Superposition in Bridge Circuit

[kbwelch17]

I'm having trouble using superposition to solve this problem. Isn't the bridge balanced and thus has no voltage across the positive and negative terminals? Also - what would happen if you shorted the positive and negative terminals?
Here's a link to the image:

[pebe]

You are quite right. The 5mA current generator across the 1K resistor will produce 5V across the resistor. That adds to the battery voltage so you effectively have 10V applied via a 1K resistor to the bridge.

The bridge is balanced (four equal 1K resistors) so there will be no voltage between its + and - terminals, and no current will flow if the two terminals are shorted together.

[kbwelch17]

I am having trouble understanding why there would be no current between them if they were shorted together. Why would the current prefer 1k ohm resistor as opposed to another?

[pebe]

If there is no voltage difference between the two terminals, then it is logical that no current can flow between them
That's what a 'balanced' bridge means.