Network Theory MCQs on “Voltage, Current and Power in a Delta Connected System”.
1. In a delta connected system, the voltage across the terminals R and Y is 400∠0⁰. Calculate the line voltage VRY. Assume RRY phase sequence.
A. 400∠0⁰
B. 400∠120⁰
C. 400∠-120⁰
D. 400∠240⁰
Answer: A
Clarification: In a balanced delta-connected system we know |VRY| = |VPh|, and it is displaced by 120⁰, therefore the line voltage VRY is VRY = 400∠0⁰V.
2. In a delta connected system, the voltage across the terminals R and Y is 400∠0⁰. Find the line voltage VYB.
A. 400∠120⁰
B. 400∠-120⁰
C. 400∠240⁰
D. 400∠-240⁰
Answer: B
Clarification: As |VYB| = |VPh|, and is displaced by 120⁰, therefore the line voltage VYB is VYB = 400∠-120⁰V. A balanced three phase, three wire, delta connected system is referred to as mesh connection because it forms a closed circuit.
3. In a delta connected system, the voltage across the terminals R and Y is 400∠0⁰. Find the line voltage VBR.
A. 400∠240⁰
B. 400∠120⁰
C. 400∠-240⁰
D. 400∠-120⁰
Answer: C
Clarification: We know, |VBR| = |VPh|, and is displaced by 120⁰, therefore the line voltage VBR is VBR = 400∠-240⁰V. Delta connection is so called because the three branches in the circuit can be arranged in the shape of delta.
4. In delta-connected system, the currents IR, IY, IB are equal in magnitude and they are displaced by _____ from one another.
A. 0⁰
B. 60⁰
C. 90⁰
D. 120⁰
Answer: D
Clarification: In delta-connected system, the currents IR, IY, IB are equal in magnitude and they are displaced by 120⁰ from one another. From the manner of interconnection of the three phases in the circuit, it may appear that the three phase are short circuited among themselves.
5. In a delta-connected system, the currents IR = IB = IY =?
A. IPh
B. 2IPh
C. 3IPh
D. 4IPh
Answer: A
Clarification: In a delta-connected system, the currents IR = IB = IY = IPh. Since the system is balanced, the sum of the three voltages round the closed mesh is zero; consequently no current can flow around the mesh when the terminals are open.
6. The relation between IL and IPh is in a delta connected system is?
A. IL = IPh
B. IL = √3 IPh
C. IL = 3 IPh
D. IL = 3√3IPh
Answer: B
Clarification: The relation between IL and IPh is in a delta connected system is IL = √3 IPh. The arrows placed alongside the voltages of the three phases indicate that the terminals are positive during their positive half cycles.
7. The line currents are ________ behind respective phase currents in a delta connected system.
A. 120⁰
B. 90⁰
C. 60⁰
D. 30⁰
Answer: D
Clarification: In a delta connected system, all the line currents are equal in magnitude but displaced by 120⁰ from one another and the line currents are 30⁰ behind the respective phase currents.
8. In a delta connected system, the expression of power (P) is?
A. VLILcosφ W
B. √3 VLILcosφ W
C. 3VLILcosφ W
D. 3√3VLILcosφ W
Answer: B
Clarification: The total power in the delta circuit is the sum of the powers in the three phases. In a delta connected system, the expression of power (P) is P = √3VLILcosφ W.
9. A balanced delta-connected load of (2+j3) Ω per phase is connected to a balanced three-phase 440V supply. The phase current is 10A. Find the total active power.
A. 7.26W
B. 726W
C. 7260W
D. 72.6W
Answer: C
Clarification: ZPh = √(22+32) = 3.6∠56.3⁰Ω. cosφ = RPh/ZPh = 2/3.6 = 0.55. IL = √3× IPh = 17.32A. Active power = √3 VLILcosφ = √3×440×17.32×0.55= 7259.78W.
10. A balanced delta-connected load of (2+j3) Ω per phase is connected to a balanced three-phase 440V supply. The phase current is 10A. Find the apparent power.
A. 10955.67 VAR
B. 10.95567 VAR
C. 109.5567 VAR
D. 1.095567 VAR
Answer: A
Clarification: Sinφ = 0.83. Reactive power = √3 VLILsinφ. VL = 440V, IL = 17.32A. On substituting we get reactive power = √3 x 440 x 17.32 = 10955.67 VAR.