# Measurement of Parameters

### Contents

**Define the term Energy**2**Describe the construction of Induction Type Energy Meter**3**Recall the principle of operation of Induction Type Energy Meter**4**Draw the Phasor Diagram of Induction Type Energy Meter**4**Recall the deflection Torque in the Induction Type Energy Meter**5**Recall the Breaking Torque in the Induction Type Energy Meter**6**Recall the following in Induction Type Energy Meter: Energy Meter Constant, Creeping, and Phantom Loading**7**Recall the need of Wattmeter**8**Recall Electrodynamometer Type Wattmeter**9**Derive the Torque Equation of EDM Type Wattmeter**10**Recall Errors in EDM Type Wattmeter**11**Recall the methods used for Power Measurement in 3-φ Circuits**12**Recall the Single Wattmeter Method for Power Measurement in 3-φ Circuits**12**Recall the Three Wattmeter Method for the Power Measurement in 3-φ Circuits**13**Recall the Two Wattmeter Methods for the Power Measurement in 3-φ Circuits: Star-Connected Method and Unbalanced Method**14**Define and classify Resistance**15**Recall the factors affecting the value of Resistance**16**Recall the methods of measuring Resistances**17**Recall the following methods of measuring Medium Resistances: V-I Method**18**Recall the following methods of measuring Medium Resistances: Substitution Method, Wheatstone’s Bridge Method, and Ohmmeter Method**19**Recall Multimeters**19**Recall the following methods to measure Low Resistances: Kelvin’s Double Bridge Method and Potentiometer Method**20**Recall the following methods to measure High Resistances: Loss of Charge Method, Megger, Direct Deflection Method, and Megohm Bridge Method**20

Define the term Energy

Energy is a fundamental concept in physics that refers to the ability of a system to do work. It is a scalar quantity, which means it has magnitude but no direction. Energy can exist in various forms, such as kinetic energy (energy of motion), potential energy (energy stored in an object due to its position or configuration), thermal energy (energy associated with the temperature of a system), electrical energy (energy carried by an electric current), and many others.

According to the law of conservation of energy, energy cannot be created or destroyed, but can only be converted from one form to another. This means that the total amount of energy in a closed system remains constant over time, although it can be transformed from one form to another.

Energy is a crucial concept in many fields, including physics, engineering, and environmental science. It plays a central role in understanding the behaviour of physical systems, and is essential for many technological applications, from power generation and transportation to communications and computing.

Describe the construction of Induction Type Energy Meter

An induction-type energy metre, also known as an induction disk metre, is a type of electric metre that measures the amount of electrical energy consumed by a customer over a given period of time. It works on the principle of electromagnetic induction, where a magnetic field is created by an alternating current flowing through a conductor, inducing a current in a nearby conductor.

The basic construction of an induction-type energy metre consists of the following components:

- An external enclosure, which houses the metre mechanism and protects it from environmental factors.
- A metal disk or rotor, which rotates as a result of the magnetic field created by the current flowing through the metre.
- An electromagnet, which produces a magnetic field that interacts with the rotating disk.
- A set of coils, which are placed around the disk and are connected to the electromagnet. As the disk rotates, it induces a current in the coils, which is proportional to the amount of energy being consumed.
- A register, which displays the amount of energy consumed by the customer over a given period of time. The register is typically a set of dials or a digital display.

When current flows through the metre, the magnetic field created by the electromagnet interacts with the metal disk, causing it to rotate. As the disk rotates, it induces a current in the coils, which is proportional to the amount of energy being consumed. This current is then processed by the metre mechanism, which calculates the amount of energy consumed and displays it on the register.

Overall, induction-type energy metres are simple and reliable devices that have been used for many years to measure electrical energy consumption in homes and businesses. While newer digital metres have become increasingly popular, induction-type metres are still used in many parts of the world due to their low cost and durability.

