potentiometer lecture notes for RRB JE CBT2 EXAM PREPARATION

BASIC DC POTENTIOMETER
• The circuit diagram of a basic dc potentiometer is shown in Figure
2

Operation
• First, the switch S is put in the ‘operate’
position and the galvanometer key K kept
open, the battery supplies the working current
through the rheostat and the slide wire.
• The working current through the slide wire
may be varied by changing the rheostat
setting.
• The method of measuring the unknown
voltage, E1, depends upon the finding a
position for the sliding contact such that the
galvanometer shows zero deflection, i.e.,
indicates null condition, when the
galvanometer key K is closed.
3

• Zero galvanometer deflection means
that the unknown voltage E1 is equal
to the voltage drop E2, across
position a–c of the slide wire.
• Thus, determination of the values of
unknown voltage now becomes a
matter of evaluating the voltage drop
E2 along the portion a–c of the slide
wire.
4

• When the switch S is placed at ‘ calibrate’
position, a standard or reference cell is connected
to the circuit.
• This reference cell is used to standardize the
potentiometer.
• The slide wire has a uniform cross-section and
hence uniform resistance along its entire length.
• A calibrated scale in cm and fractions of cm, is
placed along the slide wire so that the sliding
Figure.
• A basic potentiometer circuit contact can be
placed accurately at any desired position along the
slide wire.
5

• Since the resistance of the slide wire is known accurately, the voltage
drop along the slide wire can be controlled by adjusting the values of
working current.
• The process of adjusting the working current so as to match the voltage
drop across a portion of sliding wire against a standard reference source
is known as ‘standardization’.
6

CROMPTON’S dc POTENTIOMETER
• The general arrangement of a laboratory-type Crompton’s dc potentiometer is shown
in Figure.
7

• It consists of a dial switch which has
fifteen (or more) steps.
• Each steep has 10 Ω resistance.
• So the dial switch has total 150 Ω
resistance.
• The working current of this
potentiometer is 10 mA and therefore
each step of dial switch corresponds to
0.1 volt.
• So the range of the dial switch is 1.5
volt
8

• The dial switch is connected in series with a circular
slide wire.
• The circular slide wire has 10 Ω resistance.
• So the range of that slide wire is 0.1 volt.
• The slide wire calibrated with 200 scale divisions and
since the total resistance of slide wire corresponds to
a voltage drop of 0.1 volt, each division of the slide
wire corresponds to volt.
• It is quite comfortable to interpolate readings up to
1/5 of a scale division and therefore with this
Crompton’s potentiometer it is possible to estimate
the reading up to 0.0001 volt.
9

Procedure for Measurement of Unknown emf
• At first, the combination of the dial switch and the slide
wire is set to the standard cell voltage.
• Let the standard cell voltage be 1.0175 volts, then the
dial resistor is put in 1.0 volt and the slide wire at
0.0175 volts setting.
• The switch ‘S’ is thrown to the calibrate position and
the galvanometer switch ‘K’ is pressed until the
rheostat is adjusted for zero deflection on the
galvanometer.
• The 10 kΩ protective resistance is kept in the circuit in
the initial stages so as to protect the galvanometer from
overload.
10

• After the null deflection on the galvanometer is approached the
protective resistance is shorted so as to increase the sensitivity of the
galvanometer.
• Final adjustment is made for the zero deflection with the help of the
rheostat.
• This completes the standardization process of the potentiometer.
11

• After completion of the standardization, the switch ‘S’ is thrown to the
operate position thereby connecting the unknown emf into the
potentiometer circuit.
• With the protective resistance in the circuit, the potentiometer is balanced
by means of the main dial and the slide wire adjustment.
• As soon as the balanced is approached, the protective resistance is shorted
and final adjustments are made to obtain true balance.
• After the final true balance is obtained, the value of the unknown emf is
read off directly from the setting of the dial switch and the slide wire.
12

• The standardization of the potentiometer is checked again by returning the
switch ‘S’ to the calibrate position.
• The dial setting is kept exactly the same as in the original standardization
process.
• If the new reading does not agree with the old one, a second measurement of
unknown emf must be made.
• The standardization again should be made after the measurement.
13

Measurement of Current by Potentiometer
• The circuit arrangement for measurement of current by a potentiometer is
shown in Figure.
14

