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# Indicating Instruments and Theory of Ammeter and Voltmeter

Indicating Instruments and Theory of Ammeter and Voltmeter

Contents

Recall the following types of Instruments 1

Determine the Torques acting in a Deflection Type Instrument 2

Recall the Types of Damping in the Deflection Type Instruments 3

Recall Moving Systems 4

Describe the Types of Supports 5

Describe the Balancing Systems and Torque/Weight Ratio 6

Recall Control Systems 7

Describe the construction and working principle of PMMC Instruments 8

Derive Torque Equation of PMMC Instruments 9

Recall the Errors in PMMC Instruments 11

Recall the Range extension of DC Ammeters 12

Recall the Effect of temperature change in Ammeter 13

Describe Multi Range Ammeters 14

Recall the range extension of DC Voltmeters 15

Describe Multirange Voltmeters 16

Recall the sensitivity of Voltmeters 17

Recall the construction and working principle of Moving Iron Instruments 18

Derive Torque Equation of Moving Iron Instruments 19

Recall Electrodynamometer Type Instruments 22

Describe the working principle of Electrodynamometer Type Instruments 23

Derive Torque Equation of Electrodynamometer Type Instruments 24

Recall Electrothermic Instruments 26

Describe the Working Principle of Hot Wire Instruments 27

Recall the Working Principle of Thermocouple Type Instruments 28

Describe the Working Principle of Electrostatic Instruments 28

Derive the Torque Equation of Electrostatic Instruments 29

Describe the Working Principle of Induction Instruments 31

Derive the Torque Equation of Induction Instruments 32

# Recall the following types of Instruments

In electrical measurements and instrumentation (EMI), the following are some types of instruments:

1. Ammeters: Ammeters are instruments used to measure the current flowing in a circuit. They are typically connected in series with the circuit and have low resistance to minimise their impact on the circuit’s operation.
2. Voltmeters: Voltmeters are instruments used to measure the voltage difference between two points in a circuit. They are typically connected in parallel with the circuit and have high resistance to minimise the current flow through them.
3. Ohmmeters: Ohmmeters are instruments used to measure the resistance of a circuit element, such as a resistor or a wire. They are typically connected in series with the circuit element and use a known current or voltage source to determine the resistance.
4. Multimeters: Multimeters are versatile instruments that can measure several electrical quantities, including voltage, current, resistance, and sometimes frequency and capacitance. They can be analog or digital and can be used in a wide range of applications.
5. Oscilloscopes: Oscilloscopes are instruments used to display and analyse the waveform of an electrical signal. They can be used to measure voltage, current, and frequency and are often used in electronics and telecommunications.
6. Function generators: Function generators are instruments used to generate electrical signals of various shapes and frequencies, such as sine waves, square waves, or triangular waves. They are often used in testing and troubleshooting electronic circuits and devices.
7. Power metres: Power metres are instruments used to measure the power or energy consumed or produced by an electrical device or circuit. They can be used to measure AC or DC power and are often used in energy management and conservation applications.

There are many other types of instruments used in EMI, and new instruments are continually being developed to meet the changing needs of the field.

# Determine the Torques acting in a Deflection Type Instrument

A deflection-type instrument is a type of measuring instrument that works based on the principle of deflection of a pointer or a coil due to the flow of current or voltage. It is also known as a pointer type instrument or a moving-coil instrument.

To determine the torques acting in a deflection-type instrument, we need to understand the basic working principle of the instrument. The torque is the turning force that is applied to the instrument to cause the pointer or coil to deflect. There are mainly two types of torques that act on a deflection-type instrument:

1. Deflecting torque: The deflecting torque is the torque that is produced by the current or voltage flowing through the instrument. It causes the pointer or coil to deflect from its rest position. The deflecting torque is given by the equation:

Td = K * I

where Td is the deflecting torque, K is a constant that depends on the instrument’s construction, and I is the current or voltage flowing through the instrument.

1. Restoring torque: The restoring torque is the torque that acts in the opposite direction to the deflecting torque. It is produced by the spring or the magnetic field in the instrument. The restoring torque tries to bring the pointer or coil back to its rest position. The restoring torque is given by the equation:

Tr = K * θ

where Tr is the restoring torque, K is a constant that depends on the instrument’s construction, and θ is the deflection angle of the pointer or coil.

As an example, consider a moving-coil voltmeter. It consists of a coil that is suspended in a magnetic field. The coil is connected to a pointer that indicates the voltage on a scale. When a voltage is applied across the coil, a current flows through it, producing a deflecting torque. The deflecting torque causes the coil to move and the pointer to indicate the voltage on the scale. The spring attached to the coil provides the restoring torque that brings the coil and the pointer back to their rest position when the voltage is removed.