Recall the principle of operation of Induction Type Energy Meter

The principle of operation of an Induction Type Energy Meter is based on the electromagnetic induction phenomenon. The basic working principle can be summarised as follows:

- The current to be measured flows through a pair of coils, called the current coils, which are wound on a laminated core.
- The magnetic field produced by the current in the current coils interacts with the magnetic field of a permanent magnet or a shunt magnet, which is fixed to the metre’s housing.
- The interaction of these magnetic fields creates a torque on an aluminium or copper disc, called the rotor or the disc.
- The rotor rotates at a speed proportional to the power or energy consumed by the load.
- A pair of voltage coils, which are also wound on the same core, are used to generate a voltage proportional to the speed of the rotor.
- The voltage generated in the voltage coils is proportional to the rate of change of flux linked with them. As the speed of the rotor increases, the rate of change of flux linked with the voltage coils increases, which results in an increase in the voltage generated in the voltage coils.
- The voltage generated in the voltage coils is rectified and used to drive the register or the dial of the metre, which indicates the amount of electrical energy consumed.

Overall, the operation of an induction-type energy metre is based on the measurement of the torque produced by the interaction of magnetic fields, which is proportional to the electrical energy consumed.

Draw the Phasor Diagram of Induction Type Energy Meter

In an induction type energy meter, the phasor diagram represents the relationship between the voltages and currents in the meter. It helps illustrate the principle of operation and how energy consumption is measured.

The phasor diagram of an induction type energy meter consists of two main components: the voltage phasor and the current phasor.

- Voltage Phasor: The voltage phasor represents the supply voltage applied across the load. It is typically shown as a phasor rotating in a counter-clockwise direction. The angle of the voltage phasor represents the phase angle difference between the supply voltage and the current.
- Current Phasor: The current phasor represents the load current flowing through the energy meter. It is typically shown as a lagging phasor with respect to the voltage phasor. The magnitude of the current phasor represents the load current magnitude, and the angle represents the phase angle difference between the voltage and current.

The angle between the voltage and current phasors represents the phase angle difference, which is used to calculate the power factor of the load. The power factor is a measure of how effectively the load utilizes the supplied power.

The induction type energy meter operates based on the principle of electromagnetic induction. The rotating magnetic field produced by the voltage and current phasors interacts with the aluminum disc inside the meter, causing it to rotate. The rotation of the disc is proportional to the energy consumed by the load.

Please note that the phasor diagram of an induction type energy meter may vary depending on the specific design and configuration of the meter. It is always recommended to refer to the manufacturer’s documentation or specific meter specifications for an accurate and detailed phasor diagram.

Recall the deflection Torque in the Induction Type Energy Meter

In an induction type energy metre, the deflection torque is the torque produced due to the interaction between the magnetic field produced by the current being measured and the magnetic field produced by the fixed coil. This torque causes the aluminium disc to rotate, which is proportional to the energy consumed. The deflection torque is given by the expression:

T_{def} = K x iB x dB x mSinθ

where T_{def} is the deflection torque, K_{i} is the metre constant, B_{d} is the flux density produced by the current being measured, B_{m} is the flux density produced by the fixed coil, and θ is the angle between the two magnetic fields.

Recall the Breaking Torque in the Induction Type Energy Meter

In an induction type energy metre, the breaking torque is the torque produced due to the interaction between the magnetic field produced by the aluminium disc and the magnetic field produced by the shading coil. The shading coil is located on one side of the disc and is used to create a phase difference between the magnetic field produced by the disc and the magnetic field produced by the electromagnets. This phase difference creates a net torque that opposes the motion of the disc, which is proportional to the energy consumed. The breaking torque is given by the expression:

T_{brk} = K x mB x sB x mSin(θ – δ)

where T_{brk} is the breaking torque, K_{m} is the metre constant, B_{s} is the flux density produced by the shading coil, δ is the angle between the magnetic field produced by the shading coil and the magnetic field produced by the fixed coil, and θ is the angle between the magnetic fields produced by the fixed coil and the electromagnets.

