DELTA–STAR AND STAR–DELTA TRANSFORMATION

To apply simple series–parallel circuit technique for the solution of network, something is required to transform the resistors connected in delta to star or vice versa. At such places, just to simplify the network delta–star or star–delta transformations applied.

2.9.1  Delta–Star Transformation

Consider a circuit shown in Figure 2.67(a), where three resistors RABRBC, and RCA are connected in delta. This circuit is converted to a star-connection circuit, as shown in Figure 2.67(b). Let the resistance be RARB, and RC.

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Fig. 2.67  (a) Delta connections (b) Equivalent star connection

For the two circuits to be equivalent, the resistance measured between any two of the terminals A, B, and C must be the same in the two cases.

RAB for star connections = RAB for delta connections.

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Similarly,

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and

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Subtracting Equation (2.62) from Equation (2.61) and adding the result to Equation (2.63), we get

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To remember this relation, we should refer to Figure 2.68. According to Equations (2.64), (2.65), and (2.66),

Resistance of any arm of image


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