# Recall the Types of Damping in the Deflection Type Instruments

Deflection type instruments, such as moving coil or moving iron instruments, use a mechanical system to measure physical quantities. These instruments may experience oscillations or vibrations that can cause errors in the readings. Damping is used to reduce or eliminate these oscillations and improve the accuracy of the instrument. There are three types of damping used in deflection type instruments:

1. Air Damping: This type of damping uses the resistance of air to reduce the amplitude of oscillations. It is commonly used in low-frequency instruments.
2. Fluid Damping: This type of damping uses the resistance of a fluid, such as oil or glycerin, to reduce the amplitude of oscillations. It is commonly used in high-frequency instruments.
3. Eddy Current Damping: This type of damping uses the resistance of eddy currents induced in a conductor to reduce the amplitude of oscillations. It is commonly used in moving coil instruments.

The choice of damping method depends on the type of instrument and the frequency range of the measurement. Overdamping can cause sluggish response, while underdamping can cause overshoot and oscillations. The damping must be carefully tuned to ensure accurate and reliable measurements.

# Recall Moving Systems

In the field of instrumentation, a moving system is a mechanical or electromechanical system that is used to measure a physical quantity by converting it into a displacement or movement of a part of the system. There are several types of moving systems used in different types of instruments, including:

1. Moving Coil Systems: This type of system uses a coil of wire that is free to move in a magnetic field. When a current flows through the coil, it experiences a force that causes it to move. Moving coil systems are commonly used in instruments such as voltmeters and ammeters.
2. Moving Iron Systems: This type of system uses a piece of iron or steel that is free to move in a magnetic field. When a current flows through a coil of wire that is wound around the iron or steel, it creates a magnetic field that interacts with the magnetic field of the iron or steel, causing it to move. Moving iron systems are commonly used in instruments such as wattmeters and power factor metres.
3. Moving Magnet Systems: This type of system uses a magnet that is free to move in a magnetic field. When a current flows through a coil of wire that is fixed to the instrument, it creates a magnetic field that interacts with the magnetic field of the magnet, causing it to move. Moving magnet systems are commonly used in instruments such as galvanometers and magnetometers.
4. Moving Vane Systems: This type of system uses a vane that is free to move in a fluid or gas. When a physical quantity, such as velocity or pressure, acts on the vane, it causes it to move. Moving vane systems are commonly used in instruments such as anemometers and pressure gauges.
5. Moving Mirror Systems: This type of system uses a mirror that is free to move in response to a physical quantity, such as displacement or strain. The movement of the mirror is then used to measure the physical quantity. Moving mirror systems are commonly used in instruments such as interferometers and strain gauges.

The choice of moving system depends on the physical quantity being measured and the accuracy and precision required for the measurement.

# Describe the Types of Supports

In measuring instruments, supports refer to the structures or components that hold the instrument and provide stability and accuracy to the measurement. There are various types of supports used in different measuring instruments, including:

1. Fixed Supports: These types of supports are rigid and do not allow any movement or vibration of the instrument. They are commonly used in high-precision instruments such as atomic force microscopes or interferometers.
2. Gimbal Supports: These types of supports allow the instrument to rotate or pivot about multiple axes. They are commonly used in navigational instruments such as gyroscopes.
3. Spring Supports: These types of supports use springs or elastic materials to dampen vibrations and provide stability to the instrument. They are commonly used in instruments such as accelerometers and seismometers.
4. Magnetic Supports: These types of supports use magnetic fields to hold and stabilise the instrument. They are commonly used in instruments such as magnetometers.
5. Air Bearings: These types of supports use a cushion of air to hold and stabilise the instrument. They are commonly used in instruments such as coordinate measuring machines.

The choice of support depends on the type of instrument, the accuracy required, and the operating environment. The support must provide stability and accuracy while minimising any vibrations or external disturbances that could affect the measurement.

# Describe the Balancing Systems and Torque/Weight Ratio

Balancing systems are used in measuring instruments to counteract external forces that could affect the accuracy of the measurement. There are two types of balancing systems:

1. Gravity balance system – uses the force of gravity to balance the moving system.
2. Spring balance system – uses a spring to balance the moving system.

The torque/weight ratio is a measure of the sensitivity of a measuring instrument. It is defined as the ratio of the torque required to move the moving system to the weight of the moving system. A high torque/weight ratio indicates that the instrument is more sensitive to small changes in the quantity being measured.

# Recall Control Systems

Control systems are an essential part of electrical measurements and instrumentation (EMI). They are used to regulate, monitor, and optimise the performance of electrical devices, processes, and systems. Some common types of control systems used in EMI include:

1. Feedback control systems: Feedback control systems use sensors to measure the output of a system and provide feedback to a controller, which adjusts the input to maintain a desired output. They are widely used in industrial and automation applications to regulate parameters such as temperature, pressure, speed, or position.
2. Proportional-integral-derivative (PID) control systems: PID control systems use a combination of proportional, integral, and derivative control actions to adjust the input and maintain a desired output. They are commonly used in industrial processes to regulate parameters such as flow, level, or pressure.
3. Open-loop control systems: Open-loop control systems use a predetermined input signal to control the output of a system. They do not have feedback mechanisms and can be less accurate than feedback control systems, but they are often simpler and less expensive.
4. Closed-loop control systems: Closed-loop control systems use feedback mechanisms to adjust the input signal based on the output of a system. They are more accurate than open-loop control systems, but they can be more complex and require more sensors and controllers.
5. Adaptive control systems: Adaptive control systems use feedback mechanisms to adjust the control parameters based on changes in the system or the environment. They can adapt to changes in the system’s dynamics and can be more robust and flexible than other types of control systems.

