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It would depend on the circuit diagram. In some cases, the circuit would be incomplete (simplest case is a battery with a wire attached to just one terminal).

Parallel branches that have a connection to the battery without going through other branches are independent of each other. Say you have two parallel branches and a battery. If you short circuit one of the branches, the other branch will not be affected but the battery will be (current through the battery would decrease because taking out a parallel branch increases resistance).

In short, it would depend on the circuit diagram. Note that for a nanosecond, there would be current in an open circuit, but after this brief time there would be no current flow in the segment of the circuit that has been shorted.

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Q: What are the circuit effects due to a short circuit or open circuit?
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