Redundant branches and combinations:
Redundant means extra, unwanted or Excessive
In an electrical network or circuit there are branches or combinations where some of the elements do not carry any current then such type of branches or combination is nothing but the redundant branches
So these mustbe removed and with removal of this type of branches will not affect the circuit at all.
There are some scenarios where this type of issue exists or occur;
Any branch or combination in an electrical circuit having an short circuited then It will become an redundant and will not carry any current.
From electrical point of view, if there is an electrical direct short circuit across the resistance or with combination of resistances then those will become inactive.
Let's consider as example in order to understand the concept with combination of resistances with short circuit:
In fig a there is an short circuit across the resistance R3, and the current will always flows from low resistance path so all current will pass through the short circuit and hence R3 will become Redundant as per circuit.
As per fig b, there is a short circuit in between combination of resistances R3 and R4. The entire current will flow thorough the short circuit across R3 and R4 and will no current will flow among them; so such combination will become useless and can be eliminated while doing simplification of the circuit.
If there is an open circuit in branch r combination so it will not carry any current and will become redundant.
As per fig there is an open circuited branch BCso branches BC and CD will not carry any current and will become redundant as per network fundamentals.