Recall the following in Induction Type Energy Meter: Energy Meter Constant, Creeping, and Phantom Loading

In an Induction Type Energy Meter, the following concepts are important:

- Energy Meter Constant: The Energy Meter Constant, also known as the Multiplication Factor or Kh, is a constant that represents the number of watt-hours or kilowatt-hours that the meter will measure per revolution of the disc. This constant is determined by the physical properties of the meter and is usually printed on the meter face or data sheet. For example, if the Energy Meter Constant is 1000, then the meter will measure 1000 watt-hours or 1 kilowatt-hour for every revolution of the disc.
- Creeping: Creeping is an unwanted phenomenon in which the disc of the meter rotates even when there is no load connected to the meter. This can result in an inaccurate measurement of energy consumption. Creeping can be caused by magnetic fields from nearby electrical equipment, vibration, or incorrect meter installation. To prevent creeping, some meters are equipped with a creep adjustment mechanism that allows the meter to be calibrated to eliminate the effect of any residual magnetic fields.
- Phantom Loading: Phantom Loading is a deliberate attempt to cheat the energy meter by connecting a small load in parallel with the main load. This small load, which is often a capacitor, causes the voltage to increase slightly, which in turn causes the meter to measure more energy than is actually being consumed. To prevent phantom loading, some meters are equipped with an anti-tamper mechanism that detects and alerts the user if any unauthorized changes are made to the meter wiring.

Recall the need of Wattmeter

A wattmeter is an electrical measuring instrument used to measure the electrical power in a circuit. It is specifically designed to measure both the active power (real power) and reactive power in AC circuits.

The need for a wattmeter arises from the following reasons:

- Power Measurement: The primary need for a wattmeter is to accurately measure the power consumed or delivered by an electrical load. It provides information about the amount of power being utilized in a circuit, allowing for efficient energy management and billing.
- Power Monitoring and Analysis: Wattmeters are used to monitor and analyze power consumption in various applications. By measuring and analyzing power parameters such as active power, reactive power, power factor, and harmonic content, wattmeters provide valuable insights into the performance and efficiency of electrical systems.
- Load Balancing: In situations where multiple loads are connected to a single power supply, a wattmeter is used to measure the power drawn by each load. This information helps in load balancing, ensuring that the loads are distributed evenly to prevent overloading or underutilization of power sources.
- Power Quality Assessment: Wattmeters play a crucial role in assessing power quality issues such as voltage fluctuations, harmonics, and power factor problems. By measuring and analyzing power parameters, wattmeters help identify and diagnose power quality issues, enabling corrective measures to be taken to maintain a stable and reliable electrical supply.
- Energy Efficiency: Wattmeters are essential for evaluating the energy efficiency of electrical devices and systems. By measuring the power consumed by different components or appliances, wattmeters provide information to optimize energy consumption, identify energy-saving opportunities, and promote energy-efficient practices.
- Electrical Safety: Wattmeters are also used for electrical safety purposes. By measuring the power in a circuit, they help ensure that the power being supplied to electrical devices or systems is within the safe operating limits, preventing overloading and potential hazards.

Overall, the need for a wattmeter arises from its ability to accurately measure and monitor power in electrical circuits, enabling efficient energy management, power quality assessment, load balancing, and promoting electrical safety and energy efficiency.

Recall Electrodynamometer Type Wattmeter

An Electrodynamometer Type Wattmeter is a type of instrument used to measure the electrical power in a circuit. It works on the principle of electromagnetic induction and is commonly used for accurate power measurements in high voltage and high current circuits. The basic construction and working principle of an Electrodynamometer Type Wattmeter can be described as follows:

Construction:

- A fixed coil (also known as the current coil) is connected in series with the circuit being measured and carries the current to be measured.
- A movable coil (also known as the potential coil) is suspended within the magnetic field of the fixed coil and is connected across the load to measure the voltage.
- Both coils are wound on a common iron core.

Working Principle:

- The current flowing through the fixed coil generates a magnetic field around it.
- The movable coil is placed within the magnetic field of the fixed coil and experiences a torque that is proportional to the product of the current and the voltage.
- The movable coil is connected to a pointer or a digital display that indicates the power being measured.

When an alternating current flows through the fixed coil, it produces a magnetic field that interacts with the magnetic field produced by the movable coil. This interaction produces a torque on the movable coil that causes it to rotate, with the amount of rotation being proportional to the product of the current and the voltage. This rotation is proportional to the power being measured, and it is indicated on a calibrated dial or display.

