The wattmeter method is used to measure power in a three-phase... | Technical Ability MCQ | Examoogle

Technical AbilityElectrical Machines and Power Systems

The wattmeter method is used to measure power in a three-phase load. The wattmeter readings are 200 W and −35 W. Find the respective values of active power and reactive power.

Option 1

Option 2

Option 3

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Correct Answer

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

Option A

Option 1

Quick Summary:

In the two-wattmeter method for measuring three-phase power, the total active power ( $P$ ) is the sum of the individual wattmeter readings ( $W_1 + W_2$ ), and the total reactive power ( $Q$ ) is given by $\sqrt{3}(W_1 - W_2)$ . Given $W_1 = 200\text{ W}$ and $W_2 = -35\text{ W}$ , the calculation follows directly from these formulas.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$P = W_1 + W_2$ — Total active power

$Q = \sqrt{3}(W_1 - W_2)$ — Total reactive power

⚙️ Working Principle

The two-wattmeter method relies on Blondel's Theorem, which states that for an $n$ -wire system, $n-1$ wattmeters are required to measure total power. By connecting the current coils in two lines and the potential coils between those respective lines and the third line, the total power is derived from the algebraic sum of the readings. When one reading is negative, it indicates a power factor less than 0.5 (specifically, the phase angle between phase voltage and current exceeds $60°$ ).

📌 Key Points

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When $W_2$ is negative, the load is highly inductive or capacitive, meaning the phase angle is greater than $60°$ .
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Active power $P = 200 + (-35) = 165\text{ W}$ .
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Reactive power $Q = \sqrt{3}(200 - (-35)) = \sqrt{3}(235) = 235\sqrt{3}\text{ VAR}$ .

✅ Advantages

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Requires only two wattmeters for balanced or unbalanced three-phase systems.
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Provides information about both active power and reactive power (via difference in readings).

❌ Disadvantages / Limitations

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If the power factor is less than 0.5, one wattmeter will give a negative reading, requiring the reversal of its current coil leads for measurement.
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Only applicable to three-wire systems.

🛠️ Applications / Uses

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Industrial motor power measurement.
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General three-phase power monitoring.

📄 Additional Information

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The total power $P$ is $200 - 35 = 165\text{ W}$ .
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The total reactive power $Q$ is $\sqrt{3} \times (200 - (-35)) = 235\sqrt{3}\text{ VAR}$ .

📊 Diagram / Illustration

✅

A is correct — The active power is $165\text{ W}$ and the reactive power is $235\sqrt{3}\text{ VAR}$ .

Core Concepts Used

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Two-wattmeter method Three-phase power measurement Power factor calculation

💡 EXAM TIP

Always remember that for $Q = \sqrt{3}(W_1 - W_2)$ , the sign convention depends on which reading is larger; a negative reading signifies that the phase angle between line voltage and phase current is greater than $60°$ .

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