Measurement of Energy MCQ Quiz - Objective Question with Answer for Measurement of Energy - Download Free PDF

Option 2 is NOT correct because eliminating high-voltage leads from PT bushings generally reduces complexity and potential points of failure, not increases them. So saying it increases short-circuit risk is incorrect.

Function of bushings in PT

• When a high-voltage conductor passes through a metal sheet or frame at earth potential, the necessary insulation is provided in the form of a bushing.
• The bushing's primary function is to prevent electrical breakdown between the enclosed conductor and the surrounding earthed metal work.
• The high voltage conductor passes through the bushing made of some insulating material (e.g., porcelain, steatite).
• In transformers, bushings are insulating devices that allow electrical conductors (such as transformer leads) to pass safely through the transformer tank or casing while preventing the high voltage from leaking to the grounded parts of the transformer.
• Their primary purpose is insulation, ensuring that the high-voltage leads are protected from the tank and the surrounding environment.
• Bushings provide a safe way to bring electrical connections out of the transformer without shorting the circuit or causing electrical faults.
• They are designed to handle high voltages and currents, while also preventing any potential dielectric breakdown between the conductor and the transformer tank.

Potential Transformer

A Potential Transformer (PT), also known as a Voltage Transformer, is an instrument transformer used to step down high voltage to a lower, measurable value for metering and protection in power systems.

PTs work on the same principle as a regular transformer but are designed for precision and safety, not power delivery.

Option 3 is NOT correct because:

• Voltage measurement accuracy in a PT depends primarily on the Ratio Error, not just the power angle (phase angle) error.
• Power angle error (or phase error) affects power and energy measurements (since they involve phase relationships), but not voltage measurement alone.
• Voltage measurement is mostly impacted by ratio error, which is the deviation from the ideal voltage transformation ratio.

Explanation:

Copper Shading in Energy Meters

Definition: Copper shading refers to the use of copper rings or shading bands provided in an energy meter to adjust the phase relationship of the fluxes produced in its electromagnetic system. This adjustment is critical to ensure accurate measurement of electrical energy consumption.

Working Principle: Energy meters work based on the interaction of magnetic flux and the induced currents in the rotating aluminum disc. The copper shading is designed to bring the flux produced by the voltage coil into exact quadrature (90-degree phase difference) with the applied voltage. This ensures that the torque developed is proportional to the power being consumed, leading to accurate readings.

Correct Option Analysis:

The correct answer is:

Option 1: Bring flux exactly in quadrature with applied voltage.

This option correctly explains the purpose of copper shading in an energy meter. By introducing copper shading, the flux generated by the voltage coil is aligned precisely at a 90-degree phase difference (quadrature) with the applied voltage. This is essential for the proper functioning of the meter, as it ensures that the torque acting on the aluminum disc is directly proportional to the real power consumed by the load. Accurate measurement of energy relies on this torque being proportional to the product of voltage, current, and the cosine of the angle between them (power factor).

Important Information:

To understand the significance of copper shading, consider the following:

• Energy meters measure the electrical energy consumed by a load in kilowatt-hours (kWh).
• The rotating aluminum disc inside the meter is subjected to magnetic flux generated by the current and voltage coils.
• The torque causing the disc to rotate is proportional to the instantaneous power being consumed.
• If the fluxes are not in proper phase alignment (quadrature), measurement errors can occur, leading to inaccurate readings.

Additional Information:

Let’s evaluate the other options:

Option 2: To increase the speed of the aluminum disc.

This option is incorrect. The purpose of copper shading is not to increase the speed of the aluminum disc but to ensure phase alignment of the flux. The speed of the disc depends on the power being consumed by the load and the torque developed. Copper shading does not directly influence the speed but ensures accurate torque development.

Option 3: To count the rotation.

This option is incorrect. Counting the rotation of the aluminum disc is done by a mechanical or electronic counter mechanism in the energy meter. Copper shading has no role in counting rotations; its primary function is to maintain the correct phase relationship between the fluxes for accurate measurement.

Option 4: To balance the system from vibration.

