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# understanding thevenin theorem

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#### PG1995

##### Full Member level 5
Hi

I'm trying to understand Thevenin's thoerem through an example problem. Given below are two scans of the example problem.

1: The author says: Because of the presence of the dependent source, however, we excite the network with a voltage source Vo...

Okay, what would the author have done if there were no dependent source?

2: Why does the author choose subscripts "o" and "oc" in Vo and Voc when the author is concerned about the terminals "a" and "b" of the circuit? Why didn't the author choose more meaningful subscripts?

3: I1 = 1/6 A, I2 = -1/18 A, I3 = -1/6 A

The above currents, I1, I2, and I3, are for three loops. The circuit consists of three loops, right? The current supplied by the 1V source is assumed to be Io. This is the current being fed to the entire circuit. The authors then says Io = -I3. Why? The I3 is the current only in ONE loop which is only one part of the circuit, then how can we equate something such as Io which is being fed into the entire circuit to something which is only being fed in a part of that entire circuit?

4: The author says: 4(I1 - I2) = Vx.
Is this correct? Previously, the author has said: -4I2 = Vx = I1 - I2.

Please help me with the above queries. It would be really kind and nice of you. Thank you.

Scans
1: part one of the example:
https://img197.imageshack.us/img197/5708/theveninpart1.jpg
2: part two of the example
https://img709.imageshack.us/img709/3244/theveninpart2.jpg

#### KerimF

Okay, what would the author have done if there were no dependent source?

We just try to find out the equivalent resistance seen at the two terminals a , b.
Note 1: Also we set the dependent source equal to zero.
Note 2: But we can also follow the same method by exiting the terminals a , b with a voltage source (or current source) as explained.

---------- Post added at 05:18 ---------- Previous post was at 05:13 ----------

Why does the author choose subscripts "o" and "oc" in Vo and Voc
oc denotes open circuit (perhaps o is for output)

---------- Post added at 05:31 ---------- Previous post was at 05:18 ----------

how can we equate something such as Io which is being fed into the entire circuit to something which is only being fed in a part of that entire circuit?

You are right to be confused but, in general, the currents of the loops affect each other. If in one loop the current is increased or decreased, new voltages would be developed on each branch that is common with an adjacent one and this, in turn, lets the current in other loops change as well (till the entire circuit reach its balance, that is, all loop equations are satisfied). The resultant current in the last loop (of a, b) is indeed the cureent we are looking for (the sign depends on the directions we assume in our calculations).

---------- Post added at 05:47 ---------- Previous post was at 05:31 ----------

The author says: 4(I1 - I2) = Vx.
Is this correct? Previously, the author has said: -4I2 = Vx = I1 - I2.

they are different for two reasons:
Reason 1:
Because they refer to different circuits.
-4I2 = Vx = I1 - I2 for fig43(a) that has no independent source.
4(I1 - I2) = Vx for fig43(b) that the independent source is included
Reason 2:
I1 and I2 are for different loops, loop 1 in fig43(a) is loop 3 in fig43(b) for example.

Points: 2

### Senthilkumar_rjpm

Points: 2

#### chuckey

Thevenin example, a 3V battery with two 1K resistors in series wired to its terminals. 1. measure the output voltage, Vo = 3 X 1/1+1 = 1.5V. 2. measure the output current on short circuit. Io = 3V/1k = .003 A. Therefore the above circuit can be represented by a 1.5V battery with a resistor of 1.5/.003 = 500 ohms in series.
What the problem?
Frank

#### PG1995

##### Full Member level 5
KerimF, thank you very much for the help. It was really kind of you. You have also guided me with another problem, thanks for that too.

chuckey, thanks.

Best wishes
PG

#### FvM

##### Super Moderator
Staff member
I'm under the impression, that you have a problem of reading. E.g.
The authors then says Io = -I3. Why? The I3 is the current only in ONE loop which is only one part of the circuit, then how can we equate something such as Io which is being fed into the entire circuit to something which is only being fed in a part of that entire circuit?
A brief view clarifies, that Io and I3 are simply designating the same loop current, only with opposite sign.

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