Overall, control systems are essential tools for optimising the performance of electrical devices and processes, improving efficiency and productivity, and ensuring safety and reliability in a wide range of applications.

# Describe the construction and working principle of PMMC Instruments

A Permanent Magnet Moving Coil (PMMC) instrument is a type of DC ammeter that uses a permanent magnet to create a magnetic field and a moving coil to measure the current flowing through the circuit. The construction and working principle of PMMC instruments can be described as follows:

Construction:

The PMMC instrument consists of a permanent magnet that creates a constant magnetic field, a moving coil that is suspended in the magnetic field by a spring, and a pointer that is attached to the coil. The coil is wound on a rectangular or circular former, and the number of turns and the wire gauge are selected based on the range and accuracy required for the instrument.

Working Principle:

When a current flows through the coil, a magnetic field is produced around the coil that interacts with the magnetic field of the permanent magnet. The interaction between these two magnetic fields produces a torque on the coil that causes it to rotate. The amount of torque produced is proportional to the product of the current flowing through the coil and the magnetic field strength.

The coil is suspended in the magnetic field by a spring that provides a restoring torque that opposes the torque produced by the current. The spring is calibrated such that the deflection of the coil is directly proportional to the current flowing through the coil. The pointer attached to the coil indicates the deflection on a calibrated scale.

The PMMC instrument is designed to measure only DC currents since the torque produced by AC currents would average to zero due to the rapid fluctuations in the magnetic field direction.

• High accuracy and sensitivity
• Low power consumption
• Linear scale calibration
• No external power source required

• Limited range of measurement
• Cannot measure AC currents
• High cost and complexity compared to other types of metres.

PMMC instruments are commonly used in laboratory applications and in electronic devices where accurate DC current measurement is required.

# Derive Torque Equation of PMMC Instruments

A Permanent Magnet Moving Coil (PMMC) instrument is a type of DC ammeter that uses a permanent magnet to create a magnetic field and a moving coil to measure the current flowing through the circuit. The torque equation for a PMMC instrument can be derived as follows:

Let N be the number of turns in the coil, B be the magnetic field strength, I be the current flowing through the coil, l be the length of the coil, and A be the cross-sectional area of the coil.

The magnetic field strength B can be expressed as:

B = μ0 * μr * H

where μ0 is the permeability of free space, μr is the relative permeability of the magnet, and H is the magnetic field intensity.

The force on each turn of the coil is given by:

F = N * I * l * B

The torque τ on the coil is equal to the force F multiplied by the distance d from the axis of rotation to the point where the force is applied:

τ = F * d = N * I * l * B * d

Substituting the expression for B, we get:

τ = N * I * l * μ0 * μr * H * d

The magnetic field intensity H can be related to the current I and the coil dimensions l and A using Ampere’s law:

H = (N * I) / (l * A)

Substituting this expression for H in the torque equation, we get:

τ = N2 * I2 * A * d * μ0 * μr / l

This equation shows that the torque on the coil is proportional to the square of the current flowing through the coil and the cross-sectional area of the coil. The torque is also inversely proportional to the length of the coil and the distance from the axis of rotation to the point where the force is applied. This equation is used to design and calibrate PMMC instruments for accurate measurement of DC currents.

• High accuracy and precision
• Good linearity
• Low power consumption
• Low cost

• Limited range of measurement
• Sensitive to external magnetic fields
• Requires a stable power source
• Slow response time

Applications of PMMC Instruments:

• Measurement of DC current and voltage
• Measurement of low-frequency AC current and voltage
• Resistance measurement with the help of a shunt

# Recall the Errors in PMMC Instruments

PMMC (Permanent Magnet Moving Coil) instruments are sensitive measuring instruments that are commonly used to measure DC voltage and current. The following are some of the errors that can occur in PMMC instruments:

1. Frictional error: The movement of the PMMC instrument’s pointer can be impeded due to friction in the bearings or pivot of the instrument. This can result in a reading that is different from the actual value.
2. Alignment error: The pointer of the PMMC instrument may not be aligned properly with the scale. This can cause the reading to be incorrect, particularly when the pointer is at an angle to the scale.
3. Temperature error: PMMC instruments are sensitive to temperature changes, and the resistance of the coil can change with temperature. This can cause the reading to be different from the actual value.
4. Hysteresis error: Hysteresis is a phenomenon where the response of a system depends on its history. In PMMC instruments, hysteresis can cause the reading to be different when the value is increasing compared to when it is decreasing.
5. Stray magnetic field error: Stray magnetic fields from other sources can cause the pointer of the PMMC instrument to deflect, resulting in an incorrect reading.
7. Scale error: The scale of the PMMC instrument may not be accurate or may be misaligned, causing the reading to be different from the actual value.

