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why star delta transformation should work

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SanjKrish

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Doubt in star delta
Here is the confusion.

The fig shows star and delta network
new.JPG

It says that P + Q= A || (B+C)

Here we consider the resistor R is in open circuited and with that assumption we calculate the equivalent resistance... what if i connect a complex network to the resistor R so that it is not open and is closed in someway...
In such a case how does star - delta transform hold true..
 
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