Flux Linkages in Parallel Current Carrying Conductors

Consider a group of parallel conductors A, B, C etc as shown in the Fig. 1. Each of these conductors carry current I_A, I_B, I_C etc.

       Consider the flux linkages with any one conductor say A. There will be flux linkages with conductor A due to its own current. Also there will be flux linkages with this conductor due to mutual inductance effects.

      
Flux linkage with conductor A due to its own current,

Fig. 1

       Flux linkages with conductor A due to the current I_B,

       Flux linkages with conductor A due to the current ,

       By adding all the above expression we will get total flux linkages with conductor A.

       In the similar way flux linkages with other conductors can be determined. This will form basis for finding inductance of any circuit.