EI2257 TRANSDUCERS AND MEASUREMENTS LABORATORY OBJECTIVES The aim of this lab is to train the students in handling the different kinds of transducers like LVDT, Hall effect, Thermocouple etc., To impart the students an adequate knowledge and work experience of the different types of AC and DC bridges, electronic measurement methods for different electronic instruments. LIST OF EXPERIMENTS 1. Displacement versus output voltage characteristics of a potentiometric transducer. 2. Characteristics of Strain gauge and Load cell. 3. Characteristics of LVDT, Hall effect transducer and Photoelectric tachometer. 4. Characteristic of LDR, thermistor and thermocouple. 5. Step response characteristic of RTD and thermocouple and Study of smart transducers.
Transcript
EI2257 TRANSDUCERS AND MEASUREMENTS LABORATORY
OBJECTIVES
The aim of this lab is to train the students in handling the
different
kinds of transducers like LVDT, Hall effect, Thermocouple etc.,
To impart the students an adequate knowledge and work
experience
of the different types of AC and DC bridges, electronic
measurement methods for different electronic instruments.
LIST OF EXPERIMENTS
1. Displacement versus output voltage characteristics of a
potentiometric transducer.
2. Characteristics of Strain gauge and Load cell.
3. Characteristics of LVDT, Hall effect transducer and Photoelectric
tachometer.
4. Characteristic of LDR, thermistor and thermocouple.
5. Step response characteristic of RTD and thermocouple and Study of
smart
transducers.
6. Wheatstone and Kelvin’s bridge for measurement of resistance.
7. Schering Bridge for capacitance measurement and Anderson Bridge
for
inductance measurement.
8. Calibration of Ammeter and Voltmeter using Student type
potentiometer.
9. Calibration of Single-phase Energy meter and wattmeter.
10. Design, Construction and calibration of series and shunt type
ohmmeters.
CONTENTS
S.
NoNAME OF THE EXPERIMENT
Page
No
1. Displacement versus output voltage characteristics of a potentiometer transducer.
3
2. Characteristics of Strain gauge and Load cell. 9
3. Characteristics of LVDT, Hall effect transducer and photoelectric tachometer.
15
4. Characteristic of LDR, thermistor and thermocouple. 26
5. Step response characteristic of RTD and thermocouple and Study of smart transducers.
38
6. Wheatstone and Kelvin’s bridge for measurement of resistance.
43
7. Schering Bridge for capacitance measurement and Anderson Bridge for inductance measurement.
50
8. Calibration of Ammeter and Voltmeter using Student type potentiometer.
57
2
9. Calibration of Single-phase Energy meter and wattmeter. 61
10. Design, Construction and calibration of series and shunt type ohmmeters.
67
1. DISPLACEMENT VERSUS OUTPUT VOLTAGE CHARACTERISTICS
OF A POTENTIOMETRIC TRANSDUCER
Aim
To study the characteristics of potentiometric transducer.
Appartus Required
S.No Component Quantity
1.Rheostat (400 Ω/1A, 115 Ω/1A, 50 Ω/1A,)
1
2. Voltmeter (0-15 V) 1
3. RPS 1
Formula Required
% E = - K 2 (K-1) * 100
K (1-K) + Rm / RP
Where, K = Xi / X t Rm = Meter resistance in Ω
Rm = Meter resistance in Ω
Xi = Length between variable end and common end
X t = Total length of potentiometer
Eo = Xi / X t (Ei)
Theory
3
A resistive potentiometer or simply a POT is used for the purpose of
voltage division. It consist of a resistive element provided with a sliding
contact (wiper).The motion of sliding contact may be translatory or
rotationally. The translational resistive elements are straight devices and
have stroke of about 2mm to 0.5m. The rotational resistive devices are
circular in shape and are used for angular displacement. The resistive
element of a potentiometer may be excited either an a.c or d.c voltage
source. The POT is a passive transducer since it requires external power
source for its operation.
Procedure
1) To analyze the loading effect of potentiometer
1. Connections are made as shown in the circuit diagram
2. Switch on the supply and vary the potentiometer wiper.
3. The voltmeter readings are noted and the above procedure is
repeated for the different positions of the pot.