Overall, Electrodynamometer Type Wattmeters are accurate and reliable instruments that can be used to measure both AC and DC power. They are commonly used in industrial and laboratory settings for power measurement and calibration purposes.

Derive the Torque Equation of EDM Type Wattmeter

The torque equation of an Electrodynamometer (EDM) Type Wattmeter can be derived as follows:

Let I and V be the rms values of the current and voltage flowing through the fixed and movable coils, respectively. Let θ be the angle between the current and voltage, and let K be the constant of proportionality that relates the torque to the product of the current and voltage.

The magnetic field produced by the fixed coil is given by:

B = K1I

where K1 is the constant of proportionality that relates the magnetic field to the current.

The magnetic field produced by the movable coil is given by:

B = K2V sinθ

where K2 is the constant of proportionality that relates the magnetic field to the voltage.

The torque on the movable coil is proportional to the product of the magnetic fields produced by the fixed and movable coils, i.e.,

T ∝ B_{fixed} × B_{movable}

Substituting the values of B_{fixed} and B_{movable}, we get:

T ∝ K1IK2V sinθ

Therefore, the torque equation for the EDM Type Wattmeter is given by:

T = KIKVsinθ

where K is the constant of proportionality that relates the torque to the product of the current and voltage.

The torque equation shows that the torque on the movable coil is proportional to the product of the current, voltage, and the sine of the phase angle between them. This torque causes the movable coil to rotate, and the angle of rotation is proportional to the power being measured.

Recall Errors in EDM Type Wattmeter

The errors in the electrodynamometer type wattmeter are due to various factors such as stray magnetic fields, friction in the bearings, temperature variations, and the resistance of the coils. Some of the common errors are:

- Temperature error: The resistance of the coils changes with temperature, which can lead to errors in measurement.
- Stray magnetic field error: The presence of external magnetic fields can affect the accuracy of the metre.
- Friction error: The friction in the bearings can cause the metre to read high or low.
- Power factor error: The metre is calibrated for a particular power factor, and if the power factor of the load is different, it can cause errors in measurement.
- Phase angle error: The phase angle between the voltage and current can affect the accuracy of the metre.

Recall the methods used for Power Measurement in 3-φ Circuits

The methods used for power measurement in 3-φ circuits are:

- Two wattmeter method: In this method, two wattmeters are used to measure the total power in a 3-φ circuit. The wattmeters are connected in such a way that the readings of the two wattmeters give the total power in the circuit.
- Three wattmeter method: In this method, three wattmeters are used to measure the total power in a 3-φ circuit. The three wattmeters are connected in such a way that the readings of the three wattmeters give the total power in the circuit.
- Single wattmeter method: In this method, only one wattmeter is used to measure the total power in a 3-φ circuit. The wattmeter is connected in such a way that it can measure the total power in the circuit.

Recall the Single Wattmeter Method for Power Measurement in 3-φ Circuits

The single-wattmeter method for power measurement in 3-φ circuits is based on the principle of superposition. In this method, the wattmeter is connected in any two phases of the 3-φ circuit, and the current in the third phase is determined by the principle of superposition.

The power in the circuit can be calculated using the formula:

P = V_{ph} * I_{ph} * cos(Φ)

Where:

P is the total power in the circuit

V_{ph} is the phase voltage

I_{ph} is the phase current

Φ is the phase angle between voltage and current

Using the principle of superposition, the total current in the circuit can be calculated as: I_{total} = I_{1} + I_{2} + I_{3}

Where: I_{1}, I_{2}, and I_{3} are the currents in the three phases

By substituting I_{total} in the formula for power, we get: P = V_{ph} * (I_{1} + I_{2} + I_{3}) * cos(Φ)

The current in the third phase can be determined by measuring the voltage between the third phase and the phase in which the wattmeter is connected, and dividing it by the impedance between the two phases.

Recall the Three Wattmeter Method for the Power Measurement in 3-φ Circuits

The Three Wattmeter Method is a technique used for the measurement of power in a 3-phase electrical circuit. This method is also known as the “Two Wattmeter Method,” and it involves the use of three wattmeters, each connected between one of the phases and the neutral wire or ground.