Overall, PMMC instruments are precise measuring instruments, but they can be affected by various errors that can cause the reading to be different from the actual value. It is important to calibrate and maintain these instruments regularly to ensure accurate readings.

# Recall the Range extension of DC Ammeters

The range extension of DC ammeters can be achieved by using shunt resistors or a multi-range selector switch.

1. Shunt Resistors:

A shunt resistor is a low resistance resistor that is connected in parallel with the ammeter to divert a portion of the current around the metre. By selecting the appropriate value of shunt resistor, the ammeter can be converted into a multi-range instrument that can measure currents of different magnitudes. The shunt resistor must be carefully chosen to ensure that it does not significantly affect the current being measured and that it can handle the power dissipated in it.

1. Multi-Range Selector Switch:

A multi-range selector switch is a switch that allows the user to select different ranges of the ammeter by changing the internal connections of the metre. The switch connects different shunt resistors in parallel with the metre to change the current range. The switch may also change the sensitivity of the metre by changing the number of turns of the coil or by changing the strength of the magnetic field.

Both methods are commonly used in practice to extend the range of DC ammeters. However, the use of shunt resistors is preferred over a multi-range selector switch as it is more accurate and has a lower cost.

# Recall the Effect of temperature change in Ammeter

Temperature change can have an effect on the accuracy of ammeters, particularly those that use a moving coil and magnetic field to measure current. This is because temperature changes can cause changes in the resistance of the coil and the shunt resistor, which can lead to errors in current measurement.

When the temperature of the ammeter increases, the resistance of the coil and shunt resistor also increases. This causes the current through the ammeter to decrease, leading to an under-reading of the actual current. Conversely, when the temperature decreases, the resistance of the coil and shunt resistor decreases, causing the current to increase and leading to an over-reading of the actual current.

To minimise the effect of temperature on ammeter accuracy, the ammeter should be designed and calibrated to operate within a specific temperature range. Additionally, the materials used in the construction of the ammeter should be selected to minimise the temperature coefficient of resistance, which is a measure of how much the resistance of a material changes with temperature.

Some ammeters may also include temperature compensation circuits that adjust the reading of the metre based on the temperature to improve accuracy. However, these circuits may introduce additional complexity and cost to the design of the ammeter.

# Describe Multi Range Ammeters

Multi Range ammeters are instruments that can measure current over multiple ranges without the need for manual range switching. They use multiple shunt resistors of different values that can be switched in and out of the circuit automatically based on the current being measured. The ammeter automatically selects the appropriate range based on the current being measured, ensuring that the instrument is not overloaded and that accurate measurements are obtained. Multi Range ammeters are commonly used in applications where the current being measured can vary widely and rapidly, such as in industrial or laboratory settings.

# Recall the range extension of DC Voltmeters

DC voltmeters are used to measure the voltage of a DC circuit. The range of a DC voltmeter determines the maximum voltage that it can measure accurately. The range of a DC voltmeter can be extended using various techniques, including:

1. Multiplier resistance: A multiplier resistance can be connected in series with the metre to increase the range of the voltmeter. The multiplier resistance should be selected such that it does not draw too much current from the circuit and does not affect the accuracy of the measurement.
2. Voltmeter range extension using a shunt: A shunt resistor can be connected in parallel with the metre to extend the range of the voltmeter. The shunt resistor should be selected such that it does not draw too much current from the circuit and does not affect the accuracy of the measurement.
3. Amplifier extension: An amplifier can be used to extend the range of the voltmeter. The voltage signal from the circuit is fed into the amplifier, which amplifies the signal to a level that can be measured by the voltmeter.
4. Range changing switch: A range changing switch can be used to switch between different ranges of the voltmeter. The switch selects a different multiplier resistance or shunt resistor depending on the voltage range being measured.

Overall, the range of a DC voltmeter can be extended using various techniques, including adding a multiplier resistance or shunt resistor, using an amplifier, or using a range changing switch. It is important to select the appropriate technique based on the requirements of the measurement and the accuracy needed.

# Describe Multirange Voltmeters

Multirange voltmeters are electronic instruments used to measure voltage across multiple ranges. These voltmeters typically have multiple selector switches or buttons that allow the user to select the range they wish to measure. The switches or buttons adjust the internal circuitry of the voltmeter, changing the input impedance, sensitivity, and gain of the instrument.

Multirange voltmeters are useful because they allow the user to measure a wider range of voltages with a single instrument, rather than having to switch between multiple instruments with different ranges. They are commonly used in electronics and electrical engineering applications, where the voltage levels being measured can vary widely.

