PMMC stands for ‘Permanent magnet moving coil'. It is one of the simple and most used instruments on board with sophisticated names. They are used on board to assist in regular maintenance of electrical equipment or when precise measurements are required. The term PMMC is the short form of 'permanent magnet moving coil'. This instrument is simple as well as most frequently used on ships with sophisticated names. These instruments are used when an exact measurement is required as well as to aid while maintaining electrical equipment. Apart from PMMC, it is also called as D'alvanometer.
- Electronic Measuring Instruments
- The basic pmmc instrument is sensitive to the temperature. The magnetic field strength and spring tension decrease with increase in temperature. The coil resistance increases with increase in the temperature. Thus pointer reads low for a given current. The meter tends to read low by approximately 0.2% per Celsius rise.
- Series ohm meter 2/3/2017 15 NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad Series Ohm Meter with PMMC of FSD current 100 A, RC=100, and standard resistance R=14.9K 16. Thanks 2/3/2017 NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad 16.
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DC voltmeter is a measuring instrument, which is used to measure the DC voltage across any two points of electric circuit. If we place a resistor in series with the Permanent Magnet Moving Coil (PMMC) galvanometer, then the entire combination together acts as DC voltmeter.
The series resistance, which is used in DC voltmeter is also called series multiplier resistance or simply, multiplier. It basically limits the amount of current that flows through galvanometer in order to prevent the meter current from exceeding the full scale deflection value. The circuit diagram of DC voltmeter is shown in below figure.
We have to place this DC voltmeter across the two points of an electric circuit, where the DC voltage is to be measured.
Apply KVL around the loop of above circuit.
$V-I_{m}R_{se}-I_{m}R_{m}=0$ (Equation 1)
$$Rightarrow V-I_{m}R_{m}=I_{m}R_{se}$$
$$Rightarrow R_{se}=frac{V-I_{m}R_{m}}{I_{m}}$$
$Rightarrow R_{se}=frac{V}{I_{m}}-R_{m}$ (Equation 2)
Where,
$R_{se}$ is the series multiplier resistance
$V$ is the full range DC voltage that is to be measured
$I_{m}$ is the full scale deflection current
$R_{m}$ is the internal resistance of galvanometer
The ratio of full range DC voltage that is to be measured, $V$ and the DC voltage drop across the galvanometer, $V_{m}$ is known as multiplying factor, m. Mathematically, it can be represented as
$m=frac{V}{V_{m}}$ (Equation 3)
From Equation 1, we will get the following equation for full range DC voltage that is to be measured, $V$.
$V=I_{m}R_{se}+I_{m}R_{m}$ (Equation 4)
The DC voltage drop across the galvanometer, $V_{m}$ is the product of full scale deflection current, $I_{m}$ and internal resistance of galvanometer, $R_{m}$. Mathematically, it can be written as
$V_{m}=I_{m}R_{m}$ (Equation 5)
Substitute, Equation 4 and Equation 5 in Equation 3.
$$m=frac{I_{m}R_{se}+I_{m}R_{m}}{I_{m}R_{m}}$$
$Rightarrow m=frac{R_{se}}{R_{m}}+1$
$Rightarrow m-1=frac{R_{se}}{R_{m}}$
$R_{se}=R_{m}left (m-1 right )$(Equation 6)
We can find the value of series multiplier resistance by using either Equation 2 or Equation 6 based on the available data.
Multi Range DC Voltmeter
In previous section, we had discussed DC voltmeter, which is obtained by placing a multiplier resistor in series with the PMMC galvanometer. This DC voltmeter can be used to measure a particular range of DC voltages.
If we want to use the DC voltmeter for measuring the DC voltages of multiple ranges, then we have to use multiple parallel multiplier resistors instead of single multiplier resistor and this entire combination of resistors is in series with the PMMC galvanometer. The circuit diagram of multi range DC voltmeter is shown in below figure.
We have to place this multi range DC voltmeter across the two points of an electric circuit, where the DC voltage of required range is to be measured. We can choose the desired range of voltages by connecting the switch s to the respective multiplier resistor.
