What is the correction factor of the wattmeter at a lagging power factor? (Where, φ is the phase angle between

Question

What is the correction factor of the wattmeter at a lagging power factor? (Where, φ is the phase angle between the voltage applied to the pressure coil and the current in the current coil and β is the angle between the voltage applied to the pressure coil and the current in the pressure coil.)

Examoogle · Accepted Answer

The correct answer is Option C: \frac{\cos \phi}{\cos \beta \cos(\phi - \beta)}. The correction factor for a wattmeter is defined as the ratio of the true power to the power measured by the instrument. For an electrodynamic wattmeter, phase shift in the pressure coil (due to inductance) causes a reading error, leading to the correction factor formula $\frac{\cos \phi}{\cos \beta \cos(\phi - \beta)}$.

Step-by-Step Solution & Concepts:
The correction factor for a wattmeter is defined as the ratio of the true power to the power measured by the instrument. For an electrodynamic wattmeter, phase shift in the pressure coil (due to inductance) causes a reading error, leading to the correction factor formula $\frac{\cos \phi}{\cos \beta \cos(\phi - \beta)}$.

Working Principle: In an ideal wattmeter, the pressure coil current is exactly in phase with the applied voltage. However, the pressure coil has some inherent inductance, causing the current to lag the voltage by an angle $\beta$. The actual reading is $P_{	ext{measured}} = VI \cos \beta \cos(\phi - \beta)$, while the true power is $P_{	ext{true}} = VI \cos \phi$. The correction factor is the ratio $\frac{P_{	ext{true}}}{P_{	ext{measured}}}$.

Key Formulas: $$	ext{Correction Factor} = \frac{\cos \phi}{\cos \beta \cos(\phi - \beta)}$$; $$P_{	ext{true}} = VI \cos \phi$$; $$P_{	ext{measured}} = VI \cos \beta \cos(\phi - \beta)$$

Key Points: The angle $\phi$ is the phase angle between load voltage and load current.; The angle $\beta$ is the phase angle of the pressure coil circuit (ideally zero).; For lagging power factor loads, $\phi$ is positive.; The correction factor is greater than 1 when the wattmeter reading is less than the true power.

Advantages: Provides a mathematical method to compensate for instrument errors.; Enables accurate power measurement using non-ideal instruments.

Disadvantages: Requires knowledge of the pressure coil phase angle $\beta$.; Calculation complexity increases with frequency variations.

Applications: Calibration of electrodynamic wattmeters.; Low power factor power measurement corrections.

Additional Info: The expression $\cos(\phi - \beta)$ is used for lagging power factor because the phase angle of the load $\phi$ is positive and the pressure coil lag $\beta$ reduces the effective phase difference.. Option D uses $\sin(\phi + \beta)$, which is incorrect for this derivation.

Answer: C is correct — The correction factor for a wattmeter measuring power at a lagging power factor is given by the ratio of true power to measured power, resulting in $\frac{\cos \phi}{\cos \beta \cos(\phi - \beta)}$.

Exam Tip: Always remember that for a lagging power factor, the error angle in the pressure coil subtracts from the load phase angle, leading to the term $\cos(\phi - \beta)$ in the denominator.

Examoogle · Answer

Option A: \frac{\cos \phi}{\cos \beta \cos(\phi + \beta)}

Examoogle · Answer

Option B: \frac{\cos \phi}{\cos \beta \sin(\phi - \beta)}

Examoogle · Answer

Option D: \frac{\cos \phi}{\cos \beta \sin(\phi + \beta)}

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