In addition to the selector switches or buttons, multirange voltmeters may also have other features, such as:

1. Automatic range selection: Some multirange voltmeters have a feature that automatically selects the appropriate range based on the input voltage.
2. Digital display: Many multirange voltmeters have a digital display that shows the measured voltage value, rather than a traditional analog metre.
3. Backlighting: Some multirange voltmeters have a backlighting feature that illuminates the display in low-light conditions.
4. Data logging: Some multirange voltmeters have a data logging feature that records the measured values over time, allowing the user to analyse the data later.

Overall, multirange voltmeters are versatile instruments that allow for more efficient and accurate voltage measurements across multiple ranges. They are commonly used in a variety of industries, including electronics, electrical engineering, and automotive.

# Recall the sensitivity of Voltmeters

The sensitivity of a voltmeter is a measure of how responsive the instrument is to changes in voltage. It is usually expressed as the amount of voltage required to produce a full-scale deflection on the metre, and is typically given in units of volts per division or millivolts per division.

For example, if a voltmeter has a sensitivity of 100 mV per division, this means that a change of 100 mV in the input voltage will produce a full-scale deflection on the metre. If the input voltage changes by a smaller amount, the deflection on the metre will be proportionally smaller.

The sensitivity of a voltmeter is an important characteristic because it determines the smallest voltage that the instrument can measure accurately. A more sensitive voltmeter will be able to measure smaller voltage changes, but may be more susceptible to noise and interference. A less sensitive voltmeter will be less susceptible to noise and interference, but may not be able to measure small changes in voltage.

In general, the sensitivity of a voltmeter should be chosen based on the requirements of the measurement. For example, if the voltage being measured is expected to be very small, a more sensitive voltmeter may be necessary. If the voltage is expected to be large, a less sensitive voltmeter may be sufficient.

The loading effect of a voltmeter refers to the phenomenon where the act of connecting the voltmeter to a circuit changes the voltage being measured. This occurs because the voltmeter has an input impedance, which is the resistance of the voltmeter’s input circuitry. When the voltmeter is connected to a circuit, it creates a parallel path for current to flow, which can alter the voltage being measured.

The loading effect is most pronounced in circuits with high source impedance and low output impedance. In such circuits, the voltmeter’s input impedance can cause a significant change in the measured voltage. This can result in inaccurate measurements and can also affect the behaviour of the circuit being measured.

To minimise the loading effect, voltmeters should have a high input impedance relative to the circuit being measured. This can be achieved by using a voltmeter with a high input resistance or by using a buffer amplifier to isolate the voltmeter from the circuit being measured. A buffer amplifier is a device that has a high input impedance and low output impedance, which allows it to isolate the voltmeter from the circuit being measured.

Overall, the loading effect of voltmeters is an important consideration when measuring voltage in electronic circuits. To minimise the effect, it is important to choose a voltmeter with a high input impedance and to use a buffer amplifier if necessary.

# Recall the construction and working principle of Moving Iron Instruments

Moving iron instruments are types of ammeters and voltmeters that use a movable piece of iron to measure current or voltage. The instruments consist of a fixed coil of wire, which is connected in series with the circuit being measured, and a movable iron piece, which is attached to a pointer that indicates the measurement on a calibrated scale.

The movable iron piece is attracted by the magnetic field created by the current flowing through the coil. The strength of the magnetic field is proportional to the current flowing through the coil, so the amount of deflection of the iron piece is also proportional to the current. Similarly, in a voltmeter, the voltage to be measured is applied across the fixed coil and the movable iron piece is deflected by the magnetic field produced by the coil, which is proportional to the applied voltage.

Moving iron instruments can be constructed in different ways, but typically consist of a fixed coil and a movable iron piece. The iron piece can be shaped in different ways, such as a flat vane, a spindle, or a pointer. The iron piece is typically mounted on a pivot that allows it to move freely in response to the magnetic field.

The working principle of moving iron instruments is based on the attraction of the iron piece to the magnetic field produced by the current flowing through the fixed coil. The amount of deflection of the iron piece is proportional to the current or voltage being measured, and this deflection is indicated on a calibrated scale. The instruments can be designed to measure AC or DC current or voltage, and can be used as ammeters or voltmeters in a wide range of applications.

# Derive Torque Equation of Moving Iron Instruments

The torque equation of a moving iron instrument relates the torque produced by the interaction between the magnetic field and the iron piece to the current flowing through the coil. The torque is proportional to the square of the current, and is given by:

T = kI2

Where T is the torque, I is the current flowing through the coil, and k is a constant that depends on the geometry of the instrument.

The torque produced by the magnetic field on the iron piece can be derived from the basic equation for the force on a current-carrying conductor in a magnetic field. The force on a conductor of length l carrying a current I in a magnetic field B is given by:

F = BIl

Where F is the force, B is the magnetic field, and l is the length of the conductor.

