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Lab Manual
Digital Logic Design
CEN-220
BAHRIA UNIVERSITY,ISLAMABAD CAMPUS
APPLIED PHYSICS
LIST OF EXPERIMENTS
Lab No. Title
Lab 1 Measurements Using Vernier Scale 3
Lab 2 Measurements Using Screw Gauge 6
Lab 3 Simple Pendulum 8
Lab 4 Seconds Pendulum 10
Lab 5 Measuring Current and Voltage 11
Lab 6 Finding Rheostat’s Resistance Value 13
Lab 7 Construction of Series and Parallel Circuits 14
Lab 8 To Find Out Frequency of A.C. mains by Melde’s Apparatus 16
Lab 9 To Determine the Rigidity Modulus of the given Wire by
Dynamical Method 20
Lab 10 To Determine Young’s Modulus of Material of a (helical) Spring 22
Lab 11 To Determine Time Constant of RC Circuits 24
Lab 12 To Convert a Galvanometer into Ammeter 26
Lab 13 To Determine Modulus of Rigidity of Material of a Thick Wire by Static
Method 28
Lab 14 To Find the Low Resistance by Carey Foster’s Bridge 31
Lab 15 To Determine Frequency of A.C. mains Using Sonometer 35
Lab 16 To Convert a Galvanometer into Ammeter 38
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Lab 1
Measurement using Vernier Scale
OBJECTIVE:
In this lab we are going to use vernier caliper to measure length of any object.
DESCRIPTION:
Most common measuring instruments have a simple scale. For example in using a ruler, the ruler is placed next to the item being measured and the mark closest to the end of the item is recorded. If we want increased precision, we use a ruler with finer divisions on the scale, that is a smaller instrument least count. This is suggested in Figure 1.
The ability to use high precision scales is limited by the spacing between the marks. Thus it is easy to have a least count of 1 mm, more difficult to have a least count of 0.2 mm, and virtually impossible to have a least count of 0.002 mm (a human hair has a diameter of about 0.050 mm.) In order to increase precision we need an auxiliary scale called a vernier scale.
Every measuring instrument has a least count. The least count is the least distance that can be accurately measured using the instrument. The smallest division on a meter rule is 1 mm. Here we use the convention that the least count of a measuring instrument is the smallest division marked on the instrument. Thus the least count of a meter rule is 1 mm.
A vernier is designed to improve the accuracy of measurement. A vernier consists of a main scale and a vernier scale.
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The vernier scale can move along the main scale. The vernier scale is constructed by taking 9 divisions of the main scale and dividing them into 10 equal parts. One main scale division = 1 mm
One vernier scale division = mmThe difference between one main scale division and one vernier scale division is:
= .
This is the least count of the vernier.
When length of an object is measured using a vernier, the vernier gets pushed along the main scale so that one end of the object is at the zero of the main scale and the other end at the zero of the vernier. At this point the zero of the vernier has gone past a main scale reading. We take this and record it as the main scale reading. Look at the vernier divisions carefully and see which of the vernier divisions coincide with one of the main scale divisions. Using these two measurements, obtain the actual length of the object as:
Actual length = main scale reading + vernier scale reading least count.
The main scale works just like a ruler: the 0-mark on the vernier is compared to a main scale and the result is written down. Use the mark next to the zero, not the mark next to the edge of the vernier. Be sure to record the value of the main scale mark that is just to the left of the vernier zero mark as is shown in the above diagram. That is, record the value of 3.3 cm rather than 3.4 cm, even though the answer is closer to 3.4 cm.
Now look closely at the vernier scale in Figure 2. Notice that 10 divisions on the vernier match 9 divisions on the main scale. This guarantees that one of the vernier markings will line up exactly with a mark on the
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main scale. Decide which vernier mark comes closest to matching a main scale mark, in our example this is vernier mark 8. Combine the two readings to give the final length of 3.38 cm. Material Main scale
reading (m)vernier scale reading
vernier scale reading × least count (m)
Actual length (m)
1 2 Ave 1 2 ave
Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6
Sheet 7
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Lab 2
Measurement using Screw Gauge
OBJECTIVE:
In this lab we are going to use screw gauge to measure length and diameter.
