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GATE 2022 IN Q.55: solution and answer

GATE 2022 · INQ.55 · 2 marks · NAT

In the balanced three-phase circuit shown, and the line-to-line r.m.s. voltage is at . The reading on the wattmeter (in watts) is _______ (round off to two decimal places)

GATE 2022 IN question 55: Three supply lines labelled R (top), Y (middle) and B (bottom) enter from the left.Tap to open full size
Figure from the GATE 2022 IN paper. It is part of the question.
Figure description

Three supply lines labelled R (top), Y (middle) and B (bottom) enter from the left. Line R passes through the current coil of a wattmeter W1 (drawn as a circle labelled 'Wattmeter', 'W1') and continues right, then down to one capacitor C_0. The wattmeter's pressure-coil lead leaves the bottom of the circle and goes down through a series resistor (zig-zag) to a node on line Y, so the pressure coil sees V_RY and the current coil carries I_R. Line Y continues right through a capacitor C_0 to the star point. Line B runs right and then up to a third capacitor C_0. The three capacitors C_0 meet at a common star point (neutral not connected to the supply): a balanced star-connected purely capacitive load, one C_0 per phase.

Answer and solution

ANSWER

The wattmeter reads about 143.97 W.

Official answer: 141.80 to 146.20Source: Official answer key, GATE 2022 IN (IIT Kharagpur)

  1. Connections. The current coil is in line R and the pressure coil (with its series resistor) is across R and Y, so the wattmeter reads .

  2. Reactance per phase.

  3. Line current (balanced star). , so

  4. Phasor angles (RYB sequence, as reference). The question does not state the phase sequence, so the standard RYB (positive) sequence is taken. In a pure capacitor the current leads its voltage by , so . The line voltage leads its phase voltage by , so .

  5. Angle between the coil quantities. leads by . In general this angle is with for a purely capacitive load, so .

  6. Wattmeter reading.

  7. Check in closed form. . The load takes no real power, but this meter pairs with a line voltage rather than its own phase voltage, so it still shows a non-zero reading.

KEY IDEA

A wattmeter reads the product of the voltage across its pressure coil, the current in its current coil and the cosine of the angle between them. Here that is and . In a balanced star load that angle is , with for pure capacitance, so the angle is and the reading is . The load takes no real power, but the meter still reads a non-zero value.

WATCH OUT FOR

Answering 0 W because a purely capacitive load takes no real power. This meter does not measure the load's real power: it pairs with the line voltage , not with . Other slips: using the phase angle instead of ; using the line voltage 440 V in place of the phase voltage when working out ; taking the RBY sequence, which flips the angle to and gives W.

From the GATE 2022 IN paper. Every question of this paper · Download the full paper · All 11 Three-phase (EE) questions, with notes

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