The basic principle behind the Three Wattmeter Method is that the total power consumed by the load in a 3-phase circuit can be calculated by measuring the power in each phase and adding them together. The three wattmeters measure the power in each phase, and their readings are used to determine the total power.

To use the Three Wattmeter Method, the following steps are typically followed:

- Connect each wattmeter between one of the phases and the neutral wire or ground.
- Measure the power in each phase using the wattmeters.
- Calculate the total power consumed by the load using the following formula:

Total Power = W1 + W2 + W3

where W1, W2, and W3 are the readings of the three wattmeters.

- Calculate the power factor of the load using the readings of the wattmeters and the voltage across the phases.

The Three Wattmeter Method is commonly used in industrial applications where power measurements are required for 3-phase circuits. This method provides accurate results and is relatively easy to implement. However, it requires the use of three wattmeters, which can be expensive and may not be practical in some situations.

Recall the Two Wattmeter Methods for the Power Measurement in 3-φ Circuits: Star-Connected Method and Unbalanced Method

The Two Wattmeter Methods for Power Measurement in 3-φ Circuits are as follows:

- Star-Connected Method:

This method is used to measure the power in a balanced three-phase system with a star (Y) connected load. Two wattmeters are connected in the system, with one wattmeter measuring the power in one of the three phases and the other wattmeter measuring the total power in the other two phases. The sum of the two readings gives the total power consumed in the three-phase system.

- Unbalanced Method:

This method is used to measure the power in an unbalanced three-phase system. Two wattmeters are connected in the system, with one wattmeter measuring the power in the most highly loaded phase and the other wattmeter measuring the total power in the other two phases. The sum of the two readings gives the total power consumed in the three-phase system. This method is less accurate than the other two methods but is more cost-effective and simpler to implement.

Define and classify Resistance

Resistance is a property of a material that resists the flow of electric current through it. It is defined as the ratio of voltage to current in a circuit element. Resistance is measured in ohms and is denoted by the symbol Ω. Resistance can be classified into two types:

- Fixed Resistance: These resistances have a fixed value and cannot be changed. Examples of fixed resistances include carbon composition resistors, wire-wound resistors, and metal film resistors.
- Variable Resistance: These resistances have a variable value and can be changed. Examples of variable resistances include potentiometers and rheostats.

Recall the factors affecting the value of Resistance

The value of resistance is affected by several factors, including:

- Length of the material: The longer the material, the higher its resistance.
- Cross-sectional area of the material: The smaller the cross-sectional area, the higher the resistance.
- Temperature: The resistance of a material increases with an increase in temperature.
- Type of material: Different materials have different resistances.
- Presence of impurities: The presence of impurities in the material increases its resistance.
- Strain or stress: The resistance of a material can change if it is subjected to strain or stress.

Recall the methods of measuring Resistances

There are several methods of measuring resistance, including:

- Ohmmeter Method: An ohmmeter is an instrument that measures resistance. It works on the principle that when a voltage is applied across a resistance, a current flows through it. The ohmmeter measures this current and displays the resistance value.
- Wheatstone Bridge Method: The Wheatstone bridge is a circuit that can be used to measure resistance accurately. It consists of four resistors, arranged in a bridge configuration. By adjusting the values of the resistors, the resistance to be measured can be balanced with the known resistance.
- Potentiometer Method: A potentiometer is a three-terminal device that can be used to measure resistance. It works on the principle that the voltage across a resistance is proportional to the current flowing through it. By adjusting the position of a slider on the potentiometer, the resistance to be measured can be balanced with a known resistance.
- Digital Multimeter Method: A digital multimeter is an instrument that can measure various electrical quantities, including resistance. It works on the principle of converting the measured quantity into a voltage or current, which is then measured and displayed on the metre.

Recall the following methods of measuring Medium Resistances: V-I Method

The V-I (voltage-current) method is a common technique for measuring medium resistances. This method involves passing a known current through the resistor and measuring the voltage across it. The resistance can then be calculated using Ohm’s law, which states that the resistance is equal to the voltage divided by the current:

R = V / I

To use the V-I method for measuring resistance, the following steps are typically followed:

- Apply a known current I to the resistor.
- Measure the voltage V across the resistor using a voltmeter.
- Calculate the resistance R using Ohm’s law:

R = V / I

This method is suitable for measuring resistances in the range of a few ohms to several hundred ohms. It is commonly used in applications such as the measurement of resistance in electrical circuits, the testing of electronic components, and the characterization of materials.

