# Network Theory Questions and Answers – Voltage, Current and Power in a Delta Connected System

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 VRY. Assume RRY phase sequence.
a) 400∠0⁰
b) 400∠120⁰
c) 400∠-120⁰
d) 400∠240⁰

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: 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.
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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

Explanation: 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

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) VLILcosφ W
b) √3 VLILcosφ W
c) 3VLILcosφ W
d) 3√3VLILcosφ W

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 = √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

Explanation: 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

Explanation: 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.

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