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## Homework Statement

For the balanced three-phase loads shown in FIGURE 3,

ZY = (15 + j15) Ω and ZΔ = (45 + j45) Ω. Determine:

**Uploaded file C1.png**

(a) the equivalent single Δ-connected load,

(b) the equivalent single Y-connected load obtained from the Δ-Y transformation of (a) above,

(c) the equivalent single Y-connected load obtained by transforming the Δ sub-load of FIGURE 3 to a Y and with the star-points of the two Y-sub-circuits connected together,

(d) the total power consumed in case (a) above if the line voltage of the three-phase supply is 415 V at 50 Hz.

## Homework Equations

## The Attempt at a Solution

For (a) P=Q=R=(15+15i)

Star "PQR" --->Delta "ABC" equivelant =

A=PQ+QR+RP/R

Since the loads QPR are all the same value and same equation form then A=B=C, ((15+15i)*(15+15i)+(15+15i)*(15+15i)+(15+15i)*(15+15i))/(15+15i)=45+i45

Delta equivelant is A=45+i45, B=45+i45, C=45+i45

For(b) The reverse of (a) I assume; Delta ---> Star =

Q=AC/A+B+C

P=AB/A+B+C

R=BC/A+B+C

Q=P=R= 15+i15

Questions seems deceptively easy for my liking

(c) Is the diagram

**C2.png**how the transformation and two Y sub-circuit connected star points should look like?

I need a hint on how to form the equations for this if it is correct(im sure its obvious but im not sure.)

Any help greatly appreciated.