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

1. If a resistor Z_{R} is connected between R and N, Z_{BR} between R and B, Z_{RY} between R and Y and Z_{BY} between B and Y form a delta connection, then after transformation to star, the impedance at R is?

a) (Z_{BR}Z_{BY})/(Z_{RY}+Z_{BY}+Z_{BR})

b) (Z_{RY}Z_{BR})/(Z_{RY}+Z_{BY}+Z_{BR})

c) (Z_{RY}Z_{BY})/(Z_{RY}+Z_{BY}+Z_{BR})

d) (Z_{RY})/(Z_{RY}+Z_{BY}+Z_{BR})

View Answer

Explanation: After transformation to star, the impedance at R is

(Z

_{RY}Z

_{BR})/(Z

_{RY}+Z

_{BY}+Z

_{BR}).

2. In the question above the impedance at Y is?

a) (Z_{RY})/(Z_{RY}+Z_{BY}+Z_{BR})

b) (Z_{BY})/(Z_{RY}+Z_{BY}+Z_{BR})

c) (Z_{RY}Z_{BY})/(Z_{RY}+Z_{BY}+Z_{BR})

d) (Z_{RY}Z_{BR})/(Z_{RY}+Z_{BY}+Z_{BR})

View Answer

Explanation: After transformation to star, the impedance at Y is

(Z

_{RY}Z

_{BY})/(Z

_{RY}+Z

_{BY}+Z

_{BR}).

3. In the question above, the impedance at B is?

a) (Z_{BR}Z_{BY})/(Z_{RY}+Z_{BY}+Z_{BR})

b) (Z_{RY}Z_{BY})/(Z_{RY}+Z_{BY}+Z_{BR})

c) (Z_{BY})/(Z_{RY}+Z_{BY}+Z_{BR})

d) (Z_{BR})/(Z_{RY}+Z_{BY}+Z_{BR})

View Answer

Explanation: After transformation to star, the impedance at Y is

(Z

_{BR}Z

_{BY})/(Z

_{RY}+Z

_{BY}+Z

_{BR}).

4. If the resistors of star connected system are Z_{R}, Z_{Y}, Z_{B} then the impedance Z_{RY} in delta connected system will be?

a) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{B}

b) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{Y}

c) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{R}

d) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/(Z_{R}+Z_{Y} )

View Answer

Explanation: After transformation to delta, the impedance Z

_{RY}in delta connected system will be (Z

_{R}Z

_{Y}+ Z

_{Y}Z

_{B}+ Z

_{B}Z

_{R})/Z

_{B}.

5. If the resistors of star connected system are Z_{R}, Z_{Y}, Z_{B} then the impedance Z_{BY} in delta connected system will be?

a) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/(Z_{B}+Z_{Y} )

b) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{B}

c) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{Y}

d) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{R}

View Answer

Explanation: After transformation to delta, the impedance Z

_{BY}in delta connected system will be (Z_R (Z

_{R}Z

_{Y}+ Z

_{Y}Z

_{B}+ Z

_{B}Z

_{R})/Z

_{R}.

6. If the resistors of star connected system are Z_{R}, Z_{Y}, Z_{B} then the impedance Z_{BR} in delta connected system will be?

a) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{Y}

b) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/_{R}

c) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/Z_{B}

d) (Z_{R}Z_{Y}+ Z_{Y}Z_{B}+ Z_{B}Z_{R})/(Z_{B}+Z_{R} )

View Answer

Explanation: After transformation to delta, the impedance Z

_{BR}in delta connected system will be (Z_R (Z

_{R}Z

_{Y}+ Z

_{Y}Z

_{B}+ Z

_{B}Z

_{R})/Z

_{Y}.

7. A symmetrical three-phase, three-wire 440V supply is connected to star-connected load. The impedances in each branch are Z_{R} = (2+j3) Ω, Z_{Y} = (1-j2) Ω, Z_{B} = (3+j4) Ω. Find Z_{RY}.

a) (5.22-j0.82) Ω

b) (-3.02+j8) Ω

c) (3.8-j0.38) Ω

d) (-5.22+j0.82) Ω

View Answer

Explanation: Z

_{RY}= (Z

_{R}Z

_{Y}+ Z

_{Y}Z

_{B}+ Z

_{B}Z

_{R})/Z

_{B}

= (3.8-j0.38) Ω.

8. Find Z_{BY} in the question 7.

a) (-5.22+j0.82) Ω

b) (5.22-j0.82) Ω

c) (3.8-j0.38) Ω

d) (-3.02+j8) Ω

View Answer

Explanation: Z

_{BY}= (Z

_{R}Z

_{Y}+ Z

_{Y}Z

_{B}+ Z

_{B}Z

_{R})/Z

_{R}

= (5.22-j0.82)Ω.

9. Find Z_{BR}.

a) (5.22-j0.82) Ω

b) (-3.02+j8) Ω

c) (-5.22+j0.82) Ω

d) (3.8-j0.38) Ω

View Answer

Explanation: Z

_{BR}= (Z

_{R}Z

_{Y}+ Z

_{Y}Z

_{B}+ Z

_{B}Z

_{R})/Z

_{Y}

= (-3.02+j8) Ω.

10. If a star connected system has equal impedances Z_{1}, then after converting into delta connected system having equal impedances Z_{2}, then?

a) Z_{2} = Z_{1}

b) Z_{2} = 2Z_{1}

c) Z_{2} = 3Z_{1}

d) Z_{2} = 4Z_{1}

View Answer

Explanation: If a star connected system has equal impedances Z

_{1}, then after converting into delta connected system having equal impedances Z

_{2}, then Z

_{2}= 3Z

_{1}.

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