DESCRIPTION:
Every measuring instrument has a least count. The least count is the least distance that can be accurately measured using the instrument. The smallest division on a meter rule is 1 mm. Here we use the convention that the least count of a measuring instrument is the smallest division marked on the instrument. Thus the least count of a meter rule is 1 mm.
The micrometer screw gauge consists of a circular scale and a linear scale. When the screw is rotated the circular scale moves over the linear scale. The distance moved by the circular scale along the linear scale for one rotation of the screw is called the pitch of the screw. The least count of the micrometer is given by:
Density of a material is given by:
It is measured in kg.m-3. When the screw is completely in, the zero of the circular scale should be at the zero of the linear scale and coincide with the horizontal line. If the zero is above the horizontal line, you have a negative error and this error needs to be added to the final reading of the circular scale. If the zero of the circular scale is below the horizontal, you have a positive error and this needs to be subtracted from the final reading of the circular scale.
Obtain the error in your micrometer reading and record it.
From the zero position, turn the screw 10 times and measure the distance moved by the circular scale along the linear scale. Divide this distance by 10 and that will be the pitch of the screw.
Obtain and record the pitch of the screw.
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Look at the round scale and obtain the number of divisions on it. Calculate the least count of the micrometer as:
When the object to be measured is placed in position, the circular scale is pushed back along the linear scale. Read and record the linear scale reading.
Read and record the circular scale reading.
The actual length = linear scale reading + circular scale reading least count.
Readings:
Material Linear scale reading (m)
Round scale reading
Round scale reading × least count (m)
diameter (m)
Radius(m)
1 2 Ave 1 2 Ave
Cylinder 1
Cylinder 2
Cylinder 3
Wire
Sphere 1
Sphere 2
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Lab 3
Simple Pendulum
OBJECTIVE:
In this lab we are going to measure time length of a simple pendulum.
DESCRIPTION:
The period of oscillation of a simple pendulum is given by
where l is the length of the pendulum and g, the acceleration due to gravity. This equation can also be written as:
Figure 1: A simple pendulum
Hold a split cork tightly using a clamp with a string passing through the split cork. Tie the pendulum bob to one end of the string leaving the other end free after passing through the split cork. The length of the
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pendulum l is measured from the bottom of the split cork to the center of the bob. Set up a pendulum of length 0.1 m and set it into oscillations of small amplitude. Measure the time taken for 10 complete oscillations. Do this three times and obtain the average time for 10 oscillations. Divide this average time by 10 to obtain the period of oscillation. Repeat the experiment for l = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 m. Record your data as follows:
l (m) Time for 10 oscillations T(s)
T2
(s2)t1 (s) t2 (s) t3 (s) Average (s)
0.10.20.30.40.50.60.70.80.91.0
Lab 4
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Seconds Pendulum
OBJECTIVE:
In this lab we are going to find out length of a pendulum by assuming its time length.
DESCRIPTION:
In this lab we will assume a time length for a pendulum and will get length of the pendulum by using this formula:
Now, after finding its length we will repeat the same procedure as in previous lab and will find out its Time Length.
Lab 5
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Measuring Current and Voltage
OBJECTIVE:
In this lab we are going learn that how to measure resistance, current and voltage.
DESCRIPTION:
Plug in the Electronics Trainer and switch it ON. Turn both voltage control knobs fully counter clock wise to zero position.
Set up the digital multimeter selector range knob to measure voltage of at least 10Volts.
Attach the positive lead of the multimeter to the positive voltage terminal of power supply of the Trainer. Similarly attach the common lead of the multimeter to the ground terminal of power supply of the Trainer and rotate the knob to such a point at which meter reads approximately positive 10Volts.
Again attach the positive lead of the multimeter to the negative voltage terminal of power supply of the Trainer. Similarly attach the common lead of the multimeter to the ground terminal of power supply of the Trainer and rotate the knob to such a point at which meter reads approximately negative 10Volts.
