The GATE Grind

GATE 2024 IN – Question 47

Measurements · Voltage current and power measurement · 2 marks · Multiple choice

For the wattmeter circuit shown, define the following angles:

$\alpha$: between load current and load voltage; $\beta$: lag of pressure-coil current behind its voltage; $\gamma$: between pressure-coil and current-coil currents; $\delta$: voltage-transformer phase angle; $\theta$: current-transformer phase angle.

For a load with lagging phase angle $\alpha$, which relation is correct?

Diagram for GATE 2024 IN question 47
  1. $\alpha=-\gamma\pm\delta\pm\theta-\beta$
  2. $\alpha=-\gamma\pm\delta\pm\theta+\beta$
  3. $\alpha=\gamma\pm\delta\pm\theta+\beta$
  4. $\alpha=\gamma\pm\delta\pm\theta-\beta$

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Correct answer: (C) $\alpha=\gamma\pm\delta\pm\theta+\beta$

Explanation

First neglect transformer phase errors. Pressure-coil current lags voltage by $\beta$, while load current lags by $\alpha$.

Thus their angular separation is $\gamma=\alpha-\beta$, or $\alpha=\gamma+\beta$. Adding the signed PT and CT phase corrections gives $\alpha=\gamma\pm\delta\pm\theta+\beta$, **C**.