Kirchoff application of the law on the completion of the networks that have many branches in parallel, will encounter many equations that must be solved at once so often make it difficult solution. Application of the theory of transformation of the triangle of stars or vice versa can overcome the above problems. Such a complex network can be simplified by replacing branches or series of connected triangles with a series-connected in a star that is equivalent to a series of triangles, or vice versa.
For example known three resistors R12, R23 and R31 are connected in a triangle as shown below:
Figure 4.7 Delta Connection
Triangular circuit as above may be replaced by a series of stars with R1, R2 and R3 where both circuits are equivalent.
Figure 4.8 Connection Star
Both kinds of the above-mentioned connection is said to be electrically equivalent, if the resistor is measured between each pair of terminals have two kinds of prices samabagi the connection. Note the triangular connection between terminals 1 and 2, there are two parallel lines, which is between R12 parallel with a number of (R23 + R31). So prisoners between terminals 1 and 2 are:
Note the star connection, between terminals 1 and 2 there are two paths in which R1 and R2 series or arrest a total of:
Prisoners between terminals 1 and 2 in both the triangle and the star should be the same, so that:
Similarly to terminal 2 and 3 as well as terminals 3 and 1, obtained price:
