Electrical measurements unit-1-measuring instruments

ELECTRICAL MEASUREMENTS
P.NARESH(PH.D), ASST. PROF.,
EEE DEPARTMENT,
RAGHU ENGG. COLLEGE(A)
VISAKHAPATNAM

▪ MEASURING INSTRUMENTS
▪ MEASUREMENT OF POWER AND POWER FACTOR
▪ MEASUREMENT OF ENERGY
▪ POTENTIOMETERS
▪ MEASUREMENT OF RESISTANCE, INDUCTANCE AND CAPACITANCE
▪ MAGNETIC MEASUREMENTs
P. Naresh(Ph.D.), Asst. Prof., EEE REC (A)
Electrical Measurements: UNIT-I MEASURING INSTRUMENTS

Functional elements of a measurement system
The main functional elements of a measurement system are
1. Primary sensing element
2. Variable conversion element
3. Variable manipulation element
4. Signal conditioning element
5. Data transmission element
6. Data presentation element.
Primary Sensing
Element
Variable Conversion
Element
Variable
Manipulation
Element
Data
Transmission
Element
Data
Presentation
Element
Data Storage &
Playback Element
Quantity to be measured
(Measurand)
Observer
Data Conditioning Elements
Figure: Functional Elements of a Measurement System

Classification of measuring instruments
Digital
Instrument
Secondary
Instrument
Absolute
Instrument
Instruments
Mechanical
Instrument
Electrical
Instrument
Electronic
Instrument
Analog
Instrument
Null
Instrument
Indicating
Instrument
Integrating
Instrument
Recording
Instrument
Figure: Classification of measuring instruments

Types of Electrical Instruments

indicating Instruments

Essentials of indicating instruments
• Indicating instruments consist essentially of a pointer which moves over a calibrated scale and which is attached to a
moving system pivoted in jewelled bearings.
• The moving system is subjected to the following 3 torques:
1. Deflecting torque or operating torque
2. Controlling torque or restoring torque
3. Damping torque
• The deflecting or operating torque (Td) is produced by utilizing one or other effects, e.g., magnetic,
electrostatic, electrodynamic, thermal, or inductive.
• Controlling torque controls the movement of the pointer on a particular scale according to the quantity of the electricity,
passing through it. The controlling forces are required to control the deflection or rotation and bring the pointer to zero
position when there is no force or stop the rotation of the disc when there is no power.
• Damping torque is one which acts on the moving system of the instrument only when it is moving and always opposes
its motion. Such damping force is necessary to bring the pointer to rest quickly, otherwise due to inertia of the
moving system, the pointer will oscillate about its final deflected position for quite some time before coming to rest in
the steady position.

The actual method of torque production depends on the type of instrument. The deflecting torque causes the moving
system (and hence the pointer attached to it) to move from its zero position.
Deflecting torque

Controlling torque
Spring
control
Gravity
control
Methods of controlling torque

Spring control
Two phosphor bronze hair springs of spiral shapes are attached to the
spindle of the moving system of the instrument. They are wound in
opposite direction.
Td α I
And for spring control Tc α 
As Tc = Td
I α 
Since deflection q is directly proportional to current I, the spring-
controlled instrument have a uniform or equally spaced scales over the
whole of their range.

Gravity control
Gravity control is obtained by attaching a
small adjustable weight to some part of the
moving system such that the two exert
torques in the opposite directions.
As shown in the figure, the controlling or
restoring torque is proportional to the sine of
the angle of deflection, i.e., Tc α Sin .

Damping torque
Air friction
damping
Eddy current
damping
Methods of damping torque

• The light aluminium piston attached to the
moving system of the instrument is arranged to
travel with a very small clearance in a fixed
chamber closed at one end.
• The cross-section of the chamber is either
circular or rectangular. Damping of the system
is affected by the compression and suction
actions of the piston on the air enclosed in the
chamber.
• In another method, light aluminium vane is mounted on the spindle of the moving system which moves in air or
in a closed sector-shaped box. Fluid-friction is similar is action to the air-friction.
• Due to greater viscosity of the oil, the damping is more effective. However, oil damping is not much used
because of several disadvantages such as objectionable creeping of oil, the necessity of using the instrument
always in vertical position and its obvious unsuitability for use in portable instruments.
Air friction damping

• A thin disc of a conducting but non-
magnetic material like copper or
aluminium is mounted on the spindle. The
disc is so positioned that its edges, when
in rotation, cut the magnetic flux between
the poles of a permanent magnet.
• Hence eddy currents are produced in the disc which flow and so produce a damping force in such a direction as
to oppose the very cause producing them (Lenz’s law). Since the cause producing them, is the rotation of the
disc, these eddy currents retard the motion of the disc and moving system.
Eddy current damping

The instruments which use the permanent magnet for creating the stationary magnetic field between which the coil moves is
known as the permanent magnet moving coil or PMMC instrument. It operates on the principle that the torque is exerted on
the moving coil placed in the field of the permanent magnet.
1. Moving Coil
2. Magnet System
3. Control system
4. Damping system
Permanent magnet moving coil (pmmc) instrument

The deflecting torque
Where, N – Number of turns of coil
B – flux density in the air gap
L, d – the vertical and horizontal length of the side.
I – current through the coil.
The spring provides the restoring torque to the moving coil which is expressed as
Where K = Spring constant.
For final deflection,
By substituting the value of equation (1) and (3) we get,
The above equation shows that the deflection torque is directly proportional to the current passing through the coil.
Torque Equation for PMMC Instrument

Advantages
1. The scale of the PMMC instruments is uniform.
2. The power consumption of the devices is very less.
3. The PMMC instruments have high accuracy because of the high torque weight ratio.
4. The single device measures the different range of voltage and current. This can be done by the use of multipliers and shunts.
Dis-Advantages
1. The PMMC instruments are only used for the direct current. The alternating current varies with the time. The rapid variation
of the current varies the torque of the coil. But the pointer can not follow the fast reversal and the deflection of the torque.
Thus, it cannot use for AC.
2. The cost of the PMMC instruments is much higher as compared to the moving coil instruments.
Errors in PMMC Instruments
In PMMC instruments the error occurs because of the ageing and the temperature effects of the instruments. The magnet,
spring and the moving coil are the main parts of the instruments which cause the error.
Advantages & Disadvantages of PMMC Instruments

The basic d.c. ammeter is nothing but a D'Arsonval galvanometer. The coil winding of a basic movement is very small and
light and hence it can carry very small currents. So as mentioned earlier, for large currents, the major part of current is
required to be bypassed using a resistance called shunt. It is shown in the Figure.

If the ordinary switch is used, while range changing, the switch
remains open and full current passes through the meter.
The meter may get damaged due to such high current. So make
before break switch is used.
The design of such switch is so that it makes contact with next
terminal before completely breaking the contact with the previous
terminal.
The range of the basic d.c. ammeter can be extended by using number of shunts and a selector switch. Such a meter is
called multirange ammeter and is shown in the Figure.

In multirange ammeter, a make before break switch is must. The Aryton shunt or the universal shunt eliminates the
possibility of having a meter without a shunt. The meter with the Aryton shunt is shown in the Figure.

The basic d.c. voltmeter is nothing but a PMMC D'Arsonoval galvanometer. The resistance is required to be connected in
series with the basic meter to use it as a voltmeter. This series resistance is called a multiplier the main function of the
multiplier is to limit the current through the basic meter so that the meter current does not exceed the full-scale deflection
value.

• The R1, R2, R3 and R4 are the four series multipliers.
When connected in series with the meter, they can give
four different voltage ranges as V1, V2, V3 and V4.
• The selector switch S is multi-position switch by which
we required multiplier can be selected in the circuit The
mathematical analysis of basic d.c. voltmeter is equally
applicable for such multirange voltmeter.

In a multirange voltmeter, the ratio of the total resistance RT to the voltage range remains same.
This ratio is nothing but the reciprocal of the full scale deflection current of the meter i.e., 1/Im This value is called sensitivity
of the voltmeter.

A moving coil instrument gives a full scale deflection for a current of 20 mA with a potential difference of 200mV across it.
Calculate 1) shunt required to use it as an ammeter to get a range of 0 - 200 mA. 2) Multiplier required to use it as a voltmeter of
range 0 – 1000 mV.

Design an Aryton shunt to provide an ammeter with the current ranges 1 A, 5 A and 10 A. A basic meter resistance is 50  and
full scale deflection current is 1 mA.

A basic D’Arsonval movement with an internal resistance of 50  and a full scale deflection current of 2 mA is to be used as a
multirange voltmeter. Design the series string of multipliers to obtain the voltage ranges of 0 -10 V, 0 - 50 V, 0 – 100 V & 0 –
500 V.

A basic D’Arsonval movement with an internal resistance of 50  and a full scale deflection current of 2 mA is to be used as a
multirange voltmeter. Design the series string of multipliers to obtain the voltage ranges of 0 -10 V, 0 - 50 V, 0 – 100 V & 0 -
500V. Use the sensitivity method.

Two different voltmeters are used to measure the voltage across Rb shown in the figure. The two meters used are
as follows: 1) Meter with sensitivity 1 K/V and range 5 V. 2) Meter with sensitivity 20 K/V and range 5 V.
Calculate (i) True voltage across Rb (ii) Reading on voltmeter -1 (iii) Reading on voltmeter - 2 (iv) % error in the
two meters (v) % Accuracy of the two voltmeters.

In Moving Iron Instruments, a plate or van of soft iron or of high permeability steel
forms the moving element of the system. The iron van is so situated that it can move in
the magnetic field produced by a stationary coil.
The moving iron Instruments are classified into two types:
1. Attraction type
2. Repulsion type

Figure: Attraction Type mi Instrument P. Naresh(Ph.D.), Asst. Prof., EEE REC (A)
The basic working principle of these instruments is very simple that a soft iron piece if brought near the magnet gets
attracted by the magnet. The construction of the attraction type instrument is shown in the Figure.
It consists of a fixed coil C and moving iron piece D. The coil is flat
and has a narrow slot like opening. The moving iron is a flat disc
which is eccentrically mounted on the spindle.
The number of tums of the fixed coil are depends on the range of the
instrument or passing large current through the coil only few turns are
required.
The controlling torque is provided by the springs but gravity control
may also be used for vertically mounted panel type instruments. The
damping torque is provided by the air friction.
The operating magnetic field in moving iron instruments is very weak.
Hence eddy current damping is not used since it requires a permanent
magnet which would affect or distort the operating field.

Figure: Repulsion Type MI Instrument
These instruments have two vanes inside the coil, the one is fixed
and other is movable.
When the current flows in the coil, both the vanes are magnetized
with like polarities induced on the same side.
Hence due to the repulsion of like polarities, there is a force of
repulsion between the two vanes causing the movement of the
moving vane.

Let current flowing in the coil = I and the energy stored in the coil = (1/2)LI2
When there is a change of current from I to (I+dI), must be accompanied by change in emf of coil.
e = d(LI) / dt = IdL/dt + LdI/dt
The electrical energy supplied by the source = eIdt = I2dL + LIdI ………………..(1)
As the current changes to (I+dI), deflection in the pointer becomes dƟ resulting into change in inductance of coil from
L to (L+dL). Let this deflection in pointer is due to deflection torque Td.
Thus mechanical work done = Td X dƟ ………………..(2)
Energy stored in Coil = (1/2)(L+dL)(I+dI)2
Change in stored energy of coil = Final Stored Energy – Initial Stored Energy
= (1/2)(L+dL)(I+dI)2 – (1/2)LI2
Neglecting second order and higher terms of differential quantities i.e. L(dI)2, 2IdIxdL and dL(dI)2
= (1/2)[ 2LIdI+I2dL]
Change in stored energy of coil = LIdI +(1/2) I2dL ……………………(3)

According to law of conservation of energy, this electrical energy supplied by the source is converted into stored energy in the coil
and mechanical work done for deflection of needle of Moving Iron Instruments.
Electrical energy supplied = Change in stored energy + Work done
⇒ I2dL + LIdI = LIdI +(1/2) I2dL + Td X d ….[from (1), (2) & (3)]
⇒ Td x dƟ = (1/2)dLI2
Deflecting torque, Td = (1/2)I2(dL/dƟ)
In moving iron instruments, the controlling torque is provided by spring. Controlling torque due to spring is given as Tc = KƟ
In equilibrium state, deflecting and controlling torque are equal.
⇒ (1/2)I2(dL/dƟ) = KƟ
Ɵ = (1/2)(I2/K)(dL/dƟ)
From the above torque equation, we observe that the angular deflection of needle of moving iron instruments is square of rms
current flowing through the coil. Therefore, the deflection of moving iron instruments is independent of direction of current.

• Hysteresis error
Due to hysteresis effect, the flux density for the same current while ascending and descending values İs different While descending, the
flux density is higher and while ascending it is lesser. So, meter reads higher for descending value of current or voltage. So, remedy for
this is to use smaller iron parts which can demagnetize quickly or to work with lower flux densities.
• Temperature error
The temperature error arises due to the effect of temperature on the temperature coefficient of the spring, this error is of the order of 0-02%
per oC change in temperature. Errors can cause due to self-heating of the coil and due to which change in resistance of the coil. So, coil and
series resistance much have low temperature coefficient Hence manganin is generally used for the series resistances.
• Stray magnetic field error
The operating magnetic field in case of moving iron instruments İs very low. Hence effect of external to Stray magnetic field can cause
error This effect depends on the direction of the stray magnetic field with respect to the operating field of the instrument.
• Frequency error
These are related to A.C. operation of the instrument. The change in frequency affects the reactance of the working coil and also affects the
magnitude of the eddy currents, this causes errors in the instrument.
• Eddy current error
when instrument is used for a.c. measurements the eddy currents are produced in the iron parts of the instrument. The eddy current affects
the instrument current causing the change in the deflecting torque This-produces the error in the meter reading. As eddy currents are
frequency dependent, frequency changes cause eddy current error,

SI. No Moving Coil (MC)
Instrument
Moving Iron (MI)
Instrument
1 Coil is moving & connected
to pointer
Coil is fixed & iron vane is
moving
2 Suitable for only DC
measurements
Suitable for both AC & DC
measurements
3 Scale is uniform Scale is non-uniform
4 Accuracy is High Accuracy is Low
5 Free from hysteresis & stray
magnetic field errors
Serious errors exist due to
hysteresis, frequency
changes and stray magnetic
fields.
6 Power consumption is low Power consumption is high

Advantages
1. It is a universal instrument which can be used for the measurement of AC and DC quantities.
2. They have high value of torque to weight ratio, hence frictional error is quite low.
3. These instruments are quite robust due to its simple construction as there is no moving part in the instrument which
carries current.
4. These instruments can be designed to provide precision and industrial grade accuracy. A well designed moving iron
instruments have a error of less than 2 % or less for DC. For AC, the accuracy of the instrument may be of the order of
0.2 to 0.3 % at 50 Hz.
Disadvantages
1. These instruments suffer from error due to hysteresis, frequency change and stray losses.
2. The scale is non-uniform and cramped at lower end. So the accurate readings are not possible at lower range.

The inductance of a moving iron instrument is given by L = (10 + 5  - ^2) µH where  is
the deflection in the radians from zero position. The spring constant is 12 X 10^-6 Nm/rad.
Estimate the deflection for a current of 5 A.

An electrodynamometer type instrument is a moving coil instrument in which the operating field is produced by another coil
which is fixed. This type of instrument can be used either as an ammeter or as a voltmeter, but is generally used as a wattmeter.
An electrodynamic type instrument consists of two fixed coils, a moving coil, control spring, damping device and magnetic
shielding arrangement.
Electrodynamic instruments are also capable of functioning as transfer instruments. Besides, their use as an
ammeter, voltmeter, and wattmeter; they are also used to transfer calibration of working instruments.
The instrument consists of a fixed coil and a moving coil. The fixed coil is usually air-
cored to avoid hysteresis effects when used on AC circuits. Fixed coils are wound with
fine wire for use as a voltmeter. But, if the instrument is to be used as an ammeter or
wattmeter, then the fixed coils are wound with heavy wire carrying the main current.
The moving coil is mounted on an Aluminium spindle. It is wound either as self
sustaining coil or else on a non-metallic former so as to prevent eddy currents. Moving
coils are also air-cored. Controlling torque is provided by two control springs. These
springs act as leads to the moving coil.
Air friction damping is provided by Aluminium vanes attached to the spindle at the
bottom. Electrical Measurements: UNIT-I MEASURING INSTRUMENTS

Let the current in fixed coil be I1 and that in moving coil be I2
L1 = Self-inductance of fixed coil
L2 = Self-inductance of moving coil
M = Mutual inductance between fixed and moving coils
The flux linkage of fixed coil Ø1 = L1i1 + Mi2
The flux linkage of moving coil Ø2 = L2i2 + Mi1
The electrical energy input to the instrument= e1i1dt + e2i2dt
But according to Faraday’s Law, e1 = d Ø1/dt and e2 = d Ø2/dt
Therefore, energy input to the instrument = i1d Ø1 + i2d Ø2
= i1d (L1i1 + Mi2) + i2d(L2i2 + Mi1)
= i1L1di1 + i1
2dL1 + i1i2dM + i1Mdi2 + i2L2di2 + i2
2dL2 +i1i2dM + i2Mdi1
Since L1 and L2 are constant, therefore dL1 = 0 and dL2 = 0
= i1L1di1 + i1i2dM + i1Mdi2 + i2L2di2 + i1i2dM + i2Mdi1 …………(1)
Some of the above input energy to electrodynamometer instruments are stored in the form of magnetic energy in the coil while
rest is converted into mechanical energy of moving coil. Thus, Energy Input = Mechanical Energy + Stored Energy

Mechanical Energy = Electrical Input – Stored Energy ………… (2)
Thus, to find the mechanical energy, we need to find the change in stored energy in the magnetic field of the coil.
Let us assume an infinitesimally small time dt for the sake of calculation of change in stored energy.
Change in stored energy = d(1/2L1i1
2 + 1/2L2i2
2 + Mi1i2)
= i1L1di1+ i2L2di2+ i1Mdi2 + i2Mdi1+ i1i2dM+(i1
2/2)dL1 + (i2
2/2)dL2
But L1 and L2 are constant, therefore dL1 = 0 and dL2 = 0
= i1L1di1+ i2L2di2+ i1Mdi2 + i2Mdi1+ i1i2dM ……(3)
From equation (1), (2) and (3), Mechanical Energy = i1i2dM
Let Td be the deflecting torque and dƟ be the change in deflection, then mechanical energy= TddƟ
Td dƟ = i1i2dM ⇒Td = i1i2dM/dƟ
The above equation gives the deflecting torque in electrodynamics or electrodynamometer instruments. It can be seen that
deflecting torque depends upon the multiplication of instantaneous value of current and rate of change of mutual inductance
between the fixed and moving coil.

Case-1: When DC quantity is being measured.
Let I1 and I2 be the current in fixed and moving coil respectively. Therefore deflecting torque Td = I1I2dM/dƟ
But this deflecting torque is controlled by the spring. Spring provides the controlling torque. The controlling torque due to
spring for a deflection of Ɵ; Tc = KƟ where K is spring constant. At equilibrium the controlling torque and deflecting torques
are equal, hence Tc = Td
⇒KƟ = I1I2dM/dƟ
⇒Ɵ = (I1I2dM/dƟ)/K
Case-2: When AC quantity is being measured.
Let i1 and i2 are sinusoidal current having a phase displacement of Ø. i1 = Im1Sinwt and i2 = Im2Sin(wt-Ø)
The instantaneous deflecting torque is given as; Td = (Im1Sinwt) [ Im2Sin(wt-Ø)]dM/dƟ
The average torque for one time period of the currents are given by Td = (I1I2CosØ)dM/dƟ
Where I1 = RMS Value of i1 and I2 = RMS value of i2
For sinusoidal alternating current, the deflecting torque is determined by the product of RMS value of coil currents and the
cosine of phase angle between them. When the instrument is used for AC, the instantaneous torque is proportional to i2. Thus,
the torque varies as the current varies but the direction of torque remains the same. Because of the inertia of the instrument, the
needle does not follow the change in torque rather it takes a position where the average torque becomes equal to the controlling
torque.

ADVANTAGES:
1. These instruments are free from hysteresis and eddy current losses.
2. They can be used on both AC and DC.
3. They are used as transfer instruments.
DISADVANTAGES:
1. Low torque/weight ratio and hence low sensitivity.
2. Costlier than PMMC and moving iron type.
3. Non-uniform scale.

The operation of all the electrostatic instruments is based on the principle that there exists a force between the two plates
with opposite charges. This force can be obtained using the principle that the mechanical work done is equal to the stored
energy if there is a relative motion of plates.
Consider two plates A and B where plate A is fixed while B is movable. Two
plates are oppositely charged and plate B is restrained by a spring connected to
fixed point. Let the force of attraction between the two plates be F newton. Let
the capacitance between the two plates be C farad. The energy stored E is the
given by,
When applied voltage increases by dV, the current flowing through capacitance
also changes and it is given by,

Also due to change in applied voltage by value dV, the
capacitance increases by DC because plate B moves
towards a fixed plate A which decreases the distance of
separation between two plates increasing net capacitance.
Thus, the net energy stored is given by,
According to law of conservation of energy,
Electrical energy supplied = Change in stored energy + Work
done
⇒ V2dC + CVdV = CVdV +(1/2) V2dC + Td X d
Deflecting torque, Td = (1/2)V2(dC/dƟ)
Controlling torque is provided by spring. Controlling torque due
to spring is given as Tc = KƟ
In equilibrium state, deflecting and controlling torque are equal.
⇒ (1/2)V2(dC/dƟ) = KƟ
⇒ Ɵ = (1/2)(V2/K)(dC/dƟ)

The two types of electrostatic voltmeter are
1. Quadrant type electrostatic voltmeter which is used to measure voltages up to 10 kV to 20 kV.
2. Attracted disc type electrostatic voltmeter which is used to measure voltages above 20 kV.
Quadrant Type Electrostatic Voltmeter
The instrument consists of four fixed metal double quadrants arranged such that there is a small air gap between the
quadrants and the total assembly forms shallow circular box. Inside this box a double sectored needle is suspended by
means of a phosphor bronze thread. The needle is suspended such that it is placed equidistant from above and below
quadrant plates as shown in the Figure.
As shown in the above figure the fixed quadrants are connected together.
The voltage to be measured either a.c. or d.c. is connected between the
fixed quadrants and the moving needle. This needle rotates due to the
electrostatic force set up due to the charge accumulation on the quadrant
plates. Then the suspension exerts a controlling torque and the needle
settles at the position where both the torques, controlling and deflection,
are equal.

