The document derives transformation formulas for converting a delta network to an equivalent star network. It considers a circuit with resistors R1, R2 and R3 in a delta configuration. By comparing resistances between terminals, it derives three equations relating the delta resistors to the equivalent star network resistors. The final transformation formulas are: R12 = R1xR2/(R1 + R2 + R3), R23 = R2xR3/(R1 + R2 + R3), and R13 = R1xR3/(R1 + R2 + R3).

1. DELTA TO STAR
P.SHREYAS
22R21A05Q2

2. DELTA TO STAR
 To convert a delta network to an equivalent star network we need to derive a
transformation formula for equating the various resistors to each other between the
various terminals. Consider the circuit below.

3. To convert a delta network to an equivalent star network we need to derive a
transformation formula for equating the various resistors to each other
between the various terminals. Consider the circuit below.
Compare the resistances between terminals A and C.
R12 + R23 = R2 In parallel with (R1 + R3)
R12 + R23 =R2(R1 + R3)/R1 + R2 + R3 ....EQ-1
Resistance between the terminals B and C
R23 + R13 = R3 In parallel with (R2 + R1)
R23 + R13 = R3 (R2 + R1)/ R3 +R2 + R1 ........EQ-2

4. Resistance between the terminals A and B .
R12 + R13 = R1 In parallel (R2 + R3)
R12 + R13 = R1(R2 + R3)/R1+R2 + R3 .....EQ-3
This now gives us three equations and taking equation 3 from equation 2 gives:
EQ-3 - .EQ-2 = R12 + R13 - R23 + R13
R12 + R13 = R1(R2 + R3)/R1+R2 + R3 - R23 + R13 = R3 (R2 + R1)/
R3 +R2 + R1
=> R12 – R23 = R1XR2 - R1XR3/R1 + R2 + R3
Then, re-writing Equation 1 will give us:
(R12 – R23) + (R12 + R23) = (R1XR2 - R1XR3/R1 + R2 + R3) +
(R1XR2 + R1XR3/R1 + R2 + R3)
= 2XR12 = 2XR1XR2/R1 + R2 + R3

5. From which gives us the final equation for resistor as:
R12 = R1XR2/R1 + R2 + R3
Similarly:
R23 = R2XR3/R1 + R2 + R3
Similarly:
R13 = R1XR3/R1 + R2 + R3

6. THANK YOU