PMMC Instrument – Construction, Working Principle, Torque Equation

The PMMC (Permanent Magnet Moving Coil) instrument is a widely used instrument in the field of electrical engineering for measuring current and voltage in direct current (DC) circuits. Its popularity is due to its accuracy, reliability, and ease of use.

Construction of PMMC Instruments

The construction of a PMMC instrument involves several key components, each playing a crucial role in its functionality:

Permanent Magnet:

At the core of the PMMC instrument lies a permanent magnet. It is usually made of strong magnetic materials like Alnico (an alloy of aluminum, nickel, and cobalt) or rare-earth magnets. The permanent magnet generates a steady magnetic field within the instrument.

Moving Coil:

A delicate coil, typically consisting of numerous turns of fine wire, is mounted on a pivoted spindle. This coil is the heart of the instrument and is responsible for the measurement of electrical quantities. The coil is designed to be lightweight and free to rotate.

Damping Mechanism:

To prevent the pointer from oscillating excessively and to ensure smooth and accurate readings, a damping mechanism is incorporated. This usually involves a vane attached to the coil, moving through a magnetic field or air, which offers resistance to the coil’s movement.

Pointer and Scale:

A pointer is fixed to the coil spindle, and its movement is synchronized with the coil. As the coil experiences the mechanical force due to the interaction with the magnetic field, the pointer moves over a calibrated scale, displaying the measurement in appropriate units.

Control Springs:

Precision control springs are utilized to provide the necessary torque to the coil, allowing it to return to its original position when the current through the coil is zero. These springs ensure that the instrument is not affected by external vibrations or disturbances.

Housing:

The entire assembly of the PMMC instrument is enclosed within a robust housing made of non-magnetic material. This housing not only protects the delicate components from external damage but also shields the magnetic field from external influences.

Principle of operation of PMMC Instrument

The fundamental principle governing PMMC instruments is based on the interaction between magnetic fields and electric currents. When a current flows through a coil placed in a magnetic field, a mechanical force is generated, causing the coil to move. By employing suitable mechanisms, this motion can be converted into a pointer movement, indicating the measured electrical quantity on a calibrated scale.

Characteristics of PMMC Instrument

1. Full scale deflection current:

The Full Scale Deflection current, also known as the Full Scale Current or the Rated Current, is the maximum current that a PMMC instrument can handle while producing the maximum deflection on its scale. When the measured current equals the FSD current, the pointer of the PMMC instrument deflects to its maximum position, indicating that the input is at its highest measurable value.

The FSD current is a crucial parameter as it defines the upper limit of the measurable current range for the PMMC instrument. Choosing an appropriate FSD current is essential to ensure that the instrument is capable of accurately measuring the intended electrical quantity. If the FSD current is set too low, the instrument’s sensitivity increases, but it becomes limited in measuring higher currents. Conversely, if the FSD current is set too high, the sensitivity to smaller currents diminishes, making it less effective in measuring low current values.

2. Internal Resistance:

The internal resistance plays a critical role in determining the voltage drop across the PMMC instrument when a current passes through it. As a result, it affects the actual current being measured and may lead to inaccuracies in the readings displayed on the instrument’s scale.

In ideal conditions, a PMMC instrument would have zero internal resistance. However, in reality, this is not achievable. A finite internal resistance exists due to the coil windings, connections, and other components used in the instrument’s construction. Manufacturers aim to keep this internal resistance as low as possible to minimize the impact on measurement accuracy.

3. Sensitivity:

Sensitivity in PMMC instruments refers to the responsiveness of the instrument’s moving coil to changes in the input quantity being measured. A high sensitivity means that the instrument can detect even tiny variations in the input, while a lower sensitivity may require larger changes in the input to produce a noticeable deflection of the pointer.

It is given by reciprocal of full scale deflection current Im:

S = {1\over\ I_m}  ohm\ / \ volt

Torque Equation of PMMC

Let us assume,

l, d = Length of vertical and horizontal side of coil

N = Number of turns in the coil

B = Flux density in the air gap in wb/m^2

i = current through moving coil

N = Spring constant in Nm/rad

Force \ on\ each\ side \ of \ coil = N.Bil sin\alpha

Where α= Angle between direction of magnetic field and conductor

The field is radial so α = 90 degree

So, force on each side of coil = NBil

Deflecting torque (Td) = force*distance = NBild = NBiA

Where A= ld = area of coil in m^2

Here N, B, A are constants for galvanometer

Hence Td = Gi

Where, G = NBA

G= Displacement constant of galvanometer

The spring control provides a restoring torque

T_c =K\theta

Where, K = spring constant

For final steady deflection:

T_c = T_d

GI = K\theta

\theta = {G\over\ k }I

I = {K\over\ G} \theta 

Thus deflection is directly proportional to the current passing through the coil.

Advantages of PMMC Instrument

1. Accuracy:

PMMC instruments are highly accurate, making them suitable for precise measurements.

2. Stability:

Due to the permanent magnet’s constant magnetic field, the instruments exhibit excellent stability over time.

3.Low Power Consumption:

PMMC instruments consume low power, making them energy-efficient and suitable for battery-operated devices.

4. Wide Operating Range:

They can measure a wide range of electrical quantities, from small currents to large currents and voltages.

Errors in PMMC Instrument

Frictional Error

One of the most prevalent errors in PMMC instruments is frictional error. This error occurs due to the presence of friction between the moving parts of the instrument, leading to inaccurate readings. The friction can cause the pointer to stick or move irregularly, resulting in incorrect measurements.

Hysteresis Error

Hysteresis error is another significant problem encountered in PMMC instruments. It refers to the inconsistency in the pointer’s position while measuring the same value for increasing and decreasing currents or voltages. This discrepancy is a result of the magnetic properties of the instrument’s core material.

Parallax Error

Parallax error is a common mistake made by users during readings. It arises when the observer’s eye is not perpendicular to the pointer’s position. As a consequence, the reading appears shifted, leading to inaccurate results.

External Magnetic Field Interference

PMMC instruments can be influenced by external magnetic fields. When placed near other magnetic sources, the magnetic field lines may interfere with the instrument’s movement, causing deviations in the readings.

Temperature Effects

Temperature fluctuations can impact the accuracy of PMMC instruments. The coil’s resistance and the magnet’s strength may vary with temperature changes, leading to errors in measurements.

Overloading

Exceeding the maximum current or voltage capacity of the PMMC instrument can cause permanent damage and lead to inaccuracies in subsequent readings.

Calibration Drift

Over time, PMMC instruments may experience calibration drift, where their accuracy gradually decreases. Regular calibration is essential to mitigate this issue and maintain reliable measurements.

External Mechanical Shock

Sudden mechanical shocks or vibrations can affect the delicate components of PMMC instruments, leading to erratic behavior and incorrect readings.

Power Supply Issues

Inadequate or unstable power supply can impact the functioning of PMMC instruments, resulting in inaccurate readings or erratic pointer movements.

Aging of Components

With prolonged usage, some components of PMMC instruments, such as the coil or magnets, may experience aging or degradation, affecting the instrument’s overall accuracy

Conclusion

In conclusion, the PMMC (Permanent Magnet Moving Coil) instrument is a valuable and versatile device used for measuring direct current (DC) in various applications. Through analysis, we have observed that the PMMC instrument offers several advantages, including high accuracy, robust construction, and minimal power consumption. Its simple design ensures reliable and consistent readings over time, making it a preferred choice in many fields.

Also Read:https://smarttengineering.tech/half-wave-rectifier/

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