What is the reactive power of a 3-phase, delta-connected syste... | Technical Ability MCQ | Examoogle

Technical AbilityElectrical Machines and Power Systems

What is the reactive power of a 3-phase, delta-connected system with line voltage of 100 V and line current of 40 A if the phase difference between the voltage and the current is 36.87°?

2.155 kVAR

6.155 kVAR

4.155 kVAR

8.155 kVAR

Correct Answer

⚙️ TE • Technical Concept & PrincipleTechnical AbilityElectrical Machines and Power Systems

Option A

155 kVAR

Quick Summary:

The reactive power ( $Q$ ) in a 3-phase system is calculated using the formula $Q = \sqrt{3} V_L I_L \sin\phi$ . For a system with $V_L = 100 \text{ V}$ , $I_L = 40 \text{ A}$ , and $\phi = 36.87°$ , the value is $\sqrt{3} \times 100 \times 40 \times \sin(36.87°) \approx 4156 \text{ VAR}$ or $4.156 \text{ kVAR}$ .

⚙️TETechnical SolutionConcept & Principle

📜 Standard Reference & Code Clause

IS 12065:1987

💡 Explanation

🔢 Key Formulas

$Q = \sqrt{3} V_L I_L \sin\phi$ — Formula for 3-phase reactive power

$\sin(36.87°) \approx 0.6$ — Trigonometric value for the given angle

⚙️ Working Principle

In a 3-phase system, the total reactive power is the sum of the reactive power in the three individual phases. Since $Q_L = V_{ph} I_{ph} \sin\phi$ and in delta connection $V_L = V_{ph}$ while $I_L = \sqrt{3} I_{ph}$ , the total reactive power simplifies to $\sqrt{3} V_L I_L \sin\phi$ . The phase angle $36.87°$ corresponds to a power factor of $0.8$ , where $\sin(36.87°) = 0.6$ .

📌 Key Points

▸
In delta connection, line voltage equals phase voltage ( $V_L = V_{ph}$ )
▸
Line current is related to phase current by $I_L = \sqrt{3} I_{ph}$
▸
Reactive power is measured in VAR (Volt-Ampere Reactive)
▸
The power factor angle $\phi$ is the phase difference between phase voltage and phase current

✅ Advantages

▸
Higher power transfer efficiency in 3-phase systems
▸
Allows for calculation of VAR compensation requirements for grid stability

❌ Disadvantages / Limitations

▸
Requires precise measurement of phase angle
▸
Reactive power does not perform useful mechanical work

🛠️ Applications / Uses

▸
AC motor power analysis
▸
Transmission line reactive compensation sizing

📄 Additional Information

▸
The value $\sin(36.87°)$ is derived from the common $3-4-5$ triangle, where $\sin\phi = 3/5 = 0.6$ .
▸
Option B (6.155 kVAR) usually results from mistakenly using $\cos\phi$ instead of $\sin\phi$ or misplacing the $\sqrt{3}$ factor.

📊 Diagram / Illustration

✅

C is correct — The calculated reactive power using $Q = \sqrt{3} V_L I_L \sin\phi$ yields approximately 4.156 kVAR.

Core Concepts Used

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Three-phase circuit theory Delta connection relationships Reactive power definition

💡 EXAM TIP

Always verify if the question asks for Active Power ( $P = \sqrt{3} V_L I_L \cos\phi$ ) or Reactive Power ( $Q = \sqrt{3} V_L I_L \sin\phi$ ) before calculating.

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