1. The value of the 3 resistances when connected in star connection is_________
a) 2.32ohm,1.22ohm, 4.54ohm
b) 3.55ohm, 4.33ohm, 5.67ohm
c) 2.78ohm, 1.67ohm, 0.83ohm
d) 4.53ohm, 6.66ohm, 1.23ohm
Explanation: Following the delta to star conversion:
R1=10*5/(10+5+3) = 2.78 ohm
R2=10*3/(10+5+3) = 1.67 ohm
R3=5*3/(10+5+3) = 0.83 ohm.
2. Which, among the following is the right expression for converting from delta to star?
a) R1=Ra*Rb/(Ra+Rb+Rc), R2=Rb*Rc/(Ra+Rb+Rc), R3=Rc*Ra/(Ra+Rb+Rc)
b) R1=Ra/(Ra+Rb+Rc), R2=Rb/(Ra+Rb+Rc), Rc=/(Ra+Rb+Rc)
c) R1=Ra*Rb*Rc/(Ra+Rb+Rc), R2=Ra*Rb/(Ra+Rb+Rc), R3=Ra/(Ra+Rb+Rc)
d) R1=Ra*Rb*Rc/(Ra+Rb+Rc), R2=Ra*Rb*Rc/(Ra+Rb+Rc), R3=Ra*Rb*Rc/(Ra+Rb+Rc)
Explanation: After converting to star, each star connected resistance is equal to the ratio of product of the resistances it is connected to and the total sum of the resistances. Hence R1=Ra*Rb/(Ra+Rb+Rc), R2=Rb*Rc/(Ra+Rb+Rc), R3=Rc*Ra/(Ra+Rb+Rc).
3. Find the equivalent star network.
a) 2.3ohm, 2.3ohm, 2.3ohm
b) 1.2ohm, 1.2ohm, 1.2ohm
c) 3.3ohm, 3.3ohm, 3.3ohm
d) 4.5ohm, 4.5ohm, 4.5ohm
Explanation: The 6 ohm and 9 ohm resistances are connected in parallel. Their equivalent resistances are: 6*9/(9+6)=3.6 ohm.
The 3 3.6 ohm resistors are connected in delta. Converting to star:
R1=R2=R3= 3.6*3.6/(3.6+3.6+3.6)=1.2 ohm.
4. Star 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: The star connection is also known as the Y-connection because its formation is like the letter Y.
5. Rab is the resistance between the terminals A and B, Rbc between B and C and Rca between C and A. These 3 resistors are connected in delta connection. After transforming to star, the resistance at A will be?
a) Rab*Rac/(Rab+Rbc+Rca)
b) Rab/(Rab+Rbc+Rca)
c) Rbc*Rac/(Rab+Rbc+Rca)
d) Rac/(Rab+Rbc+Rca)
Explanation: When converting from delta to star, the resistances in star connection is equal to the product of the resistances it is connected to, divided by the total sum of the resistance.
Hence Rab*Rac/(Rab+Rbc+Rca).
6. Rab is the resistance between the terminals A and B, Rbc between B and C and Rca between C and A. These 3 resistors are connected in delta connection. After transforming to star, the resistance at B will be?
a) Rac/(Rab+Rbc+Rca)
b) Rab/(Rab+Rbc+Rca)
c) Rbc*Rab/(Rab+Rbc+Rca)
d) Rab/(Rab+Rbc+Rca)
Explanation: When converting from delta to star, the resistances in star connection is equal to the product of the resistances it is connected to, divided by the total sum of the resistance.
Hence Rab*Rbc/(Rab+Rbc+Rca).
7. Rab is the resistance between the terminals A and B, Rbc between B and C and Rca between C and A. These 3 resistors are connected in delta connection. After transforming to star, the resistance at C will be?
a) Rac/(Rab+Rbc+Rca)
b) Rab/(Rab+Rbc+Rca)
c) Rbc*Rac/(Rab+Rbc+Rca)
d) Rab/(Rab+Rbc+Rca)
Explanation: When converting from delta to star, the resistances in star connection is equal to the product of the resistances it is connected to, divided by the total sum of the resistance.
Hence Rac*Rbc/(Rab+Rbc+Rca).
8. Find the current in the circuit.
a) 0.54A
b) 0.65A
c) 0.67A
d) 0.87A
Explanation: The 3 5 ohm resistors are connected in delta. Changing it to star:
R1=R2=R3 = 1.67 ohm.
One of the 1.67 ohm resistors are connected in series with the 2 ohm resistor and another 1.67 ohm resistor is connected in series to the 3 ohm resistor.
The resulting network has a 1.67 ohm resistor connected in series with the parallel connection of the 3.67 and 4.67 resistors.
The equivalent resistance is 3.725A.
I=2/3.725 = 0.54A.
9. If a 6 ohm, 2ohm and 4ohm resistor is connected in delta, find the equivalent star connection.
a) 1ohm, 2ohm, 3ohm
b) 2ohm, 4ohm, 7ohm
c) 5ohm, 4ohm, 2ohm
d) 1ohm, 2ohm, 2/3ohm
Explanation: Using the delta to star conversion formula:
R1=2*6/(2+6+4)
R2=2*4/(2+6+4)
R3=4*6/(2+6+4).
10. If a 4ohm, 3ohm and 2ohm resistor is connected in delta, find the equivalent star connection.
a) 8/9ohm, 4/3ohm, 2/3ohm
b) 8/9ohm, 4/3ohm, 7/3ohm
c) 7/9ohm, 4/3ohm, 2/3ohm
d) 8/9ohm, 5/3ohm, 2/3ohm
Explanation: Using the delta-star conversion formula:
R1=4*3/(2+3+4)
R2=2*3/(2+3+4)
R3=2*4/(2+3+4).