Now construct a circuit by connecting a resistor of 10kohm to the positive and ground terminals of the power supply.
Attach the multimeter across the resistor to measure the voltage and note the value of voltage reading on the multimeter as shown in figure 1.
Turn off the power supply of the Trainer after measurement.
Now again turn ON the power supply of the Trainer. Connect the multimeter with the resistor to measure the current. Open the circuit and connect the positive lead of multimeter against the positive terminal of power supply through resistor and connect the common lead of multimeter to the ground terminal of power supply and note the value of current reading on the multimeter as shown in figure 2.
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Turn off the power supply of the Trainer after measurement.
Lab 6
Finding Rheostat’s Resistance Value
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OBJECTIVE:
In this lab we are going to use a rheostat and find its value using a circuit.
DESCRIPTION:
We can construct the following circuit using a rheostat.
1. Setup the circuit, Rh is the rheostat (variable resistance).
2. The current in the circuit is changed by varying the rheostat resistance Rh. This is done by sliding the rider to a new position. Activate the circuit and take three different readings of the ammeter and the voltmeter corresponding to the different rheostat settings. Be sure to use one scale setting for the three data points.
3. Record the resistance of the multimeter for the scale setting used in the acquisition of the data.
4. Repeat step 2 and 3 and record data in Data Table.
TABLE :
Rheostat Setting V ( Volts) I (Ampere) R (ohms)
1
2
3
Lab 7
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Construction of Series and Parallel Circuits
OBJECTIVE:
In this lab we will be constructing series and parallel circuits.
DESCRIPTION:
Series Circuits:1. In the simple series circuit, all components are connected end to end from only one path for current to
flow from one end of circuit to the other end as shown in figure 1.
2. It is a voltage Divider circuit, the total voltage applied to the circuit is divided into the voltage drops across each component connected in the circuit, in series circuit voltage drops across each component added up are equal to total voltage applied.
3. The total current passing through the circuit is same as the currents passing through the each component connected in the circuit, in series circuit currents passing through each component is equal to total current passing through circuit.
4. The total resistance of the circuit is divided into the resistances of the each component connected in the circuit, in series circuit resistances of each component added up is equal to total resistance of the circuit.
5. The equivalent resistance of resistors in series circuit is expressed as:
Req = R1+R2+R3……Rn
Parallel circuits:
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1. In the simple parallel circuit, all components are connected between the same two sets of electrically common points, creating multiple paths for current to flow from one end of the circuit to the other end as shown in figure 2.
2. It is a Current Divider circuit, the total current passing through the circuit is divided into the currents passing through each component connected in the circuit, and in parallel circuit currents passing through each component added up are equal to total the total current passing through the circuit.
3. The total voltages applied to the circuit is same as the voltage drops across the each component connected in the circuit, in parallel circuit voltage drops across each component is equal to total voltage applied to the circuit.
4. The total resistance of the circuit is greater than the resistances of the each component connected in the circuit, in parallel circuit resistances of each component added up is not equal to total resistance of the circuit.
5. The equivalent resistance of resistors in parallel circuit is expressed as:
1/Req = 1/R1+1/R2+1/R3……1/Rn6. Note that when only two resistors are connected in parallel, the above equation reduces to:
1/Req = 1/R1+1/R2 → Req = R1×R2 / R1+R2
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Lab 8
To Find Out Frequency of A.C. mains by Melde’s Apparatus
OBJECTIVE:
To determine the frequency of AC mains by Melde’s experiment.
DESCRIPTION:
When a string under tension is set into vibrations, transverse harmonic waves propagate along its length. When the length of string is fixed, reflected waves will also exist. The incident and reflected waves will superimpose to produce transverse stationary waves in the string. The string will vibrate in such a way that the clamped points of the string are nodes and the point of plucking is the antinode.
A string can be set into vibrations by means of an electrically maintained tuning fork, thereby producing stationary waves due to reflection of waves at the pulley. The loops are formed from the end of the pulley where it touches the pulley to the position where it is fixed to the prong of tuning fork.