In a moving iron instrument, the iron piece is free to move in response to the force produced by the magnetic field. The torque produced by this force on the iron piece is given by:

T = Fl sin θ

Where θ is the angle between the force and the lever arm of the iron piece. In a moving iron instrument, the angle θ is typically 90 degrees, so the equation simplifies to:

T = F l

Substituting the expression for F from the equation above, we get:

T = B I l2

Finally, we can substitute the expression for the magnetic field B in terms of the current I, using the equation for the magnetic field produced by a coil of wire:

B = μ₀ I N / L

Where μ₀ is the permeability of free space, N is the number of turns in the coil, and L is the length of the coil.

Substituting the expression for B in the torque equation, we get:

T = μ₀ N2 I2 l / L

This equation relates the torque produced by the magnetic field on the iron piece to the current flowing through the coil. The constant k in the original equation can be expressed in terms of the geometric parameters of the instrument.

1. Moving iron instruments can be used for both AC and DC measurements.
2. They have a linear scale.
3. They are relatively cheap compared to other types of instruments.

1. The accuracy of moving iron instruments is relatively low.
2. They have a lower power factor compared to other types of instruments.
3. The frequency response of moving iron instruments is limited.

Errors in Moving Iron Instruments:

1. Hysteresis Error: This error occurs due to the residual magnetism left in the iron vane after previous use. The error is reduced by using a compensating winding.
2. Eddy Current Error: This error is caused by the eddy currents generated in the iron vane due to the changing magnetic field. The error is reduced by using laminated iron vane.
3. Temperature Error: This error occurs due to the change in the resistance of the coil and the spring with temperature. The error is reduced by using a temperature compensating device.

# Recall Electrodynamometer Type Instruments

Electrodynamometer type instruments are a type of metre that use the principle of electromagnetic forces to measure current or voltage. They consist of a fixed coil and a movable coil, which are arranged so that the magnetic fields produced by the coils interact to produce a torque on the movable coil. The torque is proportional to the product of the currents flowing through the coils, and is used to deflect a pointer on a calibrated scale.

There are two main types of electrodynamometer instruments: attraction type and repulsion type. In attraction type instruments, the fixed coil and the movable coil are attracted to each other, while in repulsion type instruments, the coils are arranged so that they repel each other.

The working principle of an electrodynamometer instrument is based on the interaction between the magnetic fields produced by the coils. When a current flows through the fixed coil, it produces a magnetic field that interacts with the magnetic field produced by the current flowing through the movable coil. This interaction produces a torque on the movable coil, which is proportional to the product of the currents.

The movable coil is suspended by a torsion spring, which provides a restoring torque that opposes the torque produced by the magnetic fields. The amount of deflection of the movable coil is proportional to the torque produced by the magnetic fields, and is indicated on a calibrated scale.

Electrodynamometer instruments are highly accurate and can be used to measure both AC and DC currents and voltages. They are commonly used in laboratory settings, as well as in high-precision industrial applications. However, they are more expensive and delicate than other types of metres, and require careful handling and calibration.

# Describe the working principle of Electrodynamometer Type Instruments

Electrodynamometer type instruments work on the principle of electromagnetic forces. They use a fixed coil and a movable coil, which are arranged in such a way that the magnetic fields produced by the coils interact to produce a torque on the movable coil.

When a current flows through the fixed coil, it produces a magnetic field that interacts with the magnetic field produced by the current flowing through the movable coil. This interaction produces a torque on the movable coil, which is proportional to the product of the currents.

The movable coil is suspended by a torsion spring, which provides a restoring torque that opposes the torque produced by the magnetic fields. The amount of deflection of the movable coil is proportional to the torque produced by the magnetic fields, and is indicated on a calibrated scale.

There are two main types of electrodynamometer instruments: attraction type and repulsion type. In attraction type instruments, the fixed coil and the movable coil are attracted to each other, while in repulsion type instruments, the coils are arranged so that they repel each other.

In attraction type instruments, the fixed coil is wound in such a way that the magnetic field produced by the current flowing through the coil is concentrated at the centre of the coil. The movable coil is mounted at the centre of the fixed coil, and is free to rotate about a vertical axis. When a current flows through the movable coil, it produces a magnetic field that interacts with the magnetic field produced by the fixed coil. This interaction produces a torque on the movable coil, which causes it to rotate until the restoring torque provided by the torsion spring balances the torque produced by the magnetic fields.

In repulsion type instruments, the fixed coil is wound in such a way that the magnetic field produced by the current flowing through the coil is concentrated at the ends of the coil. The movable coil is mounted so that its ends are close to the ends of the fixed coil, and is free to rotate about a horizontal axis.

# Derive Torque Equation of Electrodynamometer Type Instruments

The torque equation of electrodynamometer type instruments can be derived using the principle of interaction between magnetic fields and electric currents. Let I1 be the current flowing through the fixed coil and I2 be the current flowing through the movable coil. Let B be the magnetic flux density of the field in which the coils are placed. Let l1 and l2 be the lengths of the fixed and movable coils, respectively. Let N1 and N2 be the number of turns in the fixed and movable coils, respectively.