One limitation of the V-I method is that it can be affected by errors due to variations in the current or voltage source used. Therefore, care must be taken to ensure that the current and voltage measurements are accurate and that the resistance is measured under stable conditions.

Recall the following methods of measuring Medium Resistances: Substitution Method, Wheatstone’s Bridge Method, and Ohmmeter Method

Substitution Method: In this method, a known resistance is substituted for the unknown resistance, and the current and voltage values are measured. The unknown resistance can be calculated from the measured values using Ohm’s law.

Wheatstone’s Bridge Method: This method is based on the principle of null deflection. A Wheatstone’s bridge circuit is used to balance the unknown resistance with a known resistance. The bridge is balanced when the current through the galvanometer is zero, indicating that the unknown resistance is equal to the known resistance.

Ohmmeter Method: This method is based on the principle of current measurement. An ohmmeter is used to measure the current flowing through the unknown resistance. The resistance can be calculated from the measured current and the voltage applied to the circuit. The ohmmeter circuit can be designed using different techniques, such as moving coil, moving iron, or digital methods.

Recall Multimeters

Multimeters are versatile electrical measuring instruments used to measure several electrical parameters such as voltage, current, resistance, and continuity. Multimeters can be analog or digital and can be used for different types of circuits such as DC, AC, or both. Some multimeters also have advanced features like temperature measurement, frequency measurement, and data logging. Multimeters come with different ranges and accuracies, and the user can select the appropriate range based on the magnitude of the electrical parameter being measured.

Recall the following methods to measure Low Resistances: Kelvin’s Double Bridge Method and Potentiometer Method

Kelvin’s Double Bridge Method and Potentiometer Method are two common methods used to measure low resistances.

In Kelvin’s Double Bridge Method, a four-arm bridge circuit is used where one pair of arms is made up of a standard resistance and the other pair of arms is made up of the unknown resistance to be measured. A voltmeter is connected across one diagonal of the bridge circuit, and a battery and a galvanometer are connected across the other diagonal. The bridge is balanced by adjusting the standard resistance until the galvanometer shows zero deflection. The value of the unknown resistance can be calculated from the known values of the other resistances in the circuit.

In the Potentiometer Method, a potentiometer is used to measure the voltage across the unknown resistance. The potentiometer is a resistive voltage divider circuit that allows the voltage across the unknown resistance to be measured directly. The resistance of the potentiometer is adjusted until the voltage across the unknown resistance is zero, indicating that the potentiometer is balanced. The value of the unknown resistance can be calculated from the known values of the resistances in the potentiometer circuit.

Recall the following methods to measure High Resistances: Loss of Charge Method, Megger, Direct Deflection Method, and Megohm Bridge Method

The four methods to measure high resistances are:

- Loss of Charge Method: This method involves charging the capacitor to a known voltage and then connecting it to the resistor under test. The time taken for the voltage to decay to a certain level is then measured, and the resistance is calculated using the equation R = t/C, where R is the resistance, t is the time taken for the voltage to decay, and C is the capacitance of the capacitor.
- Megger: A Megger is a specialised instrument designed for measuring high resistances. It works by applying a high voltage to the resistor under test and measuring the resulting current. The resistance is then calculated using Ohm’s Law: R = V/I, where R is the resistance, V is the voltage applied, and I is the resulting current.
- Direct Deflection Method: This method involves using a sensitive galvanometer to measure the current flowing through the resistor under test. The galvanometer is connected in series with a known resistance, and the current is measured with and without the resistor under test. The resistance is then calculated using Ohm’s Law: R = (V1-V2)/I, where R is the resistance, V1 is the voltage with the resistor under test, V2 is the voltage without the resistor under test, and I is the current.
- Megohm Bridge Method: This method involves using a specialised instrument called a megohm bridge to measure high resistances.