Turning off a source, which is usually used in solving circuits with superposition method, means setting its value equal to zero. For a voltage source, setting the voltage equal to zero means that it produces zero voltage between its terminals. Therefore, the voltage source must insure that the voltage across two terminals is zero. Replacing the source with a short circuit can do that. Thus, voltage sources become a short circuit when turned off.
For a current source, setting the current equal to zero means that it produces zero current. Therefore, the current source must insure that no current flows through its branch. An open circuit can do that. Hence, to turn off a current source it should be replaced by an open circuit.
How about dependent sources? The voltage/current of a dependent source is dependent on other variables of the circuit. Therefore, dependent sources cannot be turned off.
Example I: Turn off sources one by one.
Solution:
I) The voltage source:
II) The current source:
Example 2: For each source, leave the source on and turn off all other sources.
Solution
I. 
:
II. 
:
III. 
:
IV. 
:
Example 3: For each source, leave the source on and turn off all other sources.
Solution
I. :
II.
Recall that dependent sources cannot be turned off.
notes are very helpfull. Thank you.
my question is about a 2A current source in series with a 10 ohm resistor, and there is an unknown voltage across the branch. I understand the current source will supply 2 amps of current, regardless of the voltage across it. However, does the 10 ohm resistor also have 2 amps of current thru it (and 20 volts across it) always, completely independent of the voltage across the branch, or does the total current thru the branch (and current thru the resistor) depend on the voltage across the branch? (i may be answering my own question, that is if the voltage influenced the resistor, it would also have to pull more than 2 amps through the current source, and since that impedence is infinite, that can’t be. Is this correct, that the current through the 10 ohm resistor will always be 2 amps?) If this is true, is the voltage across the branch equal to the voltage across the resistor, i.e. 20 volts?
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What if the current the dependent voltage source depends on is zero? Do we consider it as short circuit?