What happens to the reading of a wattmeter when the power factor of a circuit is changed from unity power fact

Question

What happens to the reading of a wattmeter when the power factor of a circuit is changed from unity power factor to leading power factor?

Examoogle · Accepted Answer

The correct answer is Option D: The wattmeter reading decreases. The reading of an electrodynamic wattmeter is given by $P = VI \cos \phi$, where $\phi$ is the phase angle between voltage and current. As the power factor $\cos \phi$ moves from unity ($\phi = 0^\circ$) toward a leading or lagging state ($\phi 
eq 0^\circ$), the value of $\cos \phi$ decreases from 1, resulting in a decrease in the measured real power.

Step-by-Step Solution & Concepts:
The reading of an electrodynamic wattmeter is given by $P = VI \cos \phi$, where $\phi$ is the phase angle between voltage and current. As the power factor $\cos \phi$ moves from unity ($\phi = 0^\circ$) toward a leading or lagging state ($\phi 
eq 0^\circ$), the value of $\cos \phi$ decreases from 1, resulting in a decrease in the measured real power.

Working Principle: An electrodynamic wattmeter consists of a fixed current coil and a moving potential coil. The torque produced is proportional to the instantaneous product of voltage and current, $T \propto vi$. The average deflection torque, which determines the reading, is proportional to the average value of this product, resulting in $T_{avg} = K \cdot VI \cos \phi$. Any deviation of the power factor from unity causes $\cos \phi

Key Formulas: $P = VI \cos \phi$ — The power measured by the wattmeter; $T_d = I_c I_p M \cos \phi$ — The average deflecting torque of the wattmeter where $I_c$ is current coil current, $I_p$ is potential coil current, and $M$ is mutual inductance

Key Points: Electrodynamic wattmeters are designed to measure real power in AC circuits.; The reading is directly proportional to the cosine of the phase angle between voltage and current.; At unity power factor, $\cos \phi = 1$, which represents the maximum possible reading for fixed V and I values.; Leading or lagging power factor implies a shift in phase, decreasing the power factor component $\cos \phi$.

Advantages: Can be used for both AC and DC measurements; High accuracy in standard power frequency ranges

Disadvantages: Low torque-to-weight ratio compared to PMMC; Susceptible to errors from external magnetic fields

Applications: Industrial power measurement; Laboratory wattmeter calibration

Additional Info: The wattmeter measures active power ($P$) only, whereas reactive power ($Q$) is measured using a varmeter.. Option B is incorrect because electrodynamic wattmeters operate on the electrodynamic principle, which inherently accounts for phase displacement, allowing them to measure power at any power factor (within instrumental limits).

Answer: D is correct — The wattmeter reading decreases as the power factor $\cos \phi$ becomes less than unity, reducing the active power component being measured.

Exam Tip: Remember that wattmeters measure real power ($P = VI \cos \phi$); if the power factor decreases, the real power reading must decrease even if the apparent power ($S=VI$) remains constant.

Examoogle · Answer

Option A: The wattmeter reading increases

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Option B: The wattmeter cannot measure the leading power factor

Examoogle · Answer

Option C: The wattmeter reading remains unchanged

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