4. The graphs are plotted between i) eo / ei vs K ii) % E vs Xi
5. The above steps are repeated for the potentiometer with load
2) To analyze the characteristics of the potentiometer
1. Connections are made as shown in the circuit diagram
2. Switch on the supply and vary the potentiometer wiper.
3. The voltmeter readings are noted and the above procedure is
repeated for the different positions of the pot.
4. The graphs are plotted between displacement vs output voltage
4
5
Without load: Xt = ; Rm = ; Rp =
Sl.Noei
(volts)
eo
(volts)
Xi
(cm)K =Xi /X t eo / ei % E
With load: Xt = ; Rm = ; Rp =
Sl.Noei
(volts)
eo
(volts)
Xi
(cm)
K
=Xi /X t
eo / ei % E Load
6
Tabulation: Xt =
Sl.Noei
(volts)
eo
(volts)
Xi
(cm)
7
Result
8
2 A). CHARACTERISTICS OF STRAIN GAUGE
Aim
To study the characteristics of strain gauge
Apparatus Required
1. Strain gauge Kit
2. Unknown weights
3. Multimeter
Principle and Theory
If a metal conductor is stretched or compressed, its resistance
changes on account of fact that both length and diameter of conductor
change. Also there is a change in the valve of resistivity of the conductor
when it is strained and this property is called piezo resistive effect.
Therefore, resistance strain gauges are also known as piezo resistive
gauges.
When a gauge is subjected to positive strain, is length increases
while its area of cross section decreases .So the resistance of a conductor
is proportional to its length and inversely proportional its area of cross
section.
Resistance of Unstrained gauge R = ( ρL/A)
The gauge factor is defined as the ratio of per unit change in resistance
to per unit change in length. Gauge factor Gf = (∆R/R ) / (∆L/L)
Procedure
1. Connect the sensor fixed on the cantilever beam to the sensor
interface of the module using a 9 pin D – type connector.
2. The input excitation D.C voltage is varied and given to the bridge
circuit and the offset control adjust the output voltage when no load
is applied.
3. Gain control varies the gain of the signal conditioning. This unit is
calibrated to measure the load of ( 0 -1000) grams in terms of (0-5)
volt.
4. Load the beam to 100gram and measure the bridge output voltage.
9
5. Repeat step 5 by gradually increasing the load in steps of 100
grams.
6. Tabulate the readings and plot the graph of load Vs Output voltage.
10
Characteristics of Strain Gauge
STRAIN+Vcc
T
3
DISPLAY UNIT
11
Tabulation
S.N
o
Applied
Load(g)
Output
Voltage(V)
Display
ed
Load(g)
Strain
Result
12
2 B. CHARACTERISTICS OF LOAD CELL
AimTo study the characteristics of strain gauge load cell.
Apparatus Required
1. Strain gauge load cell
2. Display unit
3. Weights
Theory
Mechanical Load cell is a combination of an elastic member along with
the strain gauge. It consists of a cylindrical thin elastic membrane. On the
surface of this membrane strain gauges are cemented. These strain gauges
are connected in the bridge circuit. When a force is applied on the elastic
membrane the dimensions of the strain gauges change, resulting change in
the resistance. The changes in the resistance unbalance the bridge O/P. This
unbalanced O/P voltage is proportional to the applied force or weight, which
is calibrated in terms of force (kgf).
Procedure
1 When there is no load on this steel cylinder all the four gauges will
have the same resistances. Hence the output voltage will be zero. (To
adjust the calibrating screw for zero setting in display unit)
2 When an unknown weight being measured is applied on the steel
cylinder, the balancing of the wheat stone’s bridge is affected and the
change in resistance proportional to the weight is displayed.
3 For different values of unknown weight the o/p of display unit is
measured and tabulated and plot the graph between input weights Vs
output voltage.
