Here is a technique which helps in some circuits....
THE RECIPROCITY THEOREM
The reciprocity theorem states that, in any branch(AC) of a circuit, the current(I1) due to single source of voltage(E) elsewhere in the network(BD) is equal to the current(I) through the branch(BD) in which the voltage source was originally placed when the source is placed in the branch(AC) in which current (I1) originally flowed.
see figure 1.
here suppose the question is given that we are to find current in branch AC.
Then just shift the emf from the original position (in branch BD) to the branch AC (the branch in which current is to be found). It is to be noted that The emf is to be shifted without changing the polarity as shown in figure 2..
Then according to Reciprocity Theorem,
the current(I) in the branch BD in fig. 2 = the current (I1) in branch AC in fig. 1.
Note :-
This method is applicable only when the circuit is NOT a multisource network. The network should not have any time varying element.