There are two types of the electrical connections in the quadrant electrometer,
1. Heterostatic connection
2. Idiostatic connection.
Heterostatic Connection
In this type of connection, a high voltage battery is used to charge the needle to a voltage considerably higher than the
voltage to be measured. The connection diagram is as shown in the Figure. In this connection, the quadrants are connected
together in diagonally opposite pairs. The moving vane i.e., needle is positively charged due to battery. The deflecting force
due to top and bottom quadrants on movable needle cancels each other on both sides. The only deflecting force responsible
is force of attraction between left quadrants and right moving sector and force of repulsion between right quadrant and left
moving sector.

Idiostatic Connection
This is connection generally used in commercial instruments. In this type of connection, needle is connected to any one of
the pairs of quadrants as shown in the Figure, directly without external voltage.
The moving needle is negatively charged, the left-hand quadrant
is negatively charged and the right-hand quadrant is positively
charged. The force of attraction on needle due to top and bottom
parts of right-hand quadrant cancel each other.
So there is no motion of needle due to right hand quadrant
Similarly the force of repulsion on needle due to top and bottom
parts of left-hand quadrant also cancel each other.
Thus, the right hand positively charged quadrant attract the part of the needle near to left hand quadrant while the left
hand negatively charged quadrant repels the part of the needle to right hand quadrant. This rotates the needle and hence
the pointer.

Attracted Disc Type Electrostatic Voltmeter
Attracted Disc Electrostatic Voltmeter
The attracted disc type instruments are generally used for the measurement of voltages above 20 kV.
The system consists of two plates such that one plate can move freely while other is fixed, Both the plates are perfectly
insulated from each other The voltage to be measured is applied across the plates as a supply voltage as shown in the Figure.
Due to the supply voltage, electrostatic field gets produced which develops a force of attraction between the two plates. Due
to the force of attraction, the movable plate gets deflected. In this mechanism the controlling torque is provided by a spring.

A transformer that is used to measure electrical quantities like current, voltage, power, frequency and power factor is
known as an instrument transformer. These transformers are mainly used with relays to protect the power system.
The Purpose of the instrument transformer is to step down the voltage & current of the AC system because the level of
voltage & current in a power system is extremely high. So designing the measuring instruments with high voltage &
current is difficult as well as expensive. In general, these instruments are mainly designed for 5 A & 110 V.
The measurement of high-level electrical quantities can be done using a device namely instrument transformer. These
transformers play an essential role in current power systems.
Types of Instrument Transformers
Instrument transformers are classified into two types such as
1. Current Transformer
2. Potential Transformer
instrument Transformers

This type of transformer can be used in power systems to step down the voltage from a high level to a low level with the
help of a 5A ammeter. This transformer includes two windings like primary and secondary. The current in the secondary
winding is proportional to the current in the primary winding as it generates current in the secondary winding. The circuit
diagram of a typical current transformer is demonstrated in the following figure.
current Transformers
In this transformer, the primary winding consists of few turns and it is
connected with the power circuit in series. So it is called a series transformer.
Likewise, the secondary winding includes a number of turns and it is connected
to an ammeter directly because the ammeter includes small resistance.
Thus, the secondary winding of this transformer works almost in the condition
of a short circuit. This winding includes two terminals where one of its
terminals is connected to ground to evade the huge current. So insulation
breakdown chances will be reduced to guard the operator from huge voltage.
The secondary winding of this transformer in the above circuit is short-circuited
before disconnecting the ammeter with the help of a switch to avoid the high
voltage across the winding.

