Hello,
Yes a theoretical voltage source has 0 ohms impedance so to the current source it looks like the two resistors are in parallel, but you have to be careful with the numbers and make sure the calculation comes out right. For example, with only a 100ma current source (voltage source shorted) the total resistance is 0.9 ohms, and the voltage across the two resistors is 0.090 volts Thus the current through the 1 ohm resistor is 0.090/1=90ma, and the current through the 9 ohm resistor is 0.090/9=10ma (in this case we consider that negative). So when we connect the 10 volt source we get 1-0.010=990ma through the 9 ohm resistor and 1.09 amps through the 1 ohm resistor.
But the more general way to attack this kind of circuit is simply through the use of "Superposition". Superposition is used to simplify a circuit that has more than one source. This circuit has one voltage source and one current source, so that means superposition might help.
To use superposition to solve a circuit with two or more sources, we use the following basic procedure:
1. Short all voltage sources (this is called 'killing' a voltage source).
2. Open circuit all current sources (this is called 'killing' a current source).
3. Now that we have all sources 'killed', un-kill each source one at a time, and calculate the desired response (voltage or current), then kill that source again.
4. Add up all of the responses calculated in #3 above, that's the solution.
So applying this procedure to the circuit at hand, we would first short out the 10v source, then open circuit the current source.
We could then start by un-killing the 10v source (removing the short), then calculate the current through the 1 ohm resistor call that i1.
Next, we would again short out the 10v source, and then reconnect the current source, then calculate the current again through the 1 ohm resistor call that i2.
The solution is the total response which is simply the sum of the two currents just calculated:
iTotal=i1+i2
So in short all we had to do was apply each source one at a time and calculate the desired response using each source, then add all of those responses to get the final solution which is the total response. We just have to remember that to kill a voltage source we short it out, but to kill a current source we open circuit it. This is the theoretical procedure and for a real life practical circuit if we wanted to try this out in real life we'd have to modify it slightly.
APPLYING THIS PROCEDURE TO A REAL LIFE CIRCUIT...
One catch to doing this in real life (we usually dont do this anyway) is that when we short out a voltage source we get an infinite current, and when we open circuit a current source we get an infinite voltage, either of which will cause big problems, so we have to modify the theoretical procedure slightly if we wanted to try this out on a real life circuit with real life sources.
In the real life circuit instead of shorting out the voltage source directly, we first disconnect it from the circuit and then intead of shorting out the source itself we short out the two terminals that the source had originally connected to.
And instead of open circuiting the current source, we either disconnect it's power supply first or short it out before disconnecting it from the circuit which is required for open circuiting it.
APPLYING THIS PROCEDURE IN SPICE...
Spice has it's own issues. Often it wont let you short out a voltage source and will complain if you do, so we do the same as in real life, we disconnect one lead and short only the two original circuit terminals.
To kill a current source, often BOTH leads of the current source will have to be disconnected from the circuit and then you can short out the current source to keep the voltage developed across the current source low.