13
14
Tabulation
Sl.NoApplied
load(gm)
Weight in
tension mode
(gm)
Weight in
compression
mode (gm)
Sl.No
Actual load
(gm)
Measured
Weight (gm)% Error
Result
15
3. A) CHARACTERISTICS OF LVDTAim
To study the characteristics of LVDT and to measure the displacement
using LVDT
Apparatus Required
1. LVDT TRAINER KIT
2. LVDT transducer set up
Theory
LVDT is the abbreviation for the Linear Variable Differential
Transformer. It is a variable inductance transducer which provides an ac
voltage output proportional to the displacement of core passing through the
windings .The transformer consists of a single primary winding P and two
secondary windings S1 & S2 wound on a cylindrical former. The secondary
windings have equal number of turns and are identically placed on either
side of the primary winding. The primary winding is connected to an a.c
source. A movable shaft iron core is placed inside the former. The
displacement to be measured is applied to the arm attached to the soft iron
core. Core is made up of high permeability, Ni iron which is hydrogen
annealed. The assembly is placed in stainless steel housing and the end lids
provide electrostatic & electromagnetic shielding. Since the primary winding
is excited by an a.c current, it provides an alternating magnetic field, which
in turn induces alternating current voltages in the secondary windings. The
O/P voltages of secondary, S1 is ES1, and secondary S2 is Es2 In order to
convert the O/Ps from S1 & S2 into a single voltage signal, the two
secondary are connected in series opposition. Thus the O/P voltage of the
transducer is the difference of the two voltages differential O/P voltage, E 0 =
E S1 - E S2.
When the core is at its normal (NULL) position, the flux linking with
both the secondary windings is equal. E S1 = E S2. Since the O/P is the
difference of the two voltages, E 0 is zero at null position. If the core is
moved left from NULL, E S1 > E S2 .so the O/P voltage is in phase with the
16
primary voltage. If the core is moved right from NULL, E S1 < E S2 .so the O/P
voltage is out of phase with the primary voltage.
Procedure
1. Connect the terminals of primary of the instruments on the front panel to
the
terminals marked primary on the transducer with the help of electric
wires.
2. Identically establish connections from terminals marked as secondary.
3. Keep potentiometer on maximum in most anticlockwise position, keep
rotary switch
SW2 in left hand position.
4.The magnetic core may be displaced and the pointer may be brought to
zero
position. If the digital panel is not indicating zero use potentiometer
marked
minimum to get a zero on DPM at zero mechanical position. If the core is
displaced
in both directions the meter will indicate the value. Now the core can be
displaced by
a known amount in the range +20mm to –20 mm.
Thus the meter reading can be entered in the table.
Block Diagram of LVDT
17
18
Block Diagram
Model Graph
Differential Amplifier
A/ D converte
rDVM
Met
er r
eadi
ng (
v)
Residual voltage (v)
Displacement (mm)
Signal conditioning
unitLVDT
Displacement
19
Tabulation
Result
Input displacement (mm) Meter reading (V)RIGHT LEFT RIGHT LEFT
20
3 B). CHARACTERISTICS OF HALL EFFECT TRANSDUCER
Aim
To Study the characteristic and performance of Hall Effect voltage
transducer
Apparatus Required
1. Hall Effect voltage transducer set up
2. Multimeter
3. Patch cards
Principle
The Hall Effect voltage transducer operates on the principle of Hall
Effect .A semiconductor carrying current develops an electro motive force
when placed in a magnetic field in a direction perpendicular to the direction
of both current and magnetic field. The magnitude of the emf is proportional
to the field intensity if the current is kept stable. The output (0 – 5v d.c) of
Hall device is signal conditioned to give a input signal ( 0 – 230 v A.C)
proportional to output signal.
Procedure
1. Plug and power card into the main a.c.
2. Put the multimeter across the terminal (0-230v a.c)
3. Vary the power and note down the d.c voltage from 0 to -5v d.c
across the terminal.
4. The readings are noted and tabulated.
5. Draw a graph between input voltage and output voltage.
21
Black diagram of Hall Effect voltage transducer
Model Graph
230
V A
C50
Hz
Hall Effect Transducer
Signal Conditioning
Precision Rectifier
Filter
Micro processor Kit
Power supply
(0-5) v DC
I/P Voltage
Out
put v
olta
ge (
v)
O/P voltage Vs I/P voltage
22
Tabulation
Sl.No Input Voltage(0-230V A.C)
Output Voltage(0-5V D.C)
Result
23
3 C). CHARACTERISTICS OF PHOTOELECTRIC TACHOMETER
Aim
To obtain the characteristics of Photoelectric Tachometer.
Apparatus required
i. Photo electric tachometer
ii. Multimeter
iii. DC motor unit.
Procedure
1. Ensure the power is off to the servomotor controller unit and pulse
ON / OFF switch is in OFF position
2. Ensure the speed feedback loop is open, so that the motor is
operated on open loop.