• The unknown current I, whose value is to be measured, is passed through
a standard resistor R as shown.
• The standard resistor should be of such a value that voltage drop across it
caused by flow of current to be measured, may not exceed the range of
the potentiometer.
• Voltage drop across the standard resistor in volts divided by the value of R
in ohms gives the value of unknown current in amperes.
15

Example:
• A simple slide wire potentiometer is used for measurement of current
in a circuit. The voltage drop across a standard resistor of 0.1 Ω is
balanced at 75 cm. find the magnitude of the current if the standard
cell emf of 1.45 volt is balanced at 50 cm.
Solution
For the same working current, if 50 cm corresponds to 1.45 volt. Then
75 cm of the slide wire corresponds to
16

17
So, across the resistance 0.1 ? the voltage drop is 2.175 volt.
Then the value of the current is

Measurement of High Voltage by Potentiometer
• Special arrangements must be made to measure very high voltage by the
potentiometer (say a hundreds of volts) as this high voltage is beyond the range
of normal potentiometer.
• The volt-ratio box consists of a simple resistance potential divider with various
tapping on the input side.
18

• The arrangement is shown in
Figure.
• Each input terminal is marked
with the maximum voltage
which can be applied and with
the corresponding multiplying
factor for the potential scale.
19

• High emf to be measured is applied the
suitable input terminal of volt-ratio box and
leads to the potentiometer are taken from two
tapping points intended for this purpose.
• The potential difference across these two
points is measured by the potentiometer.
• If the voltage measured by the potentiometer is
v and k be the multiplying factor of the volt-
ratio box, then the high voltage to be measured
is V = kv volt.
20

Measurement of Resistance by Potentiometer
• The connection diagram for measuring unknown resistance with the help of
potentiometer is shown in Figure
21

• The unknown resistance R, is connected
in series with the known standard resistor
S.
• The rheostat connected in the circuit
controls the current flowing through the
circuit.
• An ammeter is also connected in the
circuit to indicate whether the value of
the working current is within the limit of
the potentiometer or not. 22

• When the two–pole double throw switch is put
in position 1, the unknown resistance is
connected to the potentiometer.
• Let the reading of the potentiometer in that
position is VR. Then
23
• The value of R can be calculated accurately since
the value of the standard resistor S is known.
• This method of measurement of resistance is used
for low value of the resistor.

Measurement of Power by Potentiometer
• In measurement of power by potentiometer the measurements are made one
across the standard resistor S connected in series with the load and another
across the volt-ratio box output terminals.
• The arrangement is shown in Figure.
24

• The load current which is exactly equal to the current through the
standard resistor S, as it is connected in series with the load, is
calculated from the voltage drop across the standard resistor divided
by the value of the standard resistor S.
• Load current
25
where VS = voltage drop across standard resistor S as measured by the
potentiometer.

• Voltage drop across the load is found
by the output terminal of the volt-ratio
box.
• If VR is the voltage drop across the
output terminal of the volt-ratio box
and VL is the voltage drop across load
then,
VL = k × VR
where k is the multiplying factor
of the volt–ratio box. 26

CALIBRATION OF VOLTMETER, AMMETER
& WATTMETER USING POTENTIOMETER
• The calibration is the process of checking the accuracy of the result by
comparing it with the standard value.
• In other words, calibration checks the correctness of the instrument by
comparing it with the reference standard.
27

CALIBRATION OF VOLTMETER
• The circuit for the calibration of the voltmeter is shown in the figure below.
28

• The circuit requires two rheostats, one for
controlling the voltage and another for
adjustment.
• The voltage-ratio box is used to step-down
the voltage to a suitable value.
• The accurate value of the voltmeter is
determined by measuring the value of the
voltage to the maximum possible range of
the potentiometer.
• The potentiometer measures the maximum
possible value of voltages.
29

Calibration of Ammeter
30
• The figure below shows the circuit for the calibration of the ammeter.

• The standard resistance is connected in
series with the ammeter which is to be
calibrated.
• The potentiometer is used for measuring
the voltage across the standard resistor.
• The below mention formula determines
the current through the standard
resistance
31

where,
Vs – voltage across the standard resistor as indicated by the
potentiometer and
S – resistance of standard resistor
• This method of calibration of the ammeter is very accurate because in this
method the value of standard resistance and the voltage across the
potentiometer is exactly known by the instrument
32

Calibrating of Wattmeter
33
• The figure below shows the circuit used for calibrating the Wattmeter.

• Wattmeter calibration is a combination of ammeter and voltmeter calibration
methods.
• Figure shows a wattmeter with its current coil connected to one dc power supply and
its voltage coil connected to another supply.
• A current limiting resistor and the standard ammeter are connected in series with
current coil, and standard voltmeter measures the voltage applied to the voltage coil.
• Once the precise voltage and current are determined for a given reading on the
wattmeter, the exact power level is determined as P=VI.
• To avoid damaging the instrument, care must be taken to avoid the specified
maximum voltage and current.
34

• The standard resistance is connected in series with the Wattmeter which is to be
calibrated.
• The low voltage supply is given to the current coil of the Wattmeter.
• The rheostat is connected in series with the coil for adjusting the value of current.
• The potential circuit is supplied from the supply.
• The volt-ratio box is used to step-down the voltage so that the potentiometer can
easily read the voltage.
• The actual value of the actual value of voltage and current is measured by using a
double pole double throw switch.
• The accurate value VI and the value of Wattmeter are compared.
36

Example:
• An electrodynamic wattmeter being calibrated indicates full scale of 120 W
on its 120V, 1 A range. The measured current and voltage are precisely 1 A
and 114 V, respectively. Determine the wattmeter error and correction
figure.
37
Solution
P = VI = 114 V x 1 A = 112 W
Error = correction figure
=114 W – 120 W = -6 W
In % Error = (-6/120) x 100% = -5%

CLASSIFICATION OF AC POTENTIOMETERS
• An ac potentiometer is same as dc potentiometer by principle.
• Only the main difference between the ac and dc potentiometer is that, in
case of dc potentiometer, only the magnitude of the unknown emf is
compared with the standard cell emf, but in ac potentiometer, the
magnitude as well as phase angle of the unknown voltage is compared to
achieve balance.
38

The following points need to be considered for the satisfactory operation of the ac
potentiometer:
1. To avoid error in reading, the slide wire and the resistance coil of an ac
potentiometer should be non-inductive.
2. The reading is affected by stray or external magnetic field, so in the time of
measurement they must be eliminated or measured and corresponding
correction factor should be introduced.
3. The sources of ac supply should be free from harmonics, because in presence
of harmonics the balance may not be achieved.
4. The ac source should be as sinusoidal as possible.
5. The potentiometer circuit should be supplied from the same source as the
voltage or current being measured.
39

• There are two general types of ac potentiometers
1. Polar Potentiometer
• As the name indicates, in these potentiometers, the unknown emf is
measured in polar form, i.e., in terms of its magnitude and relative phase.
• The magnitude is indicated by one scale and the phase with respect to
some reference axis is indicated by another scale.
Example: Drysdale polar potentiometer
40

2. Coordinate Potentiometer
• The unknown emf is measured in Cartesian form.
• Two components along and perpendicular to some standard axis are measured
and indicated directly by two different scales known as in phase (V1) and
quadrature (V2) scales (Figure).
• Provision is made in this instrument to read both positive and negative values
of voltages so that all angles up to 360° are covered.
41
Example: Gall–Tinsley and
Campbell–Larsen type potentiometer

DRYSDALE POLAR POTENTIOMETER
The different components of a Drysdale polar potentiometer is shown in
Figure.
42

• The slide wire S1 – S2 is supplied from a
phase shifting circuit for ac measurement.
• The phase shifting circuit is so arranged
that the magnitude of the voltage supplied
by it remains constant while its phase can
be varied through 360°.
• Consequently, slide wire current can be
maintained constant in magnitude but
varied in phase.
43

• The phase shifting circuit consists of two stator coils connected in
parallel supplied from the same source; their currents are made to differ
by 90° by using very accurate phase shifting technique.
• The two windings produce rotating flux which induces a secondary emf
in the rotor winding which is of constant magnitude but the phase of
which can be varied by rotating the rotor in any position.
• The phase of the rotor emf is read from the circular dial attached in the
potentiometer.
44

