What is the power ratio between power in star and delta circuit?

As we know the main function of transformer is to transfer power from one ckt to another ..so ratio will same on both side of transformer..it only change the ratio of voltage and current .

The power ratio between Star to Delta is1:3

The inpot power = The output power + the power losses

 the power ratio in the circuit if the  Star 1 the  delta will be3 and the calculation answer above by another college and for me i remamber only1/3

Power ratio is1,

As for star:

Pt=P1+P2+P3                         (P1 for phase1 ,P2 for phase2 and P3 for Phase3)

P=P1=P2=P3=Vph*Iph*cos theta

Pt=3*P

As in star connection Vline=(3)^1/2*Vph

so

Pt=3*(Vline/(3)^1/2)*Iph*cos theta

Pt-star=(3)^1/2*Vline*ILine*cos theta   as ILine=Iph

Similarly for delta connection

Pt=P1+P2+P3                         (P1 for phase1 ,P2 for phase2 and P3 for Phase3)

P=P1=P2=P3=Vph*Iph*cos theta

Pt=3*P

As in delta connection ILine=(3)^1/2*Iph

Pt=3*Vline*(Iph/(3)^1/2)*cos theta             as Vline=Vph

Pt-delta=(3)^1/2*Vline*ILine*cos theta   as Vline=Vph

As

Pt-star =Pt-delta

so

Pt-star/Pt-delta=Pt-delta/Pt-star=1

The power ratio is1:3 when referring this to a wye-delta motor starting.

normally it is1:3 ratio

The power ratio between Star to Delta is1:3

Explanation:

Lets suppose Vs be the supply voltage per phase.

So the line voltage of the supply will be Ö3Vs.

Now assume any type of load; for simplicity Im assuming it a only resistive load.

And let it be R per phase.

For Delta connected load:

Calculation for per phase power; PD= I2R

Where I à load current (per phase)

And,

I = Ö3Vs/R       {as line voltage of the supply is directly applied to the phase of the delta load}

So,

            Pd = (Ö3Vs/R )2R =3Vs2/R  watts per phase.

For3 phases:

            P3D =3Pd =3*3Vs2/R =9Vs2/R watts.

Now for Star connected load:

PS = I2R = (Vs/R)2R = Vs2/R watts

For3 phases: P3S =3PS =3 Vs2/R watts

Conclusion:

P3S / P3D  =  3Vs2/R /9Vs2/R =1/3

power is always constant in Xmer