3. Connect the motor to the output of the power amplifier in the servo
controller through (0-2) A ammeter, connect a voltmeter (0-30) V
across the motor armature.
4. Set the controller to be proportional by connecting the I controller
input to ground.
5. Set the proportional gain Kp at minimum (unity).
6. Switch on power to the motor controllers and the pulse release switch
ON position
7. Set Vref = 1 Volt slowly increase the gain Kp voltage by means of the
proportional gain adjustment pot, and find the voltage at which the
motor just starts running.
8. Vary the reference voltage in steps, and for each step, note down the
motor speed and armature voltage. Tabulate the readings.
9. Plot the graph between Speed Vs Output voltage.
24
Model Graph (Photo Electric Tachometer)
Tabulation
S.No Speed (rpm) Output Voltage (V)
Out
put v
olta
ge (
v)
Speed (rpm)
Speed Vs Output Voltage
25
26
Result
27
4 A). CHARCTERRISTICS OF LDRAim
To design and construct the circuit to draw the characteristics of LDR
by
1. Keeping the supply voltage constant and varying the distance
2. Keeping the distance constant and varying the supply voltage
Apparatus Required
1. Autotransformer
2. Lamp 40 w
3. LDR
4. (0-5) V mc
5. RPS (0-5) V
6. IC 741
7. Resistor 1 k ohms
8. Breadboard
Theory
LDR is a photoconductive cell where conducting is function of
incident light radiation. The essential element of a photoconductive cell is
ceramic substrate (Germanium, Silicon) with a layer of photoconductive
materials like Lithium sulphide & cadmium sulphide. Metallic electrodes
connect the device into the circuit. The LDR resistance decrease with
increased intensity because of higher number of electron hole pairs
generated and the high current carriers decrease the resistance of the
material. So LDR (Light Dependent resistor) is having negative resistance
coefficient.
Design
Let R max be the resistance of LDR at dark condition and R min is
the resistance of max light intensity radiation readings of the voltmeter.
Then Rf is selected so that the voltage doesn’t exceed it.
Vo = -Rf
28
Vin Ri
V = - Rf S Ri
Rf = - V Rmin S
Procedure
1. Connections are made as per circuit diagram
2. The auto transformer O/P is varied from zero to max voltage and the
corresponding O/P voltage is taken.
3. The voltage supply to the lamp is kept constant. The distance
between the supply and LDR is varied and the corresponding change
in LDR resistance is noted down.
Graph
The graph was drawn by taking
1 Auto transformer voltage in X axis and O/P voltage in Y axis
2 Distance between LDR and lamp in the X-axis and LDR output of
resistance in Y-axis
29
Circuit Diagram for Characteristics of Light Dependent Resistor (LDR)
This active transducer made of iron and Constantan metals. There are
two junctions. One of the junctions is kept as a reference and other is
subjected to the temperature. Depending on the difference in the
temperature of the two junctions it develops on output voltage without need
of any excitation. The voltage is mill volt. This voltage is suitably signal
conditioned to give an output in volts.
AD590 Thermocouple
This is a temperature sensing element with signal conditioning
electronics, all in a single monolithic integrated circuit package. It gives
current as the output signal proportional to temperature when the signal to
be transmitted over a large distance. AD590 is a better choice as a current
signal is not affected by resistance of wire. This is a low constant or linear
device. Then the output of AD590
Iout = 1 x 10-6 T Amps Or
Iout = 273 x 10-6 + 1 x 10-6 T Amps
Where ,
T – Temperature in 0C.
35
Procedure
J- Type Thermocouple:
1. Connect the two terminals of the thermocouple to the
thermocouple input and ground point.
2. Measure the displayed voltage for in the multimeter for room
temperature.
3. Now, insert the thermocouple into the water bath to start heating it
gradually
4. Using a thermometer, measure the temperature of the
corresponding thermocouple output
Voltage
5. Repeat step 4 for different temperature of water bath.
6. Tabulate the reading & plot graph of temperature Vs thermocouple
output.
AD590 Thermocouple
1. Select the thermocouple using the switch & connect the
multimeter in volts range across T3 & ground.
2. Now, switch on the power supply to the unit and start heating the
thermocouple. Insert a thermometer in water bath.
3. Now the temperature, voltage of T3 & the displayed temperature.
4. Tabulate the readings.
5. Repeat the above procedure for AD-590 by changing the sensor
select switch by connecting the multimeter in volt range across T4
& ground.
