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GATE 2025 EE – Question 58

Electrical and Electronic Measurements · Measurement of voltage, current, power, energy and power factor · 2 marks · Numerical answer

In an experiment to measure the active power drawn by a single-phase RL Load connected to an AC source through a 2 Ω resistor, three voltmeters are connected as shown in the figure below. The voltmeter readings are as follows: $V_{Source}=200\ V$, $V_R=9\ V$, $V_{Load}=199\ V$. Assuming perfect resistors and ideal voltmeters, the Load-active power measured in this experiment, is _______ W (round off to one decimal place).

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Correct answer: 79.10 to 79.90

Explanation

The current is $I=V_R/R=9/2=4.5$ A. With the resistor and load in series, $V_S^2=V_R^2+V_L^2+2V_RV_L\cos\varphi$, so $200^2=81+199^2+2(9)(199)\cos\varphi$, giving $\cos\varphi=\dfrac{318}{3582}=0.0888$. The load power is $V_LI\cos\varphi=199\times4.5\times0.0888=79.5$ W.