This set of Network Theory MCQs focuses 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 V_{RY}. Assume RYB phase sequence.

a) 400∠0⁰

b) 400∠120⁰

c) 400∠-120⁰

d) 400∠240⁰

View Answer

Explanation: In a balanced delta-connected system we know |V

_{RY}|= |V

_{Ph}|, and it is displaced by 120⁰, therefore the line voltage V

_{RY}is V

_{RY}= 400∠0⁰V.

2. In the question 1 find the line voltage V_{YB}.

a) 400∠120⁰

b) 400∠-120⁰

c) 400∠240⁰

d) 400∠-240⁰

View Answer

Explanation: As |V

_{YB}|= |V

_{Ph}|, and is displaced by 120⁰, therefore the line voltage V

_{YB}is V

_{YB}= 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 the question 1 find the line voltage V_{BR}.

a) 400∠240⁰

b) 400∠120⁰

c) 400∠-240⁰

d) 400∠-120⁰

View Answer

Explanation: We know, |V

_{BR}|= |V

_{Ph}|, and is displaced by 120⁰, therefore the line voltage V

_{BR}is V

_{BR}= 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 I_{R} , I_{Y} , I_{B} are equal in magnitude and they are displaced by _____ from one another.

a) 0⁰

b) 60⁰

c) 90⁰

d) 120⁰

View Answer

Explanation: In delta-connected system, the currents I

_{R}, I

_{Y}, I

_{B}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 I_{R} = I_{B} = I_{Y} =?

a) I_{Ph}

b) 2I_{Ph}

c) 3I_{Ph}

d) 4I_{Ph}

View Answer

Explanation: In a delta-connected system, the currents I

_{R}= I

_{B}= I

_{Y}= I

_{Ph}. 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 I_{L} and I_{Ph} is in a delta connected system is?

a) I_{L} = I_{Ph}

b) I_{L} =√3 I_{Ph}

c) I_{L} =3 I_{Ph}

d) I_{L} = 3√3I_{Ph}

View Answer

Explanation: The relation between I

_{L}and I

_{Ph}is in a delta connected system is I

_{L}=√3 I

_{Ph}. 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 is?

a) 120⁰

b) 90⁰

c) 60⁰

d) 30⁰

View Answer

Explanation: 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) V_{L}I_{L}cosφ W

b) √3 V_{L}I_{L}cosφ W

c) 3V_{L}I_{L}cosφ W

d) 3√3V_{L}I_{L}cosφ W

View Answer

Explanation: 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 = √3V

_{L}I

_{L}cosφ 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

View Answer

Explanation: Z

_{Ph}= √(2

^{2}+3

^{2})=3.6∠56.3⁰Ω. cosφ = R

_{Ph}/Z

_{Ph}= 2/3.6 = 0.55. I

_{L}= √3× I

_{Ph}= 17.32A. Active power = √3 V

_{L}I

_{L}cosφ = √3×440×17.32×0.55= 7259.78W.

10. Find the apparent power in the information provided in the question 9.

a) 10955.67 VAR

b) 10.95567 VAR

c) 109.5567 VAR

d) 1.095567 VAR

View Answer

Explanation: Sinφ = 0.83. Reactive power = √3 V

_{L}I

_{L}sinφ. V

_{L}= 440V, I

_{L}= 17.32A. On substituting we get reactive power = √3 x 440 x 17.32 = 10955.67 VAR.

**Sanfoundry Global Education & Learning Series – Network Theory.**

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