This option is incorrect. Copper shading is not used for balancing the system or reducing vibrations. Vibrations are typically addressed through mechanical design aspects of the meter, such as damping mechanisms or sturdy construction. Copper shading serves an entirely different purpose related to phase alignment.

Conclusion:

Copper shading is an essential feature in energy meters to ensure accurate measurement of electrical energy. By bringing the flux produced by the voltage coil into exact quadrature with the applied voltage, it ensures that the torque acting on the aluminum disc is proportional to the real power consumed. Misalignment of fluxes can lead to significant measurement errors, making copper shading a crucial component for the reliable operation of energy meters.

Explanation:

Given Problem:

An energy meter has a constant of 600 revolutions per kilowatt-hour (rev/kWh). The meter makes 10 revolutions in 20 seconds. We are tasked to determine the load in kilowatts (kW).

Solution:

The energy meter constant, 600 rev/kWh, indicates that for every kilowatt-hour of energy consumed, the meter's disc completes 600 revolutions. To calculate the load in kilowatts, we need to use the following relationship:

Load (in kW) = (Number of revolutions × Time Conversion Factor) / (Meter Constant × Time in Hours)

Now, let us solve the problem step by step:

Since there are 3600 seconds in an hour, the given time of 20 seconds can be converted to hours as:

Time in hours = 20 seconds ÷ 3600 seconds/hour = 1/180 hours

Load (in kW) = (Number of revolutions × Time Conversion Factor) / (Meter Constant × Time in Hours)

Load (in kW) = (10 revolutions × 1) / (600 rev/kWh × 1/180 hours)

Load (in kW) = (10 × 180) / 600

Load (in kW) = 1800 / 600

Load (in kW) = 3 kW

1. Convert the time from seconds to hours:
2. Substitute the values into the formula:
3. Simplify the equation:

Final Answer: The load is 3 kW.

Important Information:

To evaluate why the other options are incorrect, let's briefly analyze the calculations:

1. Option 1 (0.75 kW): This value would imply a much lower load than calculated. Such a result would occur if either the number of revolutions or the time interval was incorrectly used in the formula.
2. Option 2 (1.5 kW): This value is half the correct answer. This mistake could arise if the time in hours was incorrectly doubled during calculation.
3. Option 4 (6 kW): This value is double the correct answer. Such an error may occur if the number of revolutions was mistakenly doubled or the meter constant was halved.

Conclusion:

The correct solution to the problem is 3 kW, which corresponds to Option 3. This result is consistent with the energy meter's constant, the number of revolutions, and the given time interval. Proper understanding and application of the energy meter formula are essential to solving such problems accurately.

Explanation:

Meter Constant and Speed of Induction Watt Hour Meter

Definition: The meter constant of a watt-hour meter indicates the number of revolutions of the meter's disc for a specific amount of energy consumed, typically expressed in revolutions per kilowatt-hour (rev/kWh). It helps in determining the speed of the disc based on the electrical load connected to the meter.

Problem Statement: In this problem, we are tasked with calculating the speed of the meter's disc for a single-phase 240V induction watt-hour meter with a meter constant of 400 revolutions per kWh. The current is 10A, and the power factor (pf) is 0.8 lagging.

Given Data:

• Meter constant: 400 revolutions per kWh
• Voltage (V): 240 V
• Current (I): 10 A
• Power factor (pf): 0.8 (lagging)

Step-by-Step Solution:

Step 1: Calculate the power consumed (P)

The power consumed in an electrical circuit is given by the formula:

P = V × I × pf

Substituting the given values:

P = 240 × 10 × 0.8

P = 1920 W or 1.92 kW

Step 2: Determine the number of revolutions per second

From the meter constant, we know that the meter completes 400 revolutions for every 1 kWh of energy consumed. To find the revolutions per second, we first calculate the energy consumed per second (in kWh) and then use the meter constant.