6. Note down the reading & tabulate it.
7. Calculate the % error & plot the graph of temperature & voltage for
both the
sensor. The curves may be compared & studied for linearity &
accuracy.
36
Tabulation (Characteristics of Thermocouple)
S.No Temperatur
e (0C)
O / P
Voltage
Without
amp (mV)
O / P
Voltage
With amp
(V)
Displayed
Temperat
ure (0C)
Model Graph
o/p
volt
age
(v)
Wit
h a
mp
Temperature (0 C) 9
O/P
Vol
tage
(m
V)
o/p
volt
age
(v)
Wit
hout
am
p
Temperature (0 C) 9
37
38
Result
39
5 A). STEP RESPONSE CHARACTERISTICS OF RTDAim
To study the step response characteristics of RTD
Apparatus Required
1. IC 741, Resistor 1kΩ
2. Regulated power supply
3. RTD 4. Bread board
5. Stop watch 6. Connection wires
Theory
RTD is a temperature sensor. The principle of RTD is based on the fact
that electrical resistance of many metals almost directly increases with the
temperature. It is given by the equation Rt = Ro (1+ T )
Ro = resistance at 0 deg
T = temperature in C
= Temperature coefficient of resistance.
Procedure
1. Design a wheat stone bridge circuit with RTD at one arm.
2. Balance the bridge circuit by changing the value of the rheostat
connected at one end.
3. Immerse RTD in boiling water and temperature is read from mercury
thermometer.
4. At balanced condition RTD resistance value and other three arms are
connected with some value of R. The bridge circuit detects or
indicates 0 value. After some time the temperature raises and RTD
O/P of bridge circuit raises. The bridge circuit is connected to
instrumentation amplifier gives the values proportional to the
temperature of process.
5. For each degree of rise in temperature the change in the value of
unbalanced voltage is noted & the graph is drawn between time
interval vs temperature and time interval vs unbalanced O/P voltage.
40
Tabulation
Sl no
Time interval(Min)
Temperature C Resistance in Ohm
O/P voltage
Result
Characteristics of RTD
41
5 B). STEP RESPONSE CHARACTERISTICS OF THEMOCOUPLE
Aim
To study the step response characteristic of thermocouple.
Apparatus Required
1. Water tank
2. Heater 3. Thermocouple
4. Thermometer
5. Multimeter 6. Stop watch
Theory
Thermocouple consists of two conductors. Two different materials A, B
are joined together at one end to form a junction and this junction is heated
to a higher temperature with respect to the other end. And the principle
behind is Seeback effect, which states that "when two dissimilar metals are
connected, and if the two junctions are kept at different temperatures then
an e.m.f will be produced at the other end which is proportional to the
temperature". The voltage developed in the free ends is the measure of the
temperature and is also known as principle of thermoelectricity. Heated
terminal is called as hot junction and the other junction is called as
measuring junction.
Procedure
1. The thermocouple-measuring junction is introduced in water heating
glasses.
2. The reference is controlled to be at constant temperature of 00 C
3. Since those two junctions are at different temperature and the
voltage developed is measured with the help of voltmeter and the
mill voltmeter is calibrated suitable. So that the readings become an
indication of temperature.
4. The time interval Vs temp and time interval Vs voltage readings are
tabulated and the characteristic of thermocouple is drawn.
40
Step response characteristics of thermocouple
Model Graph
Thermo meter
Multimeter O/p voltage
Thermocouple
Heater
AC supply
o/p
volt
age
(v)
Time (Sec) Time (Sec)
Tem
pera
ture
(0 C
)
41
Tabulation
S.No Time interval(min)
Temperature (0C )
O / P voltage (mV)
Result
42
6 A) MEASUREMENT OF MEDIUM RESISTANCE USING WHEATSTONE BRIDGE
Aim
To measure the value of unknown resistance using the Wheatstone bridge and also to calculate the percentage error.
Apparatus Required
S.No Component Quantity
1. Wheatstone Bridge kit 1
2. Unknown Resistors Few
3.Regulated power supply(0 -5V)
1
4. Connecting wires Few
FormulaR4= ( R2R3 )/R1
DerivationRatio arms : ac & adStandard arm: bc
R2 & R1 Fixed resistances in Ω.R3 Standard variable resistance in Ω.R4 Unknown resistance in Ω.I1,I2, I3 & I4 Current flowing through ac,ad,bc & bd arms respectively
The bridge is balanced whenI1 R1 = I2 R2 -- 1.
