solve for Vth using the equation you derived earlier. As for Rth, both of your proposed solutions are correct. You can choose either one depending on which one is more convenient for your calculations. Keep up the good work in your studies of circuit analysis and Thevenin equivalents!