Energy consumed per second (in kWh):

The energy consumed per second in kWh is calculated as:

Energy (kWh) = Power (kW) × Time (hours)

For 1 second, time = 1/3600 hours:

Energy = 1.92 × (1/3600)

Energy = 0.000533 kWh

Revolutions per second:

The revolutions per second can be calculated using the meter constant:

Revolutions per second = Energy (kWh) × Meter constant

Revolutions per second = 0.000533 × 400

Revolutions per second = 0.2132 revolutions/second

Step 3: Convert revolutions per second to revolutions per minute (rpm)

To convert revolutions per second to revolutions per minute, multiply by 60:

Revolutions per minute (rpm) = Revolutions per second × 60

Revolutions per minute = 0.2132 × 60

Revolutions per minute = 12.8 rpm

Final Answer:

The speed of the meter disc is 12.8 rpm.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 16.02 rpm

This option is incorrect. The value of 16.02 rpm is higher than the actual calculation. This might result from incorrectly assuming a higher energy consumption or misinterpreting the meter constant.

Option 3: 18.2 rpm

This option is also incorrect. It overestimates the revolutions per minute, likely due to a similar error in the calculation of power or energy consumed.

Option 4: 21.1 rpm

This option is incorrect as well. It significantly overestimates the speed of the meter disc, which is inconsistent with the given meter constant and load conditions.

Conclusion:

The correct answer is Option 1: 12.8 rpm. This result is derived using the meter constant and the actual power consumed under the given load conditions. Understanding the relationship between power, energy, and the meter constant is crucial for solving such problems accurately.

Energy meter:

Energy meter or Watt-hour meter is used to measure the energy in kWh.

It is an integrating type instrument.

Its working principle is similar to the transformer.

There are three essential mechanisms required in the energy meter named Driving torque, Braking torque, and registered mechanism.

Driving torque:

This torque is required to revolve the disc or rotate the disc.

It is obtained by the electromagnetic induction effect.

Braking torque:

It is required to rotate the disc at a constant speed.

It is obtained by using a permanent magnet placed inside the energy meter near the Aluminum disc.

Eddy currents have induced in the magnet due to the movement of the rotating disc through the magnetic field. This eddy current reacts with the flux and exerts a braking torque which opposes the motion of the disk. The speed of the disk can be controlled by changing flux.

Breaking torque of induction type single-phase energy meter is:

\({T_b} = k\frac{{{\phi ^2}}}{{{R_e}}}N \times R\)

K = constant

ϕ = flux

N = speed in rpm

R = radius of the disc

R_e = resistance in path of current (i.e. disc)

The braking torque of induction type single-phase energy meter is directly proportional to the square of the flux.

Registered mechanism:

It registers the no. of rotations or revolutions of the disc which is proportional to the energy consumed in kWh.

Meter constant = (No. of revolutions / kWh)

Points to remember:

Creeping:

Sometimes the disc of the energy meter makes the slow but continuous rotation at no load i.e. when the potential coil is excited but with no current flowing in the load called creeping error

This error may be caused due to overcompensation for friction, excessive supply voltage, vibrations, stray magnetic fields, etc

It can be reduced by making two opposite holes on the disc.

• The number of revolutions made by the energy meter per kilowatt-hour is known as the meter constant of an energy meter.
• Unit of meter constant is revolution per kilowatt-hour (rev/kWh)
• It is constant for a particular energy meter.

Meter constant = No. of revolution by meter/Energyconsumed 

Concept:

Energy consumed or measured value,

E = VI cosϕ× t × 10^-3 

Where, V = Voltage

I = current

cos ϕ = Power factor

Explanation:

Given that,

Voltage (V) = 230 V

Current (I) = 5 A

Time (t) = 5 hours

\({\rm{Energy}} = VI\cos \phi × t × {10^{- 3}}\:kWh = 230 × 5 × 5 × \cos \phi × {10^{ - 3}} = 5.75\:\cos \phi \:kWh\)

Number of revolutions = 1940

Meter constant = 400

\(Meter\;constant = \frac{{No\;of\;revolutions}}{{kWh}}\)

\(\Rightarrow 400 = \frac{{1940}}{{5.75\cos \phi }}\)

\(\Rightarrow \cos \phi = 0.84\)

Concept:

In an energy meter, Meter constant (K) is given as,

\(K=\frac{R}{E}\)

And, \(R\propto E\)

Where,

R is the number of revolution and E is the energy consumed in kWh

And, E = VItcos ϕ

Calculation:

Given that,

Voltage = 230 V

Current = 4 A

cos ϕ = 1

Energy consumed in 6 hours is given as,

E₁ = 230 × 4 × 6 × 1 = 5520 Wh

R₁ = 2208

From above concept,

\(R\propto E\)

\(\therefore R_1E_2=R_2E_1\)

Given, R₂ = 1240

Hence,

\(E_2=\frac{R_2E_1}{R_1}=\frac{1240\times5520}{2208}=3100\ Wh\)

Hence, the Energy consumed in 1240 revolution is 3.1 kWh.