If the galvanometer current is zero then the following conditions exist.I1 = I3 = E / (R1+R3) -- 2.
Also,I2 = I4 = E / (R2+R4) -- 3.
Substitute equations 2 and 3 in equation 1I1 R1 = I2 R2
[E / (R1+R3) ]R1 = [ E /( R2+R4 )] R2
R1/ (R1+R3) = R2/ (R2+R4)R1 (R2+R4) = R2 (R1+R3)
R1R2+ R1R4 = R2R1+ R2R3
R1R4 = R2R3
R4 = R2R3 / R1 Ω .Theory
43
Wheatstone bridge is used in the measurement of medium resistances. It is an accurate and reliable instrument and is extensively used in the industry. It is an instrument for making comparison measurements and operates upon a null deflection principle. This means the instrument’s indication is independent of the calibration of the null indicating instrument or any of its characteristics. Since very high degrees of accuracy can be achieved using this bridge.
Circuit Description
The bridge has four resistive arms R1, R2, R3 and R4 together with a source of emf ( a battery ) and a null detector usually a galvanometer or other sensitive current meter. The current through the galvanometer depends upon the potential difference between the points c and d. The bridge is said to be balanced when the potential difference across the galvanometer is 0V so that there is no current through the galvanometer. This occurs when the voltage from point c to point a equals the voltage from point d to point a or by referring to the other battery terminal when the voltage from point c to point b equals the voltage from point d to point b. Hence the bridge is balanced when
I1R1= I 2 R 2
R1R4=R2R3 is the expression for the balance of the Wheatstone bridge.If three of the resistances have known values then the fourth may be determined from the equation R1R4=R2R3
R4= ( R2R3 )/R1 if R4 is the unknown resistor. R3
is called the standard arm of the bridge and resistors R2 and R1 are called the ratio arms. The null detector must have sufficient sensitivity to indicate the balance position of the bridge with the required degree of precision.
Procedure
1. Connections are given as per the circuit diagram.2. The unknown resistor R4 is connected across b and d.3. The voltage in RPS is set at a particular value.4. R1 and R2 are fixed values.5. R3 is varied until the galvanometer reads zero.6. The unknown resistance can be calculated from the formula R4=( R2R3 )/R1.7. The procedure is repeated for various unknown resistances.8. The theoretical value is calculated ( by colour coding method or by using multimeter ) and the obtained practical values are compared to get the percentage error.
On solving the equation, R = ( P / Q ) S is obtained .
46
TheoryThis bridge is used to measure low resistances. It incorporates the
idea of a second set of ratio arms - hence the name double bridge - and the use of 4 terminal resistors for the low reistance arms. The first of the ratio arms is P and Q. The second set of the ratio arms p and q is used to connect the galvanometer to a point d at the appropriate potential between points m and n to eliminate the effect of connecting the lead of resistance r between the unknown resistance R and the standard resistance S. The ratio p/q is made equal to P/Q. Under balance conditions there is no current through the galvanometer which means Eab=Eamd . R =( P/Q )S is the working equation for the Kelvin Bridge. It indicates that the resistance of the connecting lead, r has no effect on the measurement, provided that the two sets of ratio arms have equal ratios. Error is introduced in case the ratios are not exactly equal. It indicates that it is desirable to keep r as small as possible in order to minimize the errors in case there is a difference between ratios P/Q and p/q. The effect of thermo-electric emfs can be eliminated by making another measurement with the battery connections reversed. The true value of R being the mean of the two readings.
Procedure
1. Connections are given as per the circuit diagram.2. Connect the unknown resistance RX
3. Switch on the power supply in the unit.4. Select the range selection switch at the point where the meter reads
least possible value of voltage.5. Vary the Potentiometer to obtain null balance.6. Switch of the unit and find out the resistance using multimeter at P17. Calculate the vale of unknown resistance using the formula
RX = (P/Q)*P1
Result
47
Circuit Diagram- KELVIN DOUBLE BRIDGE
P & Q First set of ratio armsp & q Second set of ratio armsS Standard Resistance (Ω)R Unknown Resistance (Ω)I Current flowing through the circuit (A)G GalvanometerRb Limiting resistor
Tabulation
S. No.
Q( Ω)
q( Ω)
P1( Ω)
Actual Value in
Ω(A)
Measured Value in Ω
(M)
% Error =(A-M/A * 100)
48
49
7 A) ANDERSON’S BRIDGE
Aim
The aim of this experiment is to measure the unknown value of a self Inductance using Anderson’s bridge.
