Flux Linkages of One Conductor in a Group

Flux Linkages of One Conductor in a Group

Consider a composite conductor which is made up of two or more strands which are in parallel. For simplicity let us assume that all the strands are identical and share the current equally. The sum of the currents in all the conductors is zero. Such a group of conductors is shown in the Fig. 1.13.1.

The conductors 1, 2, 3, ... n carry the currents I₁, I₂, I₃ ... I_n Let the distances of the conductors from a point P be D_lp, D_2p , D_3p ... D_np respectively. Let ψ_1p1 be flux linkages of conductor I₁ due to its own current Ij due to internal and external flux. The flux beyond point P is excluded.

Now ψ_1p2 is the flux linkage of conductor I₂ due to current I2 is equal to flux produced by I₂ between the point P and conductor 1. Again flux beyond P is neglected.

ψ_1p2 = 2 × 10-7 I₂ ln (D_2p / D₁₂)

Similarly the flux linkages ψ_1p with conductor 1 due to all the conductors in the group but the flux beyond point P is neglected.

All the flux linkages of conductor 1 are included in the above derivation. The above expression is valid only if sum of the currents is zero.