### Editorial / Best Answer

**KaranSorout**

**The power ratio between Star to Delta is 1:3**

Explanation:

Let’s suppose V_{s }be the supply voltage per phase.

So the line voltage of the supply will be Ö3V_{s.}

Now assume any type of load; for simplicity I’m assuming it a only resistive load.

And let it be ‘R’ per phase.

_{ }

For Delta connected load:

Calculation for per phase power; P_{D}= I^{2}R

Where I à load current (per phase)

And,

I = Ö3V_{s}/R {as line voltage of the supply is directly applied to the phase of the delta load}

So,

P_{d }= (Ö3V_{s}/R_{ })^{2}R = 3V_{s}^{2}/R_{ }watts per phase.

For 3 phases:

P_{3D }= 3P_{d} = 3*3V_{s}^{2}/R = 9V_{s}^{2}/R watts.

Now for Star connected load:

P_{S }= I^{2}R = (V_{s}/R)^{2}R = V_{s}^{2}/R watts

For 3 phases: P_{3S }= 3P_{S }= 3 V_{s}^{2}/R watts

Conclusion:

P_{3S }/ P_{3D = }3V_{s}^{2}/R / 9V_{s}^{2}/R = 1/3

It may be better concluded by drowing figures. If any variations, can connect to me through karan.sorout@gmail.com

## What is the power ratio between power in Star and Delta circuit?

## Editorial / Best Answer

KaranSoroutProfile Answers by KaranSorout Questions by KaranSorout

The power ratio between Star to Delta is 1:3Explanation:

Let’s suppose V

_{s }be the supply voltage per phase.So the line voltage of the supply will be Ö3V

_{s.}Now assume any type of load; for simplicity I’m assuming it a only resistive load.

And let it be ‘R’ per phase.

_{ }For Delta connected load:

Calculation for per phase power; P

_{D}= I^{2}RWhere I à load current (per phase)

And,

I = Ö3V

_{s}/R {as line voltage of the supply is directly applied to the phase of the delta load}So,

P

_{d }= (Ö3V_{s}/R_{ })^{2}R = 3V_{s}^{2}/R_{ }watts per phase.For 3 phases:

P

_{3D }= 3P_{d}= 3*3V_{s}^{2}/R = 9V_{s}^{2}/R watts.Now for Star connected load:

P

_{S }= I^{2}R = (V_{s}/R)^{2}R = V_{s}^{2}/R wattsFor 3 phases: P

_{3S }= 3P_{S }= 3 V_{s}^{2}/R wattsConclusion:

P

_{3S }/ P_{3D = }3V_{s}^{2}/R / 9V_{s}^{2}/R = 1/3It may be better concluded by drowing figures. If any variations, can connect to me through karan.sorout@gmail.com

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