GATE Electrical Engineering Electrical and Electronic Measurements Syllabus

In the two-wattmeter method, what does it mean when one wattmeter reads zero?

It indicates a power factor of 0.5 (φ = 60°), since one reading becomes cos(90°) = 0.

In the two-wattmeter method, when does one wattmeter read negative and what is done?

When the power factor is below 0.5 (φ > 60°) one wattmeter reads negative; its connections are reversed to read the magnitude and total power = W1 - W2 (larger minus smaller).

What is the total three-phase reactive power in terms of the two wattmeter readings?

Q = √3 (W1 - W2).

What causes the wattmeter pressure-coil inductance error and which way does it affect the reading?

The pressure coil has inductance, so its current lags the applied voltage slightly, introducing a phase error. It causes the wattmeter to read high for lagging power factors (and low for leading).

What are the two methods of connecting a wattmeter's pressure coil, and which is preferred for high-impedance loads?

Voltage-coil-across-load (current coil carries load + pressure coil current) and voltage-coil-on-supply-side (pressure coil sees load + current coil drop). For high-impedance (small current) loads, the voltage-coil-across-the-load connection minimizes error.

What type of instrument is an energy meter (domestic kWh meter) and what is its operating principle?

An induction-type (single-phase induction) integrating instrument; eddy currents induced in a rotating aluminium disc by shunt and series magnet fluxes produce a torque proportional to power, so disc speed ∝ power and total revolutions ∝ energy.

Why does an energy meter use an integrating mechanism rather than indicating instantaneous value?

Energy is the time-integral of power (E = ∫P dt). The rotating disc's revolutions accumulate over time, registering total energy (kWh) on a counting train.

What is the function of the braking magnet (permanent magnet) in an induction energy meter?

It induces eddy currents in the rotating disc to produce a braking (retarding) torque proportional to disc speed, making steady-state speed proportional to power and controlling the calibration/speed.

Define the 'meter constant' (K) of an energy meter.

The number of disc revolutions per kilowatt-hour (rev/kWh); energy recorded = (number of revolutions) / K.

What is 'creeping' in an induction energy meter and how is it prevented?

Creeping is the slow continuous rotation of the disc with the potential coil energized but no load current. It is prevented by drilling two diametrically opposite holes (or slots) in the disc to create a locking torque.

What is the lag adjustment (power-factor compensation) in an energy meter for?

It ensures the shunt-magnet flux lags the applied voltage by exactly 90°, so the meter reads correctly at all power factors; achieved using shading bands/copper loops on the shunt magnet.

What error does the friction at low loads cause in an energy meter, and how is it compensated?

Friction causes the meter to run slow (under-register) at light loads; it is compensated by a small friction-compensation (light-load adjustment) device that provides a small driving torque, e.g. shading loop near the shunt magnet pole.

How is power factor measured directly with a single-phase power-factor meter (electrodynamometer type)?

It uses a fixed current coil and two crossed moving (pressure) coils—one resistive, one inductive branch—so the pointer takes up a position depending on the phase angle between V and I, reading cosφ directly without a controlling spring.

How can power factor be calculated from wattmeter, voltmeter and ammeter readings in a single-phase circuit?

cosφ = W / (V·I), where W is the wattmeter reading (real power), and V·I is the apparent power.

What is the relationship between active power P, apparent power S, reactive power Q, and power factor?

S = √(P² + Q²); P = S cosφ; Q = S sinφ; power factor = cosφ = P/S.

What is the principle of a Weston frequency meter / why is power factor a function of frequency in some meters?

In crossed-coil (Weston) power-factor and frequency meters, two coils carry currents whose ratio depends on frequency or phase angle; the resultant field orientation positions the pointer to indicate frequency or power factor directly.

What instrument transformer is used to extend the range of AC ammeters and wattmeter current coils for high currents?

A current transformer (CT), which steps down the line current to a standard low value (commonly 5 A or 1 A secondary).

What instrument transformer is used to extend AC voltmeter and wattmeter pressure-coil range for high voltages?

A potential (voltage) transformer (PT/VT), which steps down high voltage to a standard low value (commonly 110 V secondary).

Why must the secondary of a current transformer never be left open-circuited?

With the secondary open, the demagnetizing secondary MMF is removed, the core flux rises sharply causing high core losses, overheating, and dangerously high secondary voltage—damaging insulation and endangering personnel.

Define ratio error and phase angle error of a current transformer.

Ratio error = (Nominal ratio - Actual ratio)/Actual ratio (deviation of actual transformation ratio from nominal). Phase angle error is the deviation from the ideal 180° phase relationship between primary and reversed secondary current phasors.

What is a DC potentiometer used to measure, and on what principle?

It measures unknown EMF/voltage by comparison (null/balance method) against a known calibrated voltage drop along a uniform resistance wire; at balance no current flows through the galvanometer, so it draws no current from the source.

Why does a potentiometer give very accurate voltage measurement compared to a voltmeter?

Because it works on the null-balance principle—at balance it draws no current from the source under test, eliminating loading error and measuring the true open-circuit EMF.

How can a DC potentiometer be used to measure current?

By passing the current through a known standard resistor and measuring the voltage drop across it with the potentiometer; I = V_measured / R_standard.

What is a Wheatstone bridge used to measure and what is the balance condition?

It measures medium resistances; at balance (galvanometer null) the products of opposite arms are equal: P/Q = R/S, i.e. R = (P/Q)·S.

Which bridge is used for measuring low resistances and why is Wheatstone bridge unsuitable for them?

Kelvin's double bridge is used for low resistances; the Wheatstone bridge is unsuitable because contact and lead resistances become comparable to the unknown low resistance, causing large errors.

Distinguish between accuracy and precision of a measuring instrument.

Accuracy is closeness of the measured value to the true value; precision is the closeness/repeatability of repeated measurements to each other (consistency), regardless of correctness.

Define the sensitivity of a measuring instrument.

Sensitivity = change in output (deflection/response) per unit change in the input quantity being measured (the ratio Δoutput/Δinput, i.e. the slope of the calibration curve).

What is the difference between absolute error and relative (percentage) error?

Absolute error = measured value - true value. Relative error = absolute error / true value (often expressed as a percentage).

What is the function of a controlling torque and damping torque in an indicating instrument?

Controlling torque opposes the deflecting torque to give a definite steady deflection (scale reading) and returns the pointer to zero; damping torque brings the pointer to rest quickly without oscillation (ideally critically damped).

Compare moving-iron and PMMC instruments on scale, AC/DC use, and quantity measured.

PMMC: uniform/linear scale, DC only, measures average value, high accuracy/sensitivity. Moving-iron: non-uniform (square-law) scale, both AC and DC, measures RMS value, lower accuracy but rugged and cheap.