exp4.Delta-star connection.pdf
Content
DC circuit laboratory
Experiment No. 4
Delta – Star connection
Aim of experiment: To study the properties of delta-star connection.
U U
Apparatus
U
1. DC circuit training system 2. Set of wires. 3. DC Power supply 4. Digital A.V.O. meter
Theory
U
In solving networks (having considerable number of branches) by the application of Kirchhoff's Laws, one sometimes experiences great difficulty due to a large number of simultaneous equation that have to be solve. However, such complicated networks can simplify by successively replacing delta meshes by equivalent star systems and vice versa.
1 R13 R12 R1
1
2 R23 3
R3
R2 2 3
Delta-connection (b) Fig (1)
Star-connection (a)
DC circuit laboratory Suppose we are given three resistance R 12 ,R 23 and R 13 connected in delta fashion between terminals 1,2 and 3 as in Fig.(1-a). So far as the respective terminals are concerned, these given three resistances can be replaced by the three resistances R 1 , R 2 and R 3 connected in star as shown in Fig.(1-b). These two arrangements will be electrically equivalent if the resistance as measured between any pair of terminals is the same in both arrangements.
1. To convert from delta connection to star connection
R1 =
R 12 × R 13 R 12 + R 23 + R 13
R 12 × R 23 R 12 + R 23 + R 13
R2 =
R3 =
R 23 × R 13 R 12 + R 23 + R 13
2. To convert from star connection to delta connection
R 12 = R 1 + R 2 +
R1 × R 2 R3
R3 × R2 R1
R 3 × R1 R2
R 23 = R 2 + R 3 +
R 13 = R 1 + R 3 +
Procedure
1. Using the DC circuit trainer, connect the circuit shown below. 2. Measure "I 1, I 2 , I 3 " practically. 3. Record your results in the table below 4. By using delta-star conversion, find the star resistance R 1 , R 2 , R 3 theoretically.
DC circuit laboratory
50Ω
I1
5V
A
20Ω
20Ω
A
I2
5V
A
5. Using the DC circuit trainer, connect the circuit shown below: 20Ω 20Ω
40Ω
I3
A
A 40Ω
I2
I1
5V
5V
A
I3
DC circuit laboratory 6. Measure "I 1 , I 2 , I 3 " practically. 7. Record your results in the table below I1 I2 Delta connection Star connection 8. Connect circuit the circuit shown in Figure below and measured the equivalent resistance between any two terminals "1-2, 2-3, 1-3" by using AVO meter. 50Ω
I3
20Ω
20Ω
1 100Ω 100Ω 40Ω
2
3
3
9. Using the DC circuit trainer, Connect circuit the circuit shown in Figure below and measured the equivalent resistance between any two terminals "12, 2-3, 1-3" by using AVO meter.
DC circuit laboratory
1
50Ω
2
100Ω
100Ω
3 Discussion
1. Comment on your results. 2. Compare between the practical and theoretical results. 3. Comment on step 8 and step 9 4. Find I T and R T for the circuit below IT
3
8v 5Ω
1.5Ω
5Ω
10Ω 2Ω 3Ω RT 2Ω 3Ω 3Ω
Experiment No. 4
Delta – Star connection
Aim of experiment: To study the properties of delta-star connection.
U U
Apparatus
U
1. DC circuit training system 2. Set of wires. 3. DC Power supply 4. Digital A.V.O. meter
Theory
U
In solving networks (having considerable number of branches) by the application of Kirchhoff's Laws, one sometimes experiences great difficulty due to a large number of simultaneous equation that have to be solve. However, such complicated networks can simplify by successively replacing delta meshes by equivalent star systems and vice versa.
1 R13 R12 R1
1
2 R23 3
R3
R2 2 3
Delta-connection (b) Fig (1)
Star-connection (a)
DC circuit laboratory Suppose we are given three resistance R 12 ,R 23 and R 13 connected in delta fashion between terminals 1,2 and 3 as in Fig.(1-a). So far as the respective terminals are concerned, these given three resistances can be replaced by the three resistances R 1 , R 2 and R 3 connected in star as shown in Fig.(1-b). These two arrangements will be electrically equivalent if the resistance as measured between any pair of terminals is the same in both arrangements.
1. To convert from delta connection to star connection
R1 =
R 12 × R 13 R 12 + R 23 + R 13
R 12 × R 23 R 12 + R 23 + R 13
R2 =
R3 =
R 23 × R 13 R 12 + R 23 + R 13
2. To convert from star connection to delta connection
R 12 = R 1 + R 2 +
R1 × R 2 R3
R3 × R2 R1
R 3 × R1 R2
R 23 = R 2 + R 3 +
R 13 = R 1 + R 3 +
Procedure
1. Using the DC circuit trainer, connect the circuit shown below. 2. Measure "I 1, I 2 , I 3 " practically. 3. Record your results in the table below 4. By using delta-star conversion, find the star resistance R 1 , R 2 , R 3 theoretically.
DC circuit laboratory
50Ω
I1
5V
A
20Ω
20Ω
A
I2
5V
A
5. Using the DC circuit trainer, connect the circuit shown below: 20Ω 20Ω
40Ω
I3
A
A 40Ω
I2
I1
5V
5V
A
I3
DC circuit laboratory 6. Measure "I 1 , I 2 , I 3 " practically. 7. Record your results in the table below I1 I2 Delta connection Star connection 8. Connect circuit the circuit shown in Figure below and measured the equivalent resistance between any two terminals "1-2, 2-3, 1-3" by using AVO meter. 50Ω
I3
20Ω
20Ω
1 100Ω 100Ω 40Ω
2
3
3
9. Using the DC circuit trainer, Connect circuit the circuit shown in Figure below and measured the equivalent resistance between any two terminals "12, 2-3, 1-3" by using AVO meter.
DC circuit laboratory
1
50Ω
2
100Ω
100Ω
3 Discussion
1. Comment on your results. 2. Compare between the practical and theoretical results. 3. Comment on step 8 and step 9 4. Find I T and R T for the circuit below IT
3
8v 5Ω
1.5Ω
5Ω
10Ω 2Ω 3Ω RT 2Ω 3Ω 3Ω
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