The magnetic field experienced by the movable coil due to the current flowing through the fixed coil is given by:

B1 = (μ0/4π) (2N1I1/l1)

Where μ0 is the permeability of free space.

Similarly, the magnetic field experienced by the movable coil due to the current flowing through itself is given by:

B2 = (μ0/4π) (2N2I2/l2)

The torque experienced by the movable coil is given by:

T = N2IAφ

Where A is the area of the coil, and φ is the angle between the magnetic field and the plane of the coil.

Substituting the expressions for B1 and B2 in the torque equation, we get:

T = (μ0/4π) (2N1I1/l1) (2N2I2/l2) A sin θ

Where θ is the angle between the two magnetic fields.

Simplifying the expression, we get:

T = KI1I2

Where K is a constant that depends on the geometry of the instrument.

1. High accuracy and precision: Electrodynamometer type instruments are known for their high accuracy and precision. They are used for precision measurements in laboratories and industrial applications.
2. Wide range of applications: Electrodynamometer type instruments can measure a wide range of electric parameters, including voltage, current, and power.
3. Robust construction: Electrodynamometer type instruments are constructed using sturdy materials and are designed to withstand harsh environments.
4. Low power consumption: Electrodynamometer type instruments consume very little power and can be used for long periods without the need for frequent calibration.

1. High cost: Electrodynamometer type instruments are relatively expensive compared to other types of measuring instruments.
2. Heavy and bulky: Electrodynamometer type instruments are often heavy and bulky, which makes them difficult to use in portable applications.
3. Limited frequency range: Electrodynamometer type instruments have a limited frequency range and are not suitable for measuring high-frequency signals.
4. Sensitivity to external magnetic fields: Electrodynamometer type instruments are sensitive to external magnetic fields, which can affect their accuracy and performance.

# Recall Electrothermic Instruments

Electrothermic Instruments is a term that can refer to a variety of instruments or devices that use heat generated by electricity to measure or perform a particular function. Some examples of electrothermic instruments include:

1. Thermocouples: These are devices that generate a small voltage when heated, which can be used to measure temperature.
2. Heating Elements: These are devices that generate heat when an electric current is passed through them. They are commonly used in ovens, heaters, and other appliances.
3. Electric Furnaces: These are devices that use electric heating elements to generate high temperatures, typically for industrial processes such as metalworking or ceramics production.
4. Induction Heating Systems: These use high-frequency electromagnetic fields to generate heat in metals or other conductive materials. They are commonly used in manufacturing and materials processing.
5. Electric Arc Furnaces: These use an electric arc to generate heat for melting metals or other materials. They are commonly used in steelmaking.

Overall, the term “Electrothermic Instruments” is quite broad and can refer to a wide range of devices that use electricity to generate heat for various purposes.

# Describe the Working Principle of Hot Wire Instruments

Hot wire instruments are a type of electrothermic instrument that is used to measure the velocity of fluid flow. The working principle of a hot wire instrument is based on the relationship between the temperature of a heated wire and the velocity of the fluid flowing over it.

A fine wire made of a high-resistance material such as platinum or tungsten is heated to a constant temperature using an electric current. When the fluid flows over the wire, it cools it down, and the temperature of the wire decreases. The amount of cooling depends on the velocity of the fluid. The change in temperature of the wire is measured using a Wheatstone bridge or another temperature-sensing element, and the velocity of the fluid is calculated using a calibration curve or equation.

Hot wire instruments are highly sensitive and can measure low velocities of fluids with high accuracy.

1. High sensitivity: Hot wire instruments are highly sensitive and can measure low velocities of fluids with high accuracy.
2. Wide range of applications: Hot wire instruments can be used to measure the velocity of fluids in a wide range of applications, including aerodynamics, fluid mechanics, and heat transfer.
3. Real-time measurement: Hot wire instruments provide real-time measurement of fluid velocity, which is useful in process control and monitoring.

1. Fragility: Hot wire instruments are fragile and can be easily damaged if mishandled or exposed to high temperatures.
2. Limited range: Hot wire instruments have a limited range of operation and are not suitable for measuring very high velocities of fluids.
3. High cost: Hot wire instruments are relatively expensive compared to other types of flow metres.

# Recall the Working Principle of Thermocouple Type Instruments

Thermocouple type instruments are a type of electrothermic instrument that is used to measure temperature. The working principle of a thermocouple is based on the Seebeck effect, which states that when two dissimilar metals are joined together, an electric potential is generated across the junction when there is a temperature difference between the two junctions.

A thermocouple is made by joining two different metals, such as copper and iron, at one end to form a measuring junction. The other ends of the two metals are connected to a voltmeter or a data acquisition system. When the measuring junction is exposed to a temperature difference, an electric potential is generated, which is proportional to the temperature difference. The voltmeter measures the electric potential and calculates the temperature of the measuring junction using a calibration curve or equation.

Thermocouple type instruments are widely used in industrial applications due to their high accuracy and ruggedness.

