# Basic Electrical Engineering Questions and Answers – Star Delta Transformation

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This set of Basic Electrical Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Star Delta Transformation”.

1. Find the equivalent delta circuit.

a) 9.69 ohm, 35.71 ohm, 6.59 ohm
b) 10.69 ohm, 35.71 ohm, 6.59 ohm
c) 9.69 ohm, 34.71 ohm, 6.59 ohm
d) 10.69 ohm, 35.71 ohm, 7.59 ohm

Explanation: Using the star to delta conversion:
R1 = 4.53+6.66+4.53*6.66/1.23 = 35.71 ohm
R2 = 4.53+1.23+4.53*1.23/6.66 = 6.59 ohm
R3 = 1.23+6.66+1.23*6.66/4.53 = 9.69 ohm.

2. Which, among the following is the correct expression for star-delta conversion?
a) R1=Ra*Rb/(Ra+Rb+Rc), R2=Rb*Rc/(Ra+Rb+Rc), R3=Rc*Ra/(Ra+Rb+Rc)b)
b) R1=Ra/(Ra+Rb+Rc), R2=Rb/(Ra+Rb+Rc), Rc=/(Ra+Rb+Rc)
c) R1=Ra+Rb+Ra*Rb/Rc, R2=Rc+Rb+Rc*Rb/Ra, R3=Ra+Rc+Ra*Rc/Rb
d) R1=Ra*Rb/Rc, R2=Rc*Rb/Ra, R3=Ra*Rc/Rb

Explanation: After converting to delta, each delta connected resistance is equal to the sum of the two resistance it is connected to+product of the two resistances divided by the remaining resistance. Hence R1=Ra+Rb+Ra*Rb/Rc, R2=Rc+Rb+Rc*Rb/Ra, R3=Ra+Rc+Ra*Rc/Rb.

3. Find the equivalent resistance between X and Y.

a) 3.33 ohm
b) 4.34 ohm
c) 5.65 ohm
d) 2.38 ohm

Explanation: The 3 2ohm resistors are connected in star, changing them to delta, we have R1=R2=R3= 2+2+2*2/2=6 ohm.
The 3 6ohm resistors are connected in parallel to the 10 ohm 5 ohm and 10ohm resistors respectively.
This network can be further reduced to a network consisting of a 3.75ohm and 2.73ohm resistor connected in series whose resultant is intern connected in parallel to the 3.75 ohm resistor.

4. Delta connection is also known as____________
a) Y-connection
b) Mesh connection
c) Either Y-connection or mesh connection
d) Neither Y-connection nor mesh connection

Explanation: Delta connection is also known as mesh connection because its structure is like a mesh, that is, a closed loop which is planar.

5. Ra is resistance at A, Rb is resistance at B, Rc is resistance at C in star connection. After transforming to delta, what is resistance between B and C?
a) Rc+Rb+Rc*Rb/Ra
b) Rc+Rb+Ra*Rb/Rc
c) Ra+Rb+Ra*Rc/Rb
d) Rc+Rb+Rc*Ra/Rb

Explanation: After converting to the delta, each delta connected resistance is equal to the sum of the two resistances it is connected to+product of the two resistances divided by the remaining resistance. Hence, resistance between B and C = Rc+Rb+Rc*Rb/Ra.

6. Ra is resistance at A, Rb is resistance at B, Rc is resistance at C in star connection. After transforming to delta, what is resistance between A and C?
a) Ra+Rb+Ra*Rb/Rc
b) Ra+Rc+Ra*Rc/Rb
c) Ra+Rb+Ra*Rc/Ra
d) Ra+Rc+Ra*Rb/Rc

Explanation: After converting to the delta, each delta connected resistance is equal to the sum of the two resistances it is connected to+product of the two resistances divided by the remaining resistance. Hence, resistance between A and C = Ra+Rc+Ra*Rc/Rb.

7. Ra is resistance at A, Rb is resistance at B, Rc is resistance at C in star connection. After transforming to delta, what is resistance between A and B?
a) Rc+Rb+Ra*Rb/Rc
b) Ra+Rb+Ra*Rc/Rb
c) Ra+Rb+Ra*Rb/Rc
d) Ra+Rc+Ra*Rc/Rb

Explanation: After converting to the delta, each delta connected resistance is equal to the sum of the two resistances it is connected to+product of the two resistances divided by the remaining resistance. Hence, resistance between A and B = Ra+Rb+Ra*Rb/Rc.

8. If a 1ohm 2ohm and 32/3ohm resistor is connected in star, find the equivalent delta connection.
a) 34 ohm, 18.67 ohm, 3.19 ohm
b) 33 ohm, 18.67 ohm, 3.19 ohm
c) 33 ohm, 19.67 ohm, 3.19 ohm
d) 34 ohm, 19.67 ohm, 3.19 ohm

Explanation: Using the formula for delta to star conversion:
Using the formula for delta to star conversion:
R1=1+2+1*2/(32/3)
R2=1+32/3+1*(32/3)/2
R3=2+32/3+2*(32/3)/1.

9. If an 8/9ohm, 4/3ohm and 2/3ohm resistor is connected in star, find its delta equivalent.
a) 4ohm, 3ohm, 2ohm
b) 1ohm, 3ohm, 2ohm
c) 4ohm, 1ohm, 2ohm
d) 4ohm, 3ohm, 1ohm

Explanation: Using the formula for the star to delta conversion:
R1=8/9+4/3+(8/9)*(4/3)/(2/3)
R2=8/9+2/3+(8/9)*(2/3)/(4/3)
R3=2/3+4/3+(2/3)*(4/3)/(8/9).

10. Find the equivalent resistance between A and B.

a) 32ohm
b) 31ohm
c) 30ohm
d) 29ohm

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

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