# Equivalent resistance with dependent sources

Discussion in 'Homework Help' started by lll, Mar 7, 2012.

1. ### lll Thread Starter New Member

Mar 7, 2012
21
1
What strategy do I use for solving this type of problem?

There's no current in the 2-ohm resistor on the left, but I don't know what to do after that. I tried using a test source, but my answer contained a variable.

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2. ### steveb Senior Member

Jul 3, 2008
2,431
469
There are two strategies.

1. Brute force calculation
2. Intuitive simplification

It sounds like you have tried both, but still didn't get it.

For method 1, you use the test source, but you make sure that you express the unknown variable (I'm guessing you still had Ix in there) in terms of known things. The known thing will be related to your test source.

For example, let's say you decide to put a current source Io into the terminals. Then, you calculate the output voltage Vo at the terminals and then the resistance is Ro=Vo/Io. So, Ix can be related to Io, in that method.

For method 2, you already started correctly, but you need to take it further. If there is no current in that 2 ohm resistors, then there is no voltage drop, and you have a virtual short circuit across the resistor. This places the other 2 ohm resistor in parallel with the 1 ohm resistor. These parallel resistors have a net resistance of 2/3 ohms. But, that's not the complete story because the voltage source changes with Ix, which is a feedback mechanism (note that it might be positive feedback) that changes the effective impedance at the terminals.

Both methods give the same answer. Can you finish it off now? Try both methods for practice.

lll likes this.
3. ### lll Thread Starter New Member

Mar 7, 2012
21
1
Thanks! I got 1 ohm and that's what the answer key says, so good advice.