# Network Theory Questions and Answers – Star-Delta Transformation

This set of Network Theory Questions and Answers for Freshers focuses on “Star-Delta Transformation”.

1. If a resistor Rx is connected between nodes X and Y, Ry between X and Z, Rz between Y and Z to form a delta connection, then after transformation to star, the resistor at node X is?
a) RxRy/(Rx+Ry+Rz)
b) RxRz/(Rx+Ry+Rz)
c) RzRy/(Rx+Ry+Rz)
d) (Rx+Ry)/(Rx+Ry+Rz)

Explanation: After transformation to star, the resistor at node X is RxRy/(Rx+Ry+Rz) and this resistance lies between Rx, Ry in star connection.

2. If a resistor Rx is connected between nodes X and Y, Ry between X and Z, Rz between Y and Z to form a delta connection, then after transformation to star, the resistance at node Y is?
a) RzRy/(Rx+Ry+Rz)
b) RzRx/(Rx+Ry+Rz)
c) RxRy/(Rx+Ry+Rz)
d) (Rz+Ry)/(Rx+Ry+Rz)

Explanation: After transformation to star, the resistor at node Y is RzRx/(Rx+Ry+Rz) and this resistance lies between Rx, Rz in star connection.

3. If a resistor Rx is connected between nodes X and Y, Ry between X and Z, Rz between Y and Z to form a delta connection, then after transformation to star, the resistance at node Z is?
a) RyRx/(Rx+Ry+Rz)
b) RyRx/(Rx+Ry+Rz)
c) RzRy/(Rx+Ry+Rz)
d) (Rz+Rx)/(Rx+Ry+Rz)

Explanation: After transformation to star, the resistor at node Y is RzRy/(Rx+Ry+Rz) and this resistance lies between Rz, Ry in star connection.

4. If the resistors of star connected system are R1, R2, R3 then the resistance between 1 and 2 in delta connected system will be?
a) (R1R2 + R2R3 + R3R1)/R3
b) (R1R2 + R2R3 + R3R1)/R1
c) (R1R2 + R2R3 + R3R1)/R2
d) (R1R2 + R2R3 + R3R1)/(R1+R2)

Explanation: After transformation to delta, the resistance between 1 and 2 in delta connected system will be (R1R2 + R2R3 + R3R1)/R3 and this resistance lies between R1, R2 in delta connection.

5. If the resistors of star connected system are R1, R2, R3 then the resistance between 2 and 3 in delta connected system will be?
a) (R1R2 + R2R3 + R3R1)/R3
b) (R1R2 + R2R3 + R3R1)/R2
c) (R1R2 + R2R3 + R3R1)/R1
d) (R1R2 + R2R3 + R3R1)/(R3+R2)

Explanation: After transformation to delta, the resistance between 2 and 3 in delta connected system will be (R1R2 + R2R3 + R3R1)/R1 and this resistance lies between R3, R2 in delta connection.

6. If the resistors of star connected system are R1, R2, R3 then the resistance between 3 and 1 in delta connected system will be?
a) (R1R2 + R2R3 + R3R1)/R1
b) (R1R2 + R2R3 + R3R1)/R3
c) (R1R2 + R2R3 + R3R1)/R2
d) (R1R2 + R2R3 + R3R1)/(R3+R1)

Explanation: After transformation to delta, the resistance between 2 and 3 in delta connected system will be (R1R2 + R2R3 + R3R1)/R2 and this resistance lies between R1, R3 in delta connection.

7. Find the equivalent resistance at node A in the delta connected circuit shown in the figure below.

a) 1
b) 2
c) 3
d) 3.67

Explanation: Performing delta to star transformation we obtain the equivalent resistance at node A is R =(11×12)/(11+12+13)=3.67Ω.

8. Find the equivalent resistance at node C in the delta connected circuit shown below.

a) 3.66
b) 4.33
c) 5.66
d) 6.66

Explanation: Performing delta to star transformation we obtain the equivalent resistance at node A is R =(12×13)/(11+12+13)=4.33Ω.

9. Find the equivalent resistance between node 1 and node 3 in the star connected circuit shown below.

a) 30
b) 31
c) 32
d) 33

Explanation: The equivalent resistance between node 1 and node 3 in the star connected circuit is R =(10×10+10×11+11×10)/10=32Ω.

10. Find the equivalent resistance between node 1 and node 2 in the star connected circuit shown below.

a) 2
b) 29
c) 30
d) 31

Explanation: The equivalent resistance between node 1 and node 3 in the star connected circuit is R =(10×10+10×11+11×10)/11=29Ω.

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