Let, $m_{1},m_{2}, m_{2} $ and $m_{4}$ are the multiplying factors of DC voltmeter when we consider the full range DC voltages to be measured as, $V_{1} , V_{2}, V_{3}$ and $V_{4}$ respectively. Following are the formulae corresponding to each multiplying factor.
$$m_{1}=frac{V_{1}}{V_{m}}$$
$$m_{2}=frac{V_{2}}{V_{m}}$$
$$m_{3}=frac{V_{3}}{V_{m}}$$
$$m_{4}=frac{V_{4}}{V_{m}}$$
In above circuit, there are four series multiplier resistors, $R_{se1}, R_{se2}, R_{se3}$ and $R_{se4}$. Following are the formulae corresponding to these four resistors.
$$R_{se1}=R_{m}left (m_{1}-1 right )$$
$$R_{se2}=R_{m}left (m_{2}-1 right )$$
$$R_{se3}=R_{m}left (m_{3}-1 right )$$
$$R_{se4}=R_{m}left (m_{4}-1 right )$$
So, we can find the resistance values of each series multiplier resistor by using above formulae.
PMMC (Permanent Magnet Moving Coil Instruments)
The permanent magnet moving coil instrument or PMMC type instrument uses two permanent magnets in order to create stationary magnetic field. These types of instruments are only used for measuring the dc quantities as if we apply ac current to these type of instruments the direction of current will be reversed during negative half cycle and hence the direction of torque will also be reversed which gives average value of torque zero. The pointer will not deflect due to high frequency from its mean position showing zero reading. However it can measure the direct current very accurately.
Office 2003 basic key. Construction of permanent magnet moving coil instruments.
We will see the construction of these types of instruments in four parts and they are described below:
Stationary part or magnet system: In the present time we use magnets of high field intensities,high coercive force instead of using U shaped permanent magnet having soft iron pole pieces. The magnets which we are using nowadays are made up of materials like alcomax and alnico which provide high field strength.
Moving coil: The moving coil can freely moves between the two permanent magnets as shownin the figure given below. The coil is wound with many turns of copper wire and is placed on rectangular aluminum which is pivoted on jeweled bearings.
Control system: The spring generally acts as control system for PMMC instruments. The spring also serves another important function by providing the path to lead current in and out of the coil. Damping system: The damping force hence torque is provided by movement of aluminium former in the magnetic field created by the permanent magnets.
Meter: Meter of these instruments consists of light weight pointer to have free movement andscale which is linear or uniform and varies with angle
Deflecting torque Equation:
Let us derive a general expression for torque in permanent magnet moving coil instruments or PMMC instruments. We know that in moving coil instruments the deflecting torque is given
by the expression:
Td = N B l dI
where N is number of turns,
B is magnetic flux density in air gap, l is the length of moving coil,
d is the width of the moving coil, And I is the electric current.
Now for a moving coil instruments deflecting torque should be proportional to current, mathematically we can write Td = GI.
Thus on comparing we say G = NBIdl.
At steady state we have both the controlling and deflecting torques are equal.
Tc is controlling torque, on equating controlling torque with deflection torque we have GI = K.x where x is deflection thus current is given by
I = K / G x
Since the deflection is directly proportional to the current therefore we need a uniform scale on the meter for measurement of current.
Now we are going to discuss about the basic circuit diagram of the ammeter. Let us consider a circuit as shown below:
The current I is shown which breaks into two components at the point A. The two components are Is and Im. Before I comment on the magnitude values of these currents, let us know more about the construction of shunt resistance. The basic properties of shuntresistance are written below,
The electrical resistance of these shunts should not differ at higher temperature, it they should posses very low value of temperature coefficient. Also the resistance should be time independent. Last and the most important property they should posses is that they should be able to carry high value of current without much rise in temperature. Usually manganin is used for making dc resistance. Thus we can say that the value of Is much greater than the value of Im as resistance of shunt is low. From the we have,
Is .Rs = ImRm
Where Rs is resistance of shunt and Rm is the electrical resistance of the coil. Is = I – Im
M= I / Im = 1+ (Rm + Rs)
Where m is the magnifying power of the shunt.
Errors in Permanent Magnet Moving Coil Instruments
There are three main types of errors
(a) Errors due to permanent magnets:
Due to temperature effects and aging of the magnets the magnet may lose their magnetism to some extent. The magnets are generally aged by the heat and vibration treatment.