Concept:

Meter constant, \(K=\frac{R}{E}\)

Where R = revolution

E = Energy in kWh

Given actual revolution (K_A) = 500

If meter takes 86 sec to make 50 revolutions for measuring a full load of kilowatt or 1 kW

Now, Energy = Power × time = 4.4 kW × 86 sec = 378 kWsec

To convert sec to hour we have to divided by 3600

Hence, E = 378/3600 kWh

Now, Measured revolution (K_M) = \(\frac{50}{378/3600}=476\)

Error = K_M - K_A = 476 - 500 = - 24

Now, % Error = \(\frac{-24}{500}\times 100=-4.8\%\)

Concept

The meter constant of a 1ϕ energy meter is given by:

\(Meter \space constant\space = {No. \space of \space revolutions \space in \space 1 \space hr\over No. \space of \space kW \space in \space 1 \space hr}\)

Calculation

Given, V = 230 volt

I = 20 A 

cos ϕ = 1

P = VI cos ϕ 

P = 230 × 20 × 1 = 4.6 kW

No. of revolutions in 1 hr = 2300/2 = 1150

\(Meter \space constant\space = {1150 \over 4.6}\)

Meter constant = 250 revolutions / kWh

Concept:

• The number of revolutions made by the energy meter per kilowatt-hour is known as the meter constant of an energy meter.
• Unit of meter constant is revolution per kilowatt-hour (rev/kWh)
• It is constant for a particular energy meter.

Meter constant (K) = No. of revolution by meter/Energy consumed (E)

Calculation:

Number of revolution = K × E = K × P × t

\(\therefore 5 = 1200 × P × \frac{{75}}{{3600}}\)

• Creeping in the induction type energy meter is the phenomenon in which the aluminum disc rotates continuously when only the voltage is supplied to the pressure coil and no current flows through the current coil.
• It is the kind of error in which the energy meter consumes a very small amount of energy even when no load is attached to the meter.
• The creeping increases the speed of the disc even under the light load condition which increases the meter reading. Vibration, stray magnetic field and the extra voltage across the potential coil are also responsible for the creeping.
• The creeping error occurs because of excessive friction. The main driving torque is absent at no load. Hence the disc rotates because of the additional torque provided by the compensating vane.

Additional Information

• In order to prevent this creeping on no-load two holes or slots are drilled in the disc on opposite sides of the spindle
• This causes sufficient distortion of the field; The result is that the disc tends to remain stationary when one of the holes comes under one of the shunt magnets

Formula Used:

Meter Constant (K) = \(\frac{R}{E}\)

Here, R is revolution per hour

E is energy in kWh

Application:

We have,

V = 200 volts

K = 200

If the current is 20 A at 0.8 pf lagging

Hence,

P = 200 × 20 × 0.8 = 3.2 kW

Energy in 1 hour = 3.2 kWh

From the above concept,

R = EK = 3.2 × 200 = 640 revolution/hour

Now, revolution in minutes = 10.67 rpm

• Phantom loading is the phenomena in which the appliances consume electricity even when they turn off.
• The phantom loading is used for examining the current rating ability of the energy meter.
• The actual loading arrangement will waste a lot of power.
• The phantom loading consumes very less power as compared to real loading, and because of this reason, it is used for testing the meter.

Important Points:

• In phantom loading, the pressure coil and the current coil are separately excited by the supply source.
• The pressure coil is energized from the small supply voltage, and the current energises the current coil at very small voltages.
• The pressure and current coil circuit have low impedance because of which highly rated current is passed through it.
• The total current supplied for the phantom loading is the sum of the pressure coil current which is supplied at normal voltage and the current of the current coil supply at low voltages.