• Before the ac measurement, the potentiometer
is first calibrated by using dc supply for slide
wire and standard cell for test terminals T1 and
T2.
• The unknown alternating voltage to be
measured is applied across test terminals and
the balance is achieved by varying the slide
wire contact and the position of the rotor.
• The ammeter connected in the slide wire
circuit gives the magnitude of the unknown
emf and the circular dial in the rotor circuit
gives the phase angle of it.
45

• The Gall coordinate potentiometer
consists of two separate potentiometer
circuit in a single case.
• One of them is called the ‘in-phase’
potentiometer and the other one is
called the quadrature potentiometer.
• The slide-wire circuits of these two
potentiometers are supplied with two
currents having a phase difference of
90°. 46
Gall Coordinate Potentiometer

• The value of the unknown voltage is
obtained by balancing the voltages of in-
phase and quadrature potentiometers slide
wire simultaneously.
• If the measured values of in-phase and
quadrature potentiometer slide-wires are V1
and V2 respectively then the magnitude of
the unknown voltage is V = V1
2 + V2
2 and
the phase angle of the unknown voltage is
given by
q = tan
47

• W–X and Y–Z are the sliding contacts of
the in-phase and quadrature
potentiometer respectively.
• R and R' are two rheostats to control the
two slide-wire currents.
• The in-phase potentiometer slide-wire is
supplied from a single-phase supply and
the quadrature potentiometer slide-wire
is supplied from a phase-splitting device
to create a phase difference of 90°
between the two slide-wire currents. 48

• T1 and T2 are two step-down transformers having an output voltage of 6 volts.
• These transformers also isolate the potentiometer from the high-voltage supply.
• R and C are the variable resistance and capacitance for phase-splitting purpose.
• VG is a vibration galvanometer which is tuned to the supply frequency and K is the
galvanometer key.
• A is a dynamometer ammeter which is used to display the current in both the slide-wires
so that they can be maintained at a standard value of 50 mA
49

• SW1 and SW2 are two sign- changing
switches which may be necessary to reverse
the direction of unknown emf applied to the
slide wires.
• SW3 is a selector switch and it is used to
apply the unknown voltage to the
potentiometer.
50

• Operation Before using the potentiometer for ac measurements, the
current in the in-phase potentiometer slide wire is first standardized
using a standard dc cell of known value.
• The vibration galvanometer VG is replaced by a D’Arsonval
galvanometer.
• Now the in-phase slide wire current is adjusted to the standard value of
50 mA by varying the rheostat R.
• This setting is left unchanged for ac calibration; the dc supply is replaced
by ac and the D’Arsonval galvanometer by the vibration galvanometer.
51

• The magnitude of the current in the
quadrature potentiometer slide wire must be
equal to the in- phase potentiometer slide
wire current and the two currents should be
exactly in quadrature.
• The switch SW3 is placed to test position (as
shown in the Figure) so that the emf
induced in the secondary winding of mutual
inductance M is impressed across the in-
phase potentiometer wire through the
vibration galvanometer. 52

• At balance position, the current in the potentiometer wires will be exactly
equal to 50 mA in magnitude and exactly in quadrature with each other.
• The polarity difference between the two circuits is corrected by changing
switches SW1 and SW2.
53

• Lastly, the unknown voltage is applied to the potentiometer by means of the
switch SW3 and balance is obtained on both the potentiometer slide-wire by
adjusting the slide-wire setting.
• The reading of slide-wire WX gives the in-phase component (V1) and slide
wire YZ gives quadrature component (V2) of the unknown voltage.
54

Measurement of Self–inductance
• The circuit diagram for measurement of self inductance of a coil by ac
potentiometer is shown in Figure (a).
55

• A standard non-inductive resistor is connected in series with the coil under test
and two potential differences V1 and V2 are measured in magnitude and phase
by the potentiometer.
• The vector diagram is shown in Figure (b).
• Refer to this figure.
• Voltage drop across standard resistor RS, V2 = IRS
where, I= current flowing through the circuit, and RS= resistance of the
standard non-inductive resistor
56

• Voltage drop across inductive coil = V1
• Phase angle between voltage across and current through the coil = θ
• Voltage drop due to resistance of coil, IR= V1 cos θ
57

potentiometer lecture notes for RRB JE CBT2 EXAM PREPARATION

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