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finding Ix after source conversion

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PG1995

Full Member level 5
Hi

I'm really stuck here.

I was trying to solve this circuit for finding Ix. Please check this link:
https://img156.imageshack.us/img156/9926/findingix.jpg

There could be two ways t solve this. One is that I convert 2Ix dependent voltage source into a current source, or convert 4A current source into a voltage source. Frankly speaking, I don't know how to find Ix. Please help me. I have redrawn the circuit after source conversions but don't know if they are correct. Please help. It would really kind of you.

You did very well in converting the original circuit.

But since the unknown Ix is in the 10Ω branch, it is better to keep its resistor as it is to keep Ix real. Your first converted circuit has two current sources which lets the calculations be easier than the original one. (Please note that on your second circuit the 10Ω belong to an equivalent part hence it is no more a real one as it is in the original circuit. Its current is no more called Ix).

From your 1st circuit we can write (Ix will be referred by x only):

4 - 2x/5 = total current into the 10Ω and 5Ω in parallel
10*5/(10+5) = 50/15 = equivalent resistance of the circuit.
So if we multiply the current by the equivalent resistance we get the developed voltage.
(4 - 2x/5) * 50/15 = V
But
V = 10 * x
Hence
(4 - 2x/5) * 50/15 = 10x

I guess you can solve this equation... right?
Its answer is one of the followings:

Ix = 0.50505
Ix = 3.33333
Ix = 1.17646
Ix = 1.76228

Hope this help.

Kerim

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