(b) Error may appear in PMMC Instrument due to the aging of the spring.
However the error caused by the aging of the spring and the errors caused due to permanent magnet are opposite to each other, hence both the errors are compensated with each other.
Pmc Meters
$V-I_{m}R_{se}-I_{m}R_{m}=0$ (Equation 1)
$$Rightarrow V-I_{m}R_{m}=I_{m}R_{se}$$
$$Rightarrow R_{se}=frac{V-I_{m}R_{m}}{I_{m}}$$
$Rightarrow R_{se}=frac{V}{I_{m}}-R_{m}$ (Equation 2)
Where,
$R_{se}$ is the series multiplier resistance
$V$ is the full range DC voltage that is to be measured
$I_{m}$ is the full scale deflection current
$R_{m}$ is the internal resistance of galvanometer
The ratio of full range DC voltage that is to be measured, $V$ and the DC voltage drop across the galvanometer, $V_{m}$ is known as multiplying factor, m. Mathematically, it can be represented as
$m=frac{V}{V_{m}}$ (Equation 3)
From Equation 1, we will get the following equation for full range DC voltage that is to be measured, $V$.
$V=I_{m}R_{se}+I_{m}R_{m}$ (Equation 4)
The DC voltage drop across the galvanometer, $V_{m}$ is the product of full scale deflection current, $I_{m}$ and internal resistance of galvanometer, $R_{m}$. Mathematically, it can be written as
$V_{m}=I_{m}R_{m}$ (Equation 5)
Substitute, Equation 4 and Equation 5 in Equation 3.
$$m=frac{I_{m}R_{se}+I_{m}R_{m}}{I_{m}R_{m}}$$
$Rightarrow m=frac{R_{se}}{R_{m}}+1$
$Rightarrow m-1=frac{R_{se}}{R_{m}}$
$R_{se}=R_{m}left (m-1 right )$(Equation 6)
We can find the value of series multiplier resistance by using either Equation 2 or Equation 6 based on the available data.
Multi Range DC Voltmeter
In previous section, we had discussed DC voltmeter, which is obtained by placing a multiplier resistor in series with the PMMC galvanometer. This DC voltmeter can be used to measure a particular range of DC voltages.
If we want to use the DC voltmeter for measuring the DC voltages of multiple ranges, then we have to use multiple parallel multiplier resistors instead of single multiplier resistor and this entire combination of resistors is in series with the PMMC galvanometer. The circuit diagram of multi range DC voltmeter is shown in below figure.
We have to place this multi range DC voltmeter across the two points of an electric circuit, where the DC voltage of required range is to be measured. We can choose the desired range of voltages by connecting the switch s to the respective multiplier resistor.
Let, $m_{1},m_{2}, m_{2} $ and $m_{4}$ are the multiplying factors of DC voltmeter when we consider the full range DC voltages to be measured as, $V_{1} , V_{2}, V_{3}$ and $V_{4}$ respectively. Following are the formulae corresponding to each multiplying factor.
$$m_{1}=frac{V_{1}}{V_{m}}$$
$$m_{2}=frac{V_{2}}{V_{m}}$$
$$m_{3}=frac{V_{3}}{V_{m}}$$
$$m_{4}=frac{V_{4}}{V_{m}}$$
In above circuit, there are four series multiplier resistors, $R_{se1}, R_{se2}, R_{se3}$ and $R_{se4}$. Following are the formulae corresponding to these four resistors.
$$R_{se1}=R_{m}left (m_{1}-1 right )$$
$$R_{se2}=R_{m}left (m_{2}-1 right )$$
$$R_{se3}=R_{m}left (m_{3}-1 right )$$
$$R_{se4}=R_{m}left (m_{4}-1 right )$$
So, we can find the resistance values of each series multiplier resistor by using above formulae.
PMMC (Permanent Magnet Moving Coil Instruments)
The permanent magnet moving coil instrument or PMMC type instrument uses two permanent magnets in order to create stationary magnetic field. These types of instruments are only used for measuring the dc quantities as if we apply ac current to these type of instruments the direction of current will be reversed during negative half cycle and hence the direction of torque will also be reversed which gives average value of torque zero. The pointer will not deflect due to high frequency from its mean position showing zero reading. However it can measure the direct current very accurately.
