Question about source transforms

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Hi, I have a question about something I encountered while working a problem.

http://img171.imageshack.us/img171/5899/questionnz.jpg

I replaced the voltage source in series with the resistor, with a current source in parallel.

I was expecting the current through the 1M ohm resistor to stay the same. Upon inspection, they are different.

I thought about it for a long time and came up with this explanation, can you please tell me if I am thinking correctly:

1.) The resistor and current or voltage source pair can have stuff change in them, but if you draw a box around them, then the output voltage and current to the rest of the circuit is the same.

2.) Since the current through that resistor changes, the power it absorbs changes. However, I suspect:

total power absorbed by 1M ohm resistor + current source = total power absorbed by 1M ohm resistor + voltage source.

Is that correct?

Thanks.
 
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The two power sources (to the left of the 470K resistor) are equivalent.
They will deliver 9 volts open circuit and 9 microamps short circuit.

The actual current depends on the rest of the circuit.