Where,L1 – Self Inductance to be measured (H)R1- Resistance of self inductor (Ω). r1 – Resistance connected in series with self inductor (Ω). C – Fixed standard capacitor (F).r, R2 ,R3, R4 – Known non-inductive resistance(Ω).
Procedure
1. Connections are given as per the wiring diagram shown in fig.2. Connect the unknown inductance at L1 point.3. Keep r1 and r potentiometer in minimum position4. Connect A to A and B to B and CRO across P and Q5. Switch on the unit and vary the potentiometer r such that the
amplitude of sine wave decreases to a minimum value and then it will start increasing. At that point, stop the tuning and now vary the potentiometer r1 such that the amplitude of sine wave decreases and at one point it will go to minimum amplitude and then it will start increasing. Stop tuning r1.
6. Repeat the above procedure until the output is zero amplitude or minimum amplitude.
7. Remove the patching at r and find the resistance using multimeter and note down the reading according to the table given below and calculate the value of unknown inductance.
50
D
(0-5V)1 KHz
R2
L1
R4
C1
r1R3
ab
d
c
8. The balance condition is verified by connecting the bridge output (P&Q) to the input of audio power amplifier and the user can hear the minimum noise or no noise.
Circuit Diagram - Anderson’s Bridge
Tabulation
Sl.No
C (μF
)
R2
(Ω)R3
(Ω)R4
(Ω)r
(Ω)r1 (Ω)
Inductance L1
(mH) % ErrorMeasur
edActual
Result
51
52
7 B) SCHERING BRIDGE
Aim
The aim of this experiment is to measure the unknown value of a capacitor using a Schering bridge.
Where , C1 = Capacitor whose capacitance is to be determined ( F ).C2 = standard capacitor ( F ). C4 = variable capacitor ( F ). R3 = non-inductive resitance (Ω). R4 = variable non-inductive resistance in parallel with C4 (Ω).
Theory
Schering Bridge is an ac bridge extensively used for the capacitance measurements. Although it is used for the capacitance measurements in
53
general sense, it is particularly useful for measuring the insulating properties ie, for the phase angles very nearly 90 degrees. The standard arm 2 contains only a capacitor. Arm 4 contains a parallel combination of a resistor and a capacitor. The inspection of the circuit shows a strong resemblance to the comparison bridge. The standard capacitor is usually a high-quality mica capacitor for a general measurement work or an air capacitor for the insulation measurements and hence it is loss free. However it is necessary , a correction can be made for the loss angle of this capacitor . A good quality mica capacitor has a very losses ( no resistance ) and therefore a phase angle of approximately 90 degrees. An air capacitor when designed carefully, has a very stable value and a very small electric field ; the insulating material to be tested can be easily kept out of any strong fields. The balance conditions require that the sum of the phase angles of arms 1 and 4 equals the sum of the phase angles of arms 2 and 3 . Since the standard capacitor is in arm 2 the sum of the phase angles of arm 2 and 3 will be 0+90 = 90 degrees. In order to obtain the 90 degree phase angle needed for balance, the sum of the angles of arm 1 and arm 4 must equal 90 degrees, it is necessary to give arm 4 a small capacitive angle by connecting capacitor C4
in parallel with R4 . A small capacitive angle is R4 .
Procedure
1. Connections are made as per the wiring diagram show above.2. Connect the unknown capacitance at the C1(unknown ) point3. Keep R4 in minimum position4. Connect A to A and B to B5. Connect the CRO across P and Q6. Switch on the unit and vary R3 (above 2K is suggested)7. Choose C2, such that a maximum variation of output is obtained8. Vary the Potentiometer R4 such that the amplitude of sine wave
decreases and at one point it will go to a minimum of zero amplitude and then it will start increasing. Stop tuning at that point and switch off the unit.
9. Remove the patching at R4 and find the resistance using multimeter and note down the reading according to the table given below and calculate the value of unknown capacitance.