Office 2003 basic key. Construction of permanent magnet moving coil instruments.
We will see the construction of these types of instruments in four parts and they are described below:
Stationary part or magnet system: In the present time we use magnets of high field intensities,high coercive force instead of using U shaped permanent magnet having soft iron pole pieces. The magnets which we are using nowadays are made up of materials like alcomax and alnico which provide high field strength.
Moving coil: The moving coil can freely moves between the two permanent magnets as shownin the figure given below. The coil is wound with many turns of copper wire and is placed on rectangular aluminum which is pivoted on jeweled bearings.
Control system: The spring generally acts as control system for PMMC instruments. The spring also serves another important function by providing the path to lead current in and out of the coil. Damping system: The damping force hence torque is provided by movement of aluminium former in the magnetic field created by the permanent magnets.
Meter: Meter of these instruments consists of light weight pointer to have free movement andscale which is linear or uniform and varies with angle
Deflecting torque Equation:
Let us derive a general expression for torque in permanent magnet moving coil instruments or PMMC instruments. We know that in moving coil instruments the deflecting torque is given
by the expression:
Td = N B l dI
where N is number of turns,
B is magnetic flux density in air gap, l is the length of moving coil,
d is the width of the moving coil, And I is the electric current.
Now for a moving coil instruments deflecting torque should be proportional to current, mathematically we can write Td = GI.
Thus on comparing we say G = NBIdl.
At steady state we have both the controlling and deflecting torques are equal.
Tc is controlling torque, on equating controlling torque with deflection torque we have GI = K.x where x is deflection thus current is given by
I = K / G x
Since the deflection is directly proportional to the current therefore we need a uniform scale on the meter for measurement of current.
Now we are going to discuss about the basic circuit diagram of the ammeter. Let us consider a circuit as shown below:
The current I is shown which breaks into two components at the point A. The two components are Is and Im. Before I comment on the magnitude values of these currents, let us know more about the construction of shunt resistance. The basic properties of shuntresistance are written below,
The electrical resistance of these shunts should not differ at higher temperature, it they should posses very low value of temperature coefficient. Also the resistance should be time independent. Last and the most important property they should posses is that they should be able to carry high value of current without much rise in temperature. Usually manganin is used for making dc resistance. Thus we can say that the value of Is much greater than the value of Im as resistance of shunt is low. From the we have,
Is .Rs = ImRm
Where Rs is resistance of shunt and Rm is the electrical resistance of the coil. Is = I – Im
M= I / Im = 1+ (Rm + Rs)
Where m is the magnifying power of the shunt.
Errors in Permanent Magnet Moving Coil Instruments
There are three main types of errors
(a) Errors due to permanent magnets:
Due to temperature effects and aging of the magnets the magnet may lose their magnetism to some extent. The magnets are generally aged by the heat and vibration treatment.
(b) Error may appear in PMMC Instrument due to the aging of the spring.
However the error caused by the aging of the spring and the errors caused due to permanent magnet are opposite to each other, hence both the errors are compensated with each other.
Pmc Meters
(c) Change in the resistance of the moving coil with the temperature:
Generally the temperature coefficients of the value of coefficient of copper wire in moving coil is 0.04 per degree Celsius rise in temperature. Due to lower value of temperature coefficient the temperature rises at faster rate and hence the resistance increases. Due to this significant amount of error is caused.
Advantages of Permanent Magnet Moving Coil Instruments
(1)The scale is uniformly divided as the current is directly proportional to deflection of the pointer. Hence it is very easy to measure quantities from these instruments.
(2)Power consumption is also very low in these types of instruments. (3)Higher value of torque is to weight ratio.
(4)These are having multiple advantages, a single instrument can be used for measuring various quantities by using different values of shunts and multipliers.
Disadvantages of Permanent Magnet Moving Coil Instruments
Pmmc Meters Theory
(1) These instruments cannot measure ac quantities.
Pmmc Meter Working Principle
(2) Cost of these instruments is high as compared to moving iron instruments