This type of transformer can be used in power systems to step down the voltage from a high level to a lower level with
the help of a small rating voltmeter which ranges from 110 Volts to 120 Volts. A potential transformer typical circuit
diagram is illustrated below.
This transformer includes two windings like a normal transformer like primary & secondary. The primary winding of
the transformer includes a number of turns and it is connected in parallel with the circuit. So it is called a parallel
transformer.
potential Transformers
Similar to the primary winding, the secondary winding includes
fewer turns and that is connected to a voltmeter directly because
it includes huge resistance. Therefore the secondary winding
works approximately in open circuit condition.
One terminal of this winding is connected to the earth to maintain
the voltage with respect to the earth to protect the operator from a
huge voltage.

The advantages of instrument transformers are
1. These transformers use ammeter & voltmeter to measure high currents & voltages.
2. By using these transformers, several protecting devices can be operated like relays otherwise pilot lights.
3. Instrument transformer based transformers are less cost.
4. Damaged parts can be easily replaced.
5. These transformers offer electrical isolation among measuring instruments & high voltage power circuits. So that
electrical insulation requirements can be reduced in protective circuits & measuring instruments.
6. By using this transformer, various measuring instruments can be connected to a power system.
7. Low power consumption will be there in protective & measuring circuits because of the low level of voltage &
current.
The only disadvantage of instrument transformer is, these can be used simply for AC circuits but not for DC circuits
Advantages & disadvantages of instrument Transformers

Ratio’s of instRument tRansfoRmeRs
1. Actual ratio [R]
The actual transformation ratio is defined as the ratio of the magnitude of actual primary phasor to the corresponding
magnitude of actual secondary phasor. The actual ratio is also called transformation ratio.
R =
Magnitude of actual primary current
Magnitude of actual secondary current
… . . for CT
R =
Magnitude of actual primary volatge
Magnitude of actual secondary voltage
… . . for PT
2. Nominal ratio [Kn]
The nominal ratio is defined as the ratio of rated primary quantity to the rated secondary quantity, cither current or voltage.
Kn =
Rated primary current
Rated secondary current
… . . for CT
Kn =
Rated primary volatge
Rated secondary voltage
… . . for PT

3. Turns ratio [n]
n =
Number of turns of secondary winding
Number of turns of primary winding
… . . for CT
n =
Number of turns of primary winding
Number of turns of secondary winding
… . . for PT
4. Ratio Correction Factor (RCF)
It is the ratio of transformation i.e., actual ratio to the nominal ratio.
The ratio which is indicated on the name plate of a transformer is always Its nominal ratio.
Ratio’s of instRument tRansfoRmeRs

The nominal ratio of an instrument transformer does not remain constant in practice as the load on the secondary changes, it
changes because of effect of secondary current, power factor and magnetizing as well as core loss components of current
and this causes errors in the measurements.
For the particular class of transformers the specific loading at rated secondary winding voltage is specified such that the
errors do not exceed the limit. Such a permissible load is called burden of an instrument transformer thus the permissible
load across the secondary winding expressed in volt-amperes at the rated secondary winding voltage or current, such that
errors do not exceed the limit is called burden of an instrument transformer.
Burden of an Instrument Transformer
If only the impedance of the load is considered then burden due to only load can be obtained

Figure: equivalent circuit of a current transformer along with load
Theory of Current Transformers

Figure: phasor diagram of the Transformer with a lagging P.F. load
C . T. - Derivation of Actual Ratio

This is approximated value of actual ratio but practically very close to actual result, the equation (3) can be further
expanded as,

The phase angle θ is defined as the angle between reversed secondary current phasor i.e., reflected secondary
current phasor and the primary current.
Sign convention: θ is positive if reflected secondary current leads primary current. θ is negative if secondary current
lags primary current.
C . T . - Derivation of Phase Angle (θ) of Transformer

The loading of potential Transformer is very small in practice hence exciting current I0 is of the order of is, i.e., secondary
winding current. While in a normal power Transformer Io. is very small compared to Is. The equivalent circuit of potential
Transformer is shown in the Figure.
Theory of potential Transformers

Differences between Instrument and Power Transformers

Electrical measurements unit-1-measuring instruments

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