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Electricity

Hot goIITian

 Joined: 16 May 2007 Post: 158
12 Sep 2009 20:29:36 IST
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What is Star to Delta or Delta to Star Method For Solving Problems on Finding Equivalent resistance?
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What is Star to Delta or Delta to Star Method For Solving Problems on Finding Equivalent resistance?Plz Explain with example...

Blazing goIITian

Joined: 4 Apr 2009
Posts: 2068
12 Sep 2009 20:36:34 IST
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In many circuit applications, we encounter components connected together in one of two ways to form a three-terminal network: the “Delta,” or Δ (also known as the “Pi,” or π) configuration, and the “Y” (also known as the “T”) configuration.

It is possible to calculate the proper values of resistors necessary to form one kind of network (Δ or Y) that behaves identically to the other kind, as analyzed from the terminal connections alone. That is, if we had two separate resistor networks, one Δ and one Y, each with its resistors hidden from view, with nothing but the three terminals (A, B, and C) exposed for testing, the resistors could be sized for the two networks so that there would be no way to electrically determine one network apart from the other. In other words, equivalent Δ and Y networks behave identically.

There are several equations used to convert one network to the other:

Δ and Y networks are seen frequently in 3-phase AC power systems (a topic covered in volume II of this book series), but even then they're usually balanced networks (all resistors equal in value) and conversion from one to the other need not involve such complex calculations. When would the average technician ever need to use these equations?

A prime application for Δ-Y conversion is in the solution of unbalanced bridge circuits, such as the one below:

Solution of this circuit with Branch Current or Mesh Current analysis is fairly involved, and neither the Millman nor Superposition Theorems are of any help, since there's only one source of power. We could use Thevenin's or Norton's Theorem, treating R3 as our load, but what fun would that be?

If we were to treat resistors R1, R2, and R3 as being connected in a Δ configuration (Rab, Rac, and Rbc, respectively) and generate an equivalent Y network to replace them, we could turn this bridge circuit into a (simpler) series/parallel combination circuit:

After the Δ-Y conversion . . .

If we perform our calculations correctly, the voltages between points A, B, and C will be the same in the converted circuit as in the original circuit, and we can transfer those values back to the original bridge configuration.

Resistors R4 and R5, of course, remain the same at 18 Ω and 12 Ω, respectively. Analyzing the circuit now as a series/parallel combination, we arrive at the following figures:

We must use the voltage drops figures from the table above to determine the voltages between points A, B, and C, seeing how the add up (or subtract, as is the case with voltage between points B and C):

Now that we know these voltages, we can transfer them to the same points A, B, and C in the original bridge circuit:

Voltage drops across R4 and R5, of course, are exactly the same as they were in the converted circuit.

At this point, we could take these voltages and determine resistor currents through the repeated use of Ohm's Law (I=E/R):

Hot goIITian

Joined: 16 May 2007
Posts: 158
12 Sep 2009 20:39:18 IST
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@Divesh Will u plz explain how to convert one into other......

.I want star to Delta Conversion

Blazing goIITian

Joined: 4 Apr 2009
Posts: 2068
12 Sep 2009 20:43:47 IST
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It has been clearly written above ...the formulae  !

just go through it ...

refer the diagrams above .. !

Hot goIITian

Joined: 16 May 2007
Posts: 158
12 Sep 2009 20:48:49 IST
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Thanks Divesh .........

New kid on the Block

Joined: 5 Sep 2011
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5 Sep 2011 19:35:05 IST
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thanks sir

New kid on the Block

Joined: 11 Oct 2011
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11 Oct 2011 13:09:32 IST
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THANK YOU ..........HELPED ME A LOT , SIR

New kid on the Block

Joined: 15 Nov 2011
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15 Nov 2011 20:00:48 IST
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star delta solve problems

New kid on the Block

Joined: 10 Dec 2011
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10 Dec 2011 12:37:43 IST
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What is Star to Delta or Delta to Star Method For Solving Problems on Finding Equivalent resistance?

New kid on the Block

Joined: 27 Mar 2012
Posts: 1
27 Mar 2012 21:33:55 IST
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Explain different star-delta conversion techniques?

New kid on the Block

Joined: 17 Jul 2012
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17 Jul 2012 07:00:17 IST
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it was amazing... sir..!!!

New kid on the Block

Joined: 16 Aug 2012
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16 Aug 2012 18:15:44 IST
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What is Star to Delta or Delta to Star Method For Solving Problems on Finding Equivalent resistance?

New kid on the Block

Joined: 21 Aug 2012
Posts: 2
21 Aug 2012 21:57:15 IST
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thanks a lot.....it cleared many of my doubts....

New kid on the Block

Joined: 21 Aug 2012
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21 Aug 2012 22:00:26 IST
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for equivalent resistance in star v have the formula = r/3
n for equivalent resistance in delta v have the formula = 3r

Blazing goIITian

Joined: 1 Apr 2012
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22 Aug 2012 21:17:23 IST
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Thank u. Sir

New kid on the Block

Joined: 29 Sep 2012
Posts: 1
29 Sep 2012 12:33:49 IST
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Nice . But complex prob will be better

New kid on the Block

Joined: 19 Oct 2012
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19 Oct 2012 10:34:05 IST
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thank u very much my dought is solved

New kid on the Block

Joined: 16 Dec 2012
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16 Dec 2012 11:48:26 IST
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What is Star to Delta or Delta to Star Method For Solving Problems on Finding Equivalent resistance?

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