# Describe the Working Principle of Electrostatic Instruments

Electrostatic instruments are a class of measuring instruments that use the electrostatic force between two conductors to measure voltage, current, capacitance, and other electrical parameters. The working principle of electrostatic instruments is based on Coulomb’s law, which states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

One of the conductors is fixed, while the other conductor is free to move under the influence of the electrostatic force. The deflection of the moving conductor is proportional to the voltage or current being measured. The deflection can be measured using an optical or mechanical system, and the value of the voltage or current can be calculated using a calibration curve or equation.

The basic design of electrostatic instruments includes a fixed plate and a movable plate, with the movable plate suspended by a thin wire or fibre. The movable plate is deflected by the electrostatic force between the plates, and the deflection is measured to determine the value of the electrical parameter being measured.

# Derive the Torque Equation of Electrostatic Instruments

The electrostatic force between the two plates of an electrostatic instrument creates a torque that causes the movable plate to rotate. The torque is proportional to the product of the charges on the plates and the distance between them.

The torque equation for an electrostatic instrument can be derived as follows:

Let Q1 and Q2 be the charges on the fixed and movable plates, respectively. Let d be the distance between the plates, and let θ be the angle of deflection of the movable plate.

The force F between the plates is given by Coulomb’s law:

F = k(Q1Q2)/d2

where k is the Coulomb constant.

The torque T on the movable plate is given by:

T = Fd/2 * sinθ

Substituting the value of F, we get:

T = (kQ1Q2d)/2 * sinθ

The torque is proportional to the product of the charges on the plates, the distance between the plates, and the sine of the deflection angle.

1. High accuracy: Electrostatic instruments are known for their high accuracy and precision, making them ideal for laboratory and industrial applications.
2. Wide range of applications: Electrostatic instruments can measure a wide range of electrical parameters, including voltage, current, capacitance, and charge.
3. Low power consumption: Electrostatic instruments consume very little power and can be used for long periods without the need for frequent calibration.
4. Rugged construction: Electrostatic instruments are constructed using sturdy materials and are designed to withstand harsh environments.

1. High sensitivity to temperature and humidity: Electrostatic instruments are highly sensitive to temperature and humidity, which can affect their accuracy and performance.
2. Limited dynamic range: Electrostatic instruments have a limited dynamic range and are not suitable for measuring very high or low values of electrical parameters.
3. Fragility: Electrostatic instruments are fragile and can be easily damaged if mishandled or dropped.
4. High cost: Electrostatic instruments are relatively expensive compared to other types of measuring instruments.

# Describe the Working Principle of Induction Instruments

Induction instruments are a class of measuring instruments that use electromagnetic induction to measure electrical parameters. The working principle of induction instruments is based on Faraday’s law of electromagnetic induction, which states that a change in magnetic flux through a conductor induces an electromotive force (EMF) in the conductor.

Induction instruments typically consist of a movable conductor, such as an aluminium disc, placed in a magnetic field produced by a fixed coil. When a voltage or current flows through the conductor, it interacts with the magnetic field and produces a torque on the disc, causing it to rotate. The rotation of the disc is proportional to the electrical parameter being measured.

The induced EMF in the conductor is proportional to the rate of change of magnetic flux through the conductor. This EMF produces a current in the conductor, which interacts with the magnetic field and produces a force on the conductor.

# Derive the Torque Equation of Induction Instruments

The torque equation for an induction instrument can be derived as follows:

Let B be the magnetic field, φ be the magnetic flux through the conductor, I be the current flowing through the conductor, and R be the resistance of the conductor. Let r be the radius of the conductor, and N be the number of turns in the fixed coil.

The EMF induced in the conductor is given by Faraday’s law:

EMF = -dφ/dt

The current flowing through the conductor is given by Ohm’s law:

I = EMF / R

The force on the conductor is given by the Lorentz force law:

F = BIL

The torque on the conductor is given by: T = Fr = BILr

Substituting the value of I, we get:T = (B2N2πr4)/(2R) * dφ/dt

The torque is proportional to the square of the magnetic field, the square of the number of turns in the coil, the radius of the conductor, and the rate of change of magnetic flux through the conductor.

1. High accuracy: Induction instruments are known for their high accuracy and precision, making them ideal for laboratory and industrial applications.
2. Wide range of applications: Induction instruments can measure a wide range of electrical parameters, including voltage, current, power, and energy.
3. Non-contact measurement: Induction instruments do not require physical contact with the conductor being measured, which makes them safe to use and minimises the risk of damage to the conductor.
4. Rugged construction: Induction instruments are constructed using sturdy materials and are designed to withstand harsh environments.

1. Limited frequency range: Induction instruments have a limited frequency range and are not suitable for measuring high-frequency signals.
2. Non-linear response: Induction instruments have a non-linear response to changes in the electrical parameter being measured, which can make them difficult to calibrate.
3. High cost: Induction instruments are relatively expensive compared to other types of measuring instruments.
4. Limited dynamic range: Induction instruments have a limited dynamic range and are not suitable for measuring very high or low values of electrical parameters.