Milliman Theorem (or) Parallel Generator Theorem:

Definition:

By Millman’s theorem, we can replace ‘n’ number of parallel Thevenin’s equivalents into a single Thevenin’s equivalent.

Statement:

When a number of voltage sources (V1,V2,….Vn) are in parallel having internal resistances (R1, R₂, ….R) respectively, the arrangement can be replaced by a single equivalent voltage source V in series with an equivalent series resistance R.

Note: In the above case, if polarity of the source ‘V₂ is reversed, then ‘V1’ is replaced by ‘-V₂’ in the expression V’.

Properties:

  • This theorem is applicable only for linear networks i.e. the networks with R.L,C, transformer and linear controlled sources as elements.
  • The presence of dependent sources makes the network active and hence Millman’s theorem is both active as well as passive networks.

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