(i) For the transverse arrangement, the frequency is given by:
where ‘L’ is the length of thread in fundamental modes of vibrations, ‘ T ’ is the tension applied to the thread and ‘m’ is the mass per unit length of thread. If ‘p’ loops are formed in the length ‘L’ of the thread, then
(ii) For the longitudinal arrangement, when ‘p’ loops are formed, the frequency is given by
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Procedure:
1. Find the weight of pan P and arrange the apparatus as shown in figure.
2. Place a load of 4 To 5 gm in the pan attached to the end of the string
3. Passing over the pulley. Excite the tuning fork by switching on the power supply.
4. Adjust the position of the pulley so that the string is set into resonant
5. Vibrations and well defined loops are obtained. If necessary, adjust
6. The tensions by adding weights in the pan slowly and gradually. For finer adjustment, add milligram weight so that nodes are reduced to points.
7. Measure the length of say 4 loops formed in the middle part of the string. If ‘L’ is the distance in which 4 loops are formed, then distance between two consecutive nodes is L/4.
8. Note down the weight placed in the pan and calculate the tension T.
9. Tension, T= (wt. in the pan + wt. of pan) g
10. Repeat the experiment twine by changing the weight in the pan in steps of one gram and altering the position of the pulley each time to get well defined loops.
11. Measure one meter length of the thread and find its mass to find the value of m, the mass produced per unit length.
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OBSERVATIONS AND CALCULATIONS:
For longitudinal arrangement
Mass of the pan, w =……… gm
Mass per meter of thread, m =……… gm/cm
Mean frequency= ---------------- Hzs
For transverse arrangement
Mass of the pan, w =……… gmMass per meter of thread, m =……… gm/cm
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Mean frequency= ---------------- Hzs
PRECAUTIONS:
1. The thread should be uniform and inextensible.2. Well defined loops should be obtained by adjusting the tension with milligram
weights.3. Frictions in the pulley should be least possible.
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Lab 9
To Determine the Rigidity Modulus of the given Wire by dynamical method
OBJECTIVE:
To determine the rigidity Modulus of the given wire by dynamical method
DESCRIPTION:
A heavy cylindrical disc suspended from one end of a fine wire whose upper end is fixed constitutes a Torsional pendulum. The disc is turned in its old plane to twist the wire, so that on being released, it executes torsional vibrations about the wire as axis. Let be the angle through which the wire is twisted. Then the restoring couple set up in it is equal to
Where -------- is the twisting couple
per unit (radian) twist of the wire.This produces an angular acceleration (dw/dt) in the discTherefore if “I” is the moment of inertia of the disc about the wire we have:
I.
i.e the angular acceleration ( ) of the angular displacement() and therefore its motion is simple
harmonic hence time period is given by
T= 2π -----------------------
From &
In case of a circular disc whose geometric axes coincide with the axis of rotation. The moment of inertia “I” is given by
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2
1 2
2 2
I=
where M is the mass of disc and “R” is the radius of the disc. Plot a curve for l Vs T2 and calculate the slope.
× Slope dynes/cm2
Sl.NoLength of Wire l ( cm)
Time for 20 oscillationTime Per one oscillationT= (t/20)
Trial1 Trail2 Mean (t) T T2
4 40
2 60
3 80
4 100
5 120
Precautions:
1. while using vernier calipers see that the readings must be taken without any parallax error
2. Measure the thickness of wire using screw guage
3. Note the disc should be rotated along with its own axis.
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Lab 10
To Determine Young’s Modulus of Material of a (helical) Spring
OBJECTIVE:
We are going to determine the Young’s modulus of the material of a spring by recording its time period of oscillation when loaded by a certain weight.