10. The balance condition is obtained by connecting the bridge output (P&Q) to the input of audio power amplifier till the minimum noise or no noise is heard.
54
55
D
(0-5V)1 KHz
C2
C1
R4
C4
R1R3
ab
d
Circuit Diagram - Schering Bridge
Tabulation
S.No C2 (μF)
R3 (Ω)
R4 (Ω) Capacitance C1 (μF)% Error
Measured(M)
Actual (A)
Result
c
D
(0-5V)1 KHz
C2
C
R4
C4
R1R3
ab
d
c
56
8 A) CALIBRATION OF AMMETERAim
To calibrate an Ammeter using 10 wire potentiometer
Apparatus Required
1. Ammeter2. 10 wire potentiometer3. Variable Power Supply.
Formula
True Value = Vin * l/L
Vin – Supply Voltage ( volts)
L – Total Length of potentiometer
l- length of wire at which balance condition is obtained.
Correction = (I-I0)
I- True Value of current
I0 - Measured value of current.
% Error = (I – I0 ) / I * 100
Theory
The magnitude of the error and consequently the correction to be applied is determined by making a periodic comparison of PMMC meter with standards which are known to be constant. The entire procedure laid down for making, adjusting or checking a scale is such that the readings of an instrument or a measurement system confirm an accepted standard called calibration. The given ammeter is calibrated by comparing the readings of the meter with the true value using 10 wire potentiometer.
Procedure1. Connections are given as per the circuit diagram.2. The supply is given to the potentiometer3. The contact is made on the potentiometer and length is noted 4. The current for the corresponding length is noted.5. True value is calculated using the formula.6. Error is calculated using the above data.
Circuit Diagram - CALIBRATION OF AMMETER
57
Tabulation
S.No Ammeter reading (Io)
Base length (l)
True value (I)
Correction (I-Io)
% Error
Result
58
8 B) CALIBRATION OF VOLTMETERAim
To calibrate a voltmeter using 10 wire potentiometer
Apparatus Required
1. Voltmeter2. 10 wire potentiometer (Rheostat)3. Variable Power Supply.
Formula
True Value = Vin * l/L
Vin – Supply Voltage ( volts)
L – Total Length of potentiometer
l- length of wire at which balance condition is obtained.
Correction = (V-V0)
V- True Value of current
V0 - Measured value of current.
% Error = (I – I0 ) / I * 100
Theory
The magnitude of the error and consequently the correction to be applied is determined by making a periodic comparison of PMMC meter with standards which are known to be constant. The entire procedure laid down for making, adjusting or checking a scale is such that the readings of an instrument or a measurement system confirm an accepted standard called calibration. The given ammeter is calibrated by comparing the readings of the meter with the true value using 10 wire potentiometer.
Procedure1. Connections are given as per the circuit diagram.2. The supply is given to the potentiometer3. The contact is made on the potentiometer and length is noted 4. The current for the corresponding length is noted.5. True value is calculated using the formula.6. Error is calculated using the above data.
Result
59
Circuit Diagram - CALIBRATION OF VOLTMETER
Tabulation
S.No Voltmeter reading (Vo)
Base length (l)
True value (V)
Correction (v-Vo)
% Error
60
9 A) CALIBRATION OF SINGLE PHASE ENERGY METER
Aim
The aim of this experiment is to calibrate a single phase energy meter by actual loading.
Components Required
1. Voltmeter (0 - 300) V MI.2. Ammeter (0 - 5) A MI.3. Wattmeter (1500W, 5 / 10A).4. Energy Meter (230) V.5. Stop Watch.6. Lamp Load.7. Connecting wires
Formula
Measured Value = No.of revolutions / Energy meter Constant% Error = [( Calibrated Reading - Actual Reading ) / Calibrated Reading] * 100.
Energy Meter Constant:1kwh = 1200 rev.5 rev = (1000 * 3600 * 5) / 1200 = 15,000ws.
Procedure1. The connections are given as per the circuit diagram.2. The load is applied by switching the lamps and the corresponding voltage, current and energy are noted.3. At the initial condition the wattmeter reading is noted.4. The time required for the 5 revolutions is noted by using the stop
watch.5. The same procedure is repeated for various loads.6. The percentage error is calculated from the formula:% Error = (W2 - W1) / W2
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