300+ Network Theorem MCQ- Objective Question Answer for Network Theorem Quiz

161. 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_BRZ_BY)/(Z_RY + Z_BY + Z_BR)
B. (Z_RYZ_BR)/(Z_RY + Z_BY + Z_BR)
C. (Z_RYZ_BY)/(Z_RY + Z_BY + Z_BR)
D. (Z_RY)/(Z_RY + Z_BY + Z_BR)

Answer: B

After transformation to star, the impedance at R is

(Z_RYZ_BR)/(Z_RY + Z_BY + Z_BR).

162. 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 Y is?

A. (Z_RY)/(Z_RY + Z_BY + Z_BR)
B. (Z_BY)/(Z_RY + Z_BY + Z_BR)
C. (Z_RYZ_BY)/(Z_RY + Z_BY + Z_BR)
D. (Z_RYZ_BR)/(Z_RY + Z_BY + Z_BR)

Answer: C

After transformation to star, the impedance at Y is

(Z_RYZ_BY)/(Z_RY + Z_BY + Z_BR).

163. 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 B is?

A. (Z_BRZ_BY)/(Z_RY + Z_BY + Z_BR)
B. (Z_RYZ_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)

Answer: A

After transformation to star, the impedance at Y is

(Z_BRZ_BY)/(Z_RY + Z_BY + Z_BR).

164. If the resistors of a star-connected system are Z_R, Z_Y, and Z_B then the impedance Z_RY in delta connected system will be?

A. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_B
B. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_Y
C. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_R
D. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/(Z_R + Z_Y)

Answer: A

After transformation to delta, the impedance Z_RY in delta connected system will be

(Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_B.

165. If the resistors of a star-connected system are Z_R, Z_Y, Z_B then the impedance Z_BY in a delta-connected system will be?

A. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/(Z_B + Z_Y)
B. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_B
C. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_Y
D. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_R

Answer: D

After transformation to delta, the impedance Z_BY in delta connected system will be

(Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_R.

166. If the resistors of a star-connected system are Z_R, Z_Y, and Z_B then the impedance Z_BR in delta connected system will be?

A. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_Y
B. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/_R
C. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_B
D. (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/(Z_B + Z_R)

Answer: A

After transformation to delta, the impedance Z_BR in delta connected system will be

(Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_Y.

167. Asymmetrical 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

Answer: C

Z_RY = (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_B

= (3.8 − j0.38) Ω.

168. 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_BY.

A. ( − 5.22 + j0.82) Ω
B. (5.22 − j0.82) Ω
C. (3.8 − j0.38) Ω
D. ( − 3.02 + j8) Ω

Answer: B

Z_BY = (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_R

= (5.22 − j0.82)Ω.

169. 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_BR.

A. (5.22 − j0.82) Ω
B. ( − 3.02 + j8) Ω
C. ( − 5.22 + j0.82) Ω
D. (3.8 − j0.38) Ω

Answer: B

Z_BR = (Z_RZ_Y + Z_YZ_B + Z_BZ_R)/Z_Y

= ( − 3.02 + j8) Ω.

170. 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

Answer: C

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

171. Find the equivalent delta circuit in Star − Delta Transformation.

A. 9.69 ohm, 35.71 ohms, 6.59 ohm
B. 10.69 ohm, 35.71 ohms, 6.59 ohm
C. 9.69 ohm, 34.71 ohms, 6.59 ohm
D. 10.69 ohm, 35.71 ohms, 7.59 ohm

Answer: A

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.

172. Which among the following is the correct expression for star-delta conversion?

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.
R1 = Ra + Rb + Ra × Rb/Rc, R2 = Rc + Rb + Rc × Rb/Ra, R3 = Ra + Rc + Ra × Rc/Rb
R1 = Ra × Rb/Rc, R2 = Rc × Rb/Ra, R3 = Ra × Rc/Rb

Answer: C

After converting to delta, each delta connected resistance is equal to the sum of the two resistance it is connected to the + 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.

173. Find the equivalent resistance between X and Y using star-delta transformation.

A. 3.33 ohm
B. 4.34 ohm
C. 5.65 ohm
D. 2.38 ohm

Answer: D

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 ohms 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.

174. 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

Answer: B

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

175. Ra is resistance at A, Rb is resistance at B, and Rc is resistance at C in star connection. After transforming to delta, what is the 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

Answer: A

After converting to the delta, each delta-connected resistance is equal to the sum of the two resistances it is connected to the + product of the two resistances divided by the remaining resistance.

Hence, resistance between B and C

= Rc + Rb + Rc × Rb/Ra.

176. Ra is resistance at A, Rb is resistance at B, and Rc is resistance at C in star connection. After transforming to delta, what is the 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

Answer: B

After converting to the delta, each delta-connected resistance is equal to the sum of the two resistances it is connected to the + product of the two resistances divided by the remaining resistance.

Hence, the resistance between A and C

= Ra + Rc + Ra × Rc/Rb.

177. Ra is resistance at A, Rb is resistance at B, and Rc is resistance at C in star connection. After transforming to delta, what is the 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

Answer: C

After converting to the delta, each delta-connected resistance is equal to the sum of the two resistances it is connected to the + product of the two resistances divided by the remaining resistance.

Hence, resistance between A and B = Ra + Rb + Ra × Rb/Rc.

178. If a 1ohm 2ohm and 32/3ohm resistor is connected in star, find the equivalent delta connection.

A. 34 ohm, 18.67 ohms, 3.19 ohm
B. 33 ohm, 18.67 ohms, 3.19 ohm
C. 33 ohm, 19.67 ohms, 3.19 ohm
D. 34 ohm, 19.67 ohms, 3.19 ohm

Answer: A

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.

179. If an 8/9ohm, 4/3ohm, and 2/3ohm resistor are connected to the star, find its delta equivalent.

A. 4ohm, 3ohm, 2ohm
B. 1ohm, 3ohm, 2ohm
C. 4ohm, 1ohm, 2ohm
D. 4ohm, 3ohm, 1ohm

Answer: A

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).

180. Find the equivalent resistance between A and B using star-delta transformation.

A. 32ohm
B. 31ohm
C. 30ohm
D. 29ohm

Answer: D

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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