DESCRIPTION:
First , our aim is to measure the radius of the spring and the wire. We use a screw gauge to measure it. After taking a number of readings, we take the mean which gives us the best approximation. Then, the length of the wire is measured with a meter-scale. On dividing the length by the radius, we get the number of turns. Now, we fix our spring to a clamp and hang weights from it with the assumption that the weights are along theaxis. This induces an oscillation in the spring along the vertical plane. We take a stopwatch and measure the time taken for completion of 20 oscillations from which we deduce the time period (T) of oscillation. The weights are known to us. Hence, making use of the formula we deduce a number of readings for the Young’s modulus.
The mean gives us the best value of the Young’s modulus. A spring of radius R is made out of a wire of length rather mass hanging from the end be M. Force Mg exerts a couple tending to twist the wire and N is the number of turns in the spring.
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Calculations:
As , circular scale zero coincides with linear scale zero , there would not be any over-estimation or underestimation in circular scale.
where L.S.R is the Linear Scale Reading, C.S.R is the Circular Scale ReadingTotal length=L+C×0.01mean radius=mean diameter/2
S. No. Weight (gms)
Time for 20 Osc.
Time Period (sec) Mean ή (N/m2)
123
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Lab 11
To Determine Time Constant of RC Circuits
OBJECTIVE:
To determine the time constant ‘τ’ of the circuit by charging and discharging.
DESCRIPTION:
The basic circuit for charging and discharging a capacitor is shown in fig 1. If switch S1 is closed keeping S2 open, then the battery charges the capacitor and current flows through the resistor R until the capacitor is fully charged. If the charge on the capacitor at time t is q(t) , then the voltage across the capacitor C is q/C and the current through R1 is i = dq/dt . By applying Kirchhoff’s second law.
iR1 + (q/C) = ε → R1(dq/dt) + (q/C) = ε …………..(1)
which has the solution
………………….. (2)
Where q0 = Cε
The quantity t = R1C is the charging time constant which characterizes the rate at high charge is deposited on the capacitor .As t → ∞, eq (2) shows that q →Cε_ = q0. In Practice the Capacitor charges to its maximum value q0 after a time interval equal to a few time constants. Once the capacitor is fully charged then the current i through the resistor become zero.
At this point if the switch S1 is opened and S2 is closed the charge in the capacitor discharges through the resistor R2. By Kirchhoff’s second law:
with solution (taking q = q0 at t = 0)
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Thus the charge on the capacitor decays exponentially with time. In fact after a time t=R2C (equal to the discharging time constant) the charge drops from it’s initial value q0 by a factor of e-1.
Observations and results :Part A: Measurement of time constant for discharging of a capacitorR2 = ________________________C = ________________________
S. No. Discharging time (t sec) Current I (µA)1 02 103 204 305 406 507 608 709 8010 90
Results:
The value of time constant measured t = __________________ secThe value of time constant calculated t = R2C = ___________________ sec
Part B: Measurement of time constant for charging of a capacitorR1 = ________________________C = ________________________
S. No. Charging time (t sec) Current I (µA)1 02 103 204 305 406 507 608 709 8010 90
Results:
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The value of time constant measured t = __________________ secThe value of time constant calculated t = R2C = ___________________ sec
Lab 12
To Convert a Galvanometer into Ammeter
OBJECTIVE:
To convert galvanometer into ammeters of different ranges, which can be used to measure the currents in electrical circuits.
DESCRIPTION:
A galvanometer is a device used to detect the flow of the current, but not to measure. Because its scale is not marked in amperes, though its deflection is proportional to the current. Being the sensitive instrument, galvanometer cannot be used to measure large currents, because it may cause damage to the coil of the galvanometer.In order to avoid this damage and to use it as an ammeter, a low resistance is connected in parallel to the galvanometer.
As a result, even if a large amount of current is sent in the main circuit, only a very small fraction of it passes through the galvanometer. The scale is calibrated in amperes, for the total current, so as to read the current directly. To measure the current, the ammeter must be connected in series in the circuit.
The value of shunt resistance (RS) depends upon the fraction of the total current required to pass through the galvanometer. Connect the circuit as shown in the figure. The variable power supply connected gives the required potential difference to the circuit, to send the required current through the ammeter. Also select and connect the required shunt resistance Rs, across or parallel to the galvanometer, such that the galvanometer shows full deflection for the required range of current. Then the galvanometer is said to be converted into an ammeter of required range. By increasing the supply voltage, the galvanometer reading is increased in steps of 5 divisions, starting from zero, the corresponding ammeter readings are noted, in the table.
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Table
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Lab 13
To Determine Modulus of Rigidity of Material of a Thick Wire by Static Method
OBJECTIVE:
To determine the value of modulus of rigidity of the material of a wire by statical method using vertical pattern apparatus (Barton’s apparatus).
DESCRIPTION:
The vertical pattern of torsion apparatus (Barton’s apparatus)shown in figure is used for specimen available in the form of a long thin rod, whose upper end is fixed securely to a heavy metallic frame and lower end is fixed to a heavy metal cylinder C. This heavy cylinder keeps the wire vertical. Flexible cord attached to two diametrically opposite pegs on the cylinder leave it tangentially diametrically opposite points after half a turn. These cords pass over two frictionless pulleys P1 and P2, fixed in the heavy frame, and at their free end carry a pan each of equal weight. When equal loads are placed on the pans, couple acts on the cylinder which produces a twist in the rod. The twists are measured by double ended pointer which moves over the concentric circular scales graduated in degrees. The three leveling screws are provided at the base of the metallic frame supporting the rod, to make it vertical. In this case the centers of the scale fall on the axis of the rod.
The modulus of rigidity (h) is defined as the ratio of shearing stress to shearing strain.The shearing stress is the tangential force F divided by the area A on which it is applied and the shearing strain is the angle of shear f.
Procedure:
1. Level the base of the Barton’s apparatus by the levelling screws at the base using spirit level so that the wire hangs freely vertically and can be twisted without any friction.
2. Wind the thread around the thick cylinder as shown in Fig. 3.3(b), pass the two ends over the pulleys and attach the pans to them.
3. Take readings of the pointers on the circular scale with no weights on the pans.4. Add weights of 10 gm on each pan and take the readings again, repeating this until the total weight
on each pan is 50 gms. Take readings again while the weights are reduced to zero.
5. Measure the diameter of the wire using the screw gauge and the diameter of the thick cylinder using vernier caliper.
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6. Take readings of diameters along the entire length in mutually perpendicular directions to correct for any departure from uniform or circular cross-section (some places the area is elliptical hence we measure many places).
7. Measure the length of the wire which is being twisted.8. Using the vernier callipers measure the diameter of the metallic cylinder.
Figure 1: Rigid Apparatus
Observations: (A) Table for the measurement of angle of twist (q):
Mean deflection angle for 30 gm load = _______ radian.
(i) The wire should not be twisted beyond elastic limits(ii) Table for the measurement of diameter of the given wire.
Least count of screw gauge =Zero error = ±
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S. No. 1 2 3 4 5 6 7 8 9 10 MeanDiameter in one direction (in cm)Diameter perpendicular to above (in cm)Diameter of wire corrected for zero error =Radius r =(iii) Table for the measurement of diameter of the given cylinderLeast count of vernier callipers =Zero error =S. No. 1 2 3 4 5 6 7 8 9 10 MeanDiameter in one direction (in cm)Diameter perpendicular to above (in cm)Diameter (D) of cylinder corrected for zero error =(iv) Length of the wire l =
For Calculation of Modulus of Rigidity:
Precautions:
1. First of all base of the instrument should be levelled using sprit level.2. The wire must be of uniform circular cross-section, free of links, hanging freely and vertically,
firmly clamped at the top.3. Too much weight must not be put on the pans; else the wire may twist beyond elastic limit.4. The wire should be trained before the readings are taken.5. The radius of the wire must be taken carefully since its fourth power is occurring in the formula.6. The pulleys should be frictionless.7. Load should be increased of decreased gradually and gently.8. The chord wound round the cylinder should be thin and strong.9. Before starting experiment ensure that the upper end of the rod is firmly clamped. 10. If it is not so, the rod may slip at this end on application of load.11. The length of the wire, it measured between the two clamps.
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Lab 14
To Find the Low Resistance by Carey Foster’s Bridge
OBJECTIVE:
We are going to determine the value of an unknown resistance using Carey Foster Bridge to take into account the specific resistivity (ρ) of the bridge wire.
DESCRIPTION:
The Carey Foster Bridge is an electrical circuit that can be used to measure very small resistances. The aim of the experiment is to determine the resistance per unit length, ρ of the Carey Foster bridge wire and hence to find the resistance of a given wire of low resistance. The experimental circuit diagram for the experiment is shown in Figure 1. There are four gaps in this arrangement. The standard low resistances, P and Q, of 2 Ω each are connected in the inner gaps 2 and 3. The known resistance, i.e., the fractional resistance box X and the unknown resistance Y whose resistance is to be determined are connected in the outer gaps 1 and 4, respectively. A one meter long resistance wire EF of uniform area of cross section is soldered to the ends of two copper strips. Since the wire has uniform cross-sectional area, the resistance per unit length is the same along the wire. A galvanometer G is connected between terminal B and the jockey D, which is a knife edge contact that can be moved along the meter wire EF and pressed to make electrical contact with the wire. A lead accumulator with a key K in series is connected between terminals A and C.
Figure 1: Circuit Diagram For the Carey Foster Bridge
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The galvanometer when the jockey is pressed to make electrical contact with the wire; this position is called the balance point or null point. The bridge has its highest sensitivity when all four of the resistances, P, Q, X and Y, have similar magnitudes. The four points A, B, C and D in Figure 1 exactly correspond to the points labeled A, B, C and D in the circuit diagram of Wheatstone’s bridge in Figure 1, and thus the Carey Foster Bridge effectively works like a Wheatstone’s bridge. If the balance point is located at a distance l1 from E, then we can write the condition of balance as
where α and β are the end corrections at the left and right ends. These end corrections include the resistances of the metal strips to which the wire is soldered, the contact resistances between the wire and the strips, and they also allow for the non-coincidence of the ends of the wire with the zero and one hundred division marks on the scale. If the positions of X and Y are interchanged, i.e., X is put in gap 4 and Y in gap 1, and the balance point is found at a distance l2 from E, then the balance condition becomes:
By simplifying the above equations, we have:
Y = X – (l2 – l1)ρ
This relation shows the difference between the known and unknown resistance is equal to the resistance of the bridge wire between the two balance points. Once we know X, l2, l1and ρ, we can determine the unknown resistance Y.
Procedure:
1. Make the circuit connections as shown in Figure 3. In this part of the experiment Y is a copper strip that has negligible resistance and X is a fractional resistance box. You need to (a) ensure that the wires and copper strip are clean and the terminals are screwed down tightly, (b) remove any deposits from the battery terminals and (c) close tightly all of the plugs in the resistance box; these precautions will minimize any contact resistance between the terminals and the connecting wire.
2. Plug in the battery key so that a current flows through the bridge. Note that you should remove the battery plug when you are not taking measurements so that the battery does not become drained.
3. Press down the jockey so that the knife edge makes contact with the wire, and observe the galvanometer deflection. Release the jockey.
4. Move the jockey to different positions along the wire and repeat step 3 at each place until you locate the position of the null point, where there is no deflection of the galvanometer. This point should be
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near the middle of the bridge wire. Take care that the jockey is pressed down gently to avoid damaging the wire and distorting its cross section, and do not move the jockey while it is in contact with the wire.
5. Note the balancing length, l1, in your laboratory notebook, using a table with the layout shown in Table 1.
6. Reverse the connections to the terminals of the battery and record the balancing length for reverse current in the table in your notebook. By averaging readings with forward and reverse currents, you will be able to eliminate the effect of any thermo emfs.
7. Take out the plug from the fractional resistance box that inserts a resistance of 0.1 Ω, and repeat steps 3 – 5.
8. Increase resistance X in steps of 0.1 Ω and repeat steps 3 – 5 each time.
9. Interchange the copper strip and fractional resistance box, and repeat steps 3 – 5 for the same set of resistances. The corresponding balancing lengths, measured from the same end of the bridge wire, should be recorded as l2 in your data table.
10. Remove the copper strip and insert the unknown low resistance in one of the outer gaps of the bridge. 11. Repeat the entire sequences of steps as described in the procedure from 1 to 9. Record your
measurements in your laboratory notebook. A suggested format is shown in Table 2.
Observations
Table 1: Determination of ρ for Carey Foster bridge wire
S. No.X / Ω
Position of balance point with copper strip in the
l2 – l1/ cm
ρ = X / (l2 – l1) / Ω
right gap, l1 / cm left gap, l2 / cmdirect
currentreverse current
meandirect
currentreverse current
mean
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Table 2: Determination of an unknown low resistance using a Carey Foster bridge.
S. No.X / Ω
Position of balance point with copper strip in the
l2 – l1/ cm
ρ = X / (l2 – l1) / Ω
right gap, l1 / cm left gap, l2 / cmdirect
currentreverse current
meandirect
currentreverse current
mean
Calculations:
1. Determine an average value for (l2 – l1) for each value of X from each row of data in your version of Table 1.
1. Then calculate values of ρ for the bridge wire from these values of (l2 – l1), using the formula ρ = X / (l2 – l1).
2. Use these results to calculate a mean value of ρ in SI units. 3. Use Equation (8) to calculate a value of the unknown resistance Y from each row of data in your
version of Table 2. 4. Then use these results to calculate a mean value of Y.
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Lab 15
To Determine Frequency of A.C. mains using Sonometer
OBJECTIVE:
We are going to determine the Frequency of A.C. mains using Sonometer.
DESCRIPTION:
A sonometer consists of a wooden box AB about 1 metre long. Italso carries a wire of uniform cross-section and made of non-magnetic material usually brass. One end of this wire is fixed to a peg at one end of the box. This wire after passing over a pulley at the other end of the box carries a hanger at the other end. Tension is produced in the wire by placing suitable load on this hanger. There are three knife-edge-bridges over the box. Two of them are fixed near the ends of the box while the third one, can be slided along the length of the wire supporting it. The vibrations of the wire alone can not produce audible sound. But the sound box helps in making this sound louder. When wire vibrates, these vibrations are communicated to the box and the enclosed air in it. Since the box has a large surface and volume it produces sufficient vibrations in air to make it audible. A permanent horse-shoe magnet is mounted vertically in the middle of the wire with wire passing between its poles. The magnet produces a magnetic field in the horizontal plane and perpendicular to the length of the wire. When the alternating current from mains after being stepped down to 6 or 9 volt is passed through the wire, it begins to vibrate in vertical plane. By adjusting the position of the bridge resonance can be obtained.
Procedure:
1. Arrange the apparatus as shown in Figure 1.2. Put some weights on the pan and the magnet on the board between the bridges in such a position
as to produce magnetic field at right angles to the wire.3. Connect the primary of the step-down transformer to A.C. mains.4. Now vary the position of the bridges slowly and symmetrically with respect to the magnet till a
stage is reached when the wire vibrates with maximum amplitude. This is the position of resonance. Measure the distance between bridges. Repeat this step 3 or 4 times to find mean value of l.
5. Repeat above steps with load on the hanger increasing in steps of 100 gm till maximum allowable limit is reached. Corresponding to each load find mean l.
6. Repeat the experiment with load decreased in the same steps in which it was increased.7. From readings with increasing and decreasing load find mean value of l corresponding toeach
load.8. Weigh the specimen wire, measure its length and hence calculate its linear density.
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Figure 1: Barton’s apparatusObservations:
1. Measurement of ‘T’ and ‘l‘Mass of the pan =
S. No.Total Load (Including
hanger M gms.)
Length in resonance I ‘cm’Mean Length
Load Inreasing Load Decreseaing
1
2
3
4
5
2. Measurement of ‘m’—(i) Mass of the specimen wire = gm(ii) Length of the specimen wire = cm
Calculations: Linear density of the wire m = gm