Short circuit current distribution

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Hi, After adding a wire across a circuit to section off part of the load in the form of a short circuit, I am still seeing a couple of milliamps flowing through the load. Is this due to the fact that the wires used to create the short circuit will have a small amount of resistance, hence preventing all the currrent flowing through the short circuit?
 
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Yes.

The remaining series load will determine the current. The current will be shared by the short and the shorted part of the load in proportion to the reciprocal of their respective resistances.

In reality there is no such thing as a perfect short circuit. There will be a voltage difference across the short. That will result in a residual current through the higher resistance original load path.