Network Theory Questions and Answers – Star to Delta and Delta to Star Transformation

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Star to Delta and Delta to Star Transformation”.

1. If a resistor ZR is connected between R and N, ZBR between R and B, ZRY between R and Y and ZBY between B and Y form a delta connection, then after transformation to star, the impedance at R is?
a) (ZBRZBY)/(ZRY+ZBY+ZBR)
b) (ZRYZBR)/(ZRY+ZBY+ZBR)
c) (ZRYZBY)/(ZRY+ZBY+ZBR)
d) (ZRY)/(ZRY+ZBY+ZBR)

Explanation: After transformation to star, the impedance at R is
(ZRYZBR)/(ZRY+ZBY+ZBR).

2. If a resistor ZR is connected between R and N, ZBR between R and B, ZRY between R and Y and ZBY between B and Y form a delta connection, then after transformation to star, the impedance at Y is?
a) (ZRY)/(ZRY+ZBY+ZBR)
b) (ZBY)/(ZRY+ZBY+ZBR)
c) (ZRYZBY)/(ZRY+ZBY+ZBR)
d) (ZRYZBR)/(ZRY+ZBY+ZBR)

Explanation: After transformation to star, the impedance at Y is
(ZRYZBY)/(ZRY+ZBY+ZBR).

3. If a resistor ZR is connected between R and N, ZBR between R and B, ZRY between R and Y and ZBY between B and Y form a delta connection, then after transformation to star, the impedance at B is?
a) (ZBRZBY)/(ZRY+ZBY+ZBR)
b) (ZRYZBY)/(ZRY+ZBY+ZBR)
c) (ZBY)/(ZRY+ZBY+ZBR)
d) (ZBR)/(ZRY+ZBY+ZBR)

Explanation: After transformation to star, the impedance at Y is
(ZBRZBY)/(ZRY+ZBY+ZBR).

4. If the resistors of star connected system are ZR, ZY, ZB then the impedance ZRY in delta connected system will be?
a) (ZRZY + ZYZB + ZBZR)/ZB
b) (ZRZY + ZYZB + ZBZR)/ZY
c) (ZRZY + ZYZB + ZBZR)/ZR
d) (ZRZY + ZYZB + ZBZR)/(ZR+ZY)

Explanation: After transformation to delta, the impedance ZRY in delta connected system will be (ZRZY + ZYZB + ZBZR)/ZB.

5. If the resistors of star connected system are ZR, ZY, ZB then the impedance ZBY in delta connected system will be?
a) (ZRZY + ZYZB + ZBZR)/(ZB+ZY)
b) (ZRZY + ZYZB + ZBZR)/ZB
c) (ZRZY + ZYZB + ZBZR)/ZY
d) (ZRZY + ZYZB + ZBZR)/ZR

Explanation: After transformation to delta, the impedance ZBY in delta connected system will be (ZRZY + ZYZB + ZBZR)/ZR.
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6. If the resistors of star connected system are ZR, ZY, ZB then the impedance ZBR in delta connected system will be?
a) (ZRZY + ZYZB + ZBZR)/ZY
b) (ZRZY + ZYZB + ZBZR)/R
c) (ZRZY + ZYZB + ZBZR)/ZB
d) (ZRZY + ZYZB + ZBZR)/(ZB+ZR)

Explanation: After transformation to delta, the impedance ZBR in delta connected system will be (ZRZY + ZYZB + ZBZR)/ZY.

7. A symmetrical three-phase, three-wire 440V supply is connected to star-connected load. The impedances in each branch are ZR = (2+j3) Ω, ZY = (1-j2) Ω, ZB = (3+j4) Ω. Find ZRY.
a) (5.22-j0.82) Ω
b) (-3.02+j8) Ω
c) (3.8-j0.38) Ω
d) (-5.22+j0.82) Ω

Explanation: ZRY = (ZRZY + ZYZB + ZBZR)/ZB
= (3.8-j0.38) Ω.

8. A symmetrical three-phase, three-wire 440V supply is connected to star-connected load. The impedances in each branch are ZR = (2+j3) Ω, ZY = (1-j2) Ω, ZB = (3+j4) Ω. Find ZBY.
a) (-5.22+j0.82) Ω
b) (5.22-j0.82) Ω
c) (3.8-j0.38) Ω
d) (-3.02+j8) Ω

Explanation: ZBY = (ZRZY + ZYZB + ZBZR)/ZR
= (5.22-j0.82)Ω.

9. A symmetrical three-phase, three-wire 440V supply is connected to star-connected load. The impedances in each branch are ZR = (2+j3) Ω, ZY = (1-j2) Ω, ZB = (3+j4) Ω. Find ZBR.
a) (5.22-j0.82) Ω
b) (-3.02+j8) Ω
c) (-5.22+j0.82) Ω
d) (3.8-j0.38) Ω

Explanation: ZBR = (ZRZY + ZYZB + ZBZR)/ZY
= (-3.02+j8) Ω.

10. If a star connected system has equal impedances Z1, then after converting into delta connected system having equal impedances Z2, then?
a) Z2 = Z1
b) Z2 = 2Z1
c) Z2 = 3Z1
d) Z2 = 4Z1

Explanation: If a star connected system has equal impedances Z1, then after converting into delta connected system having equal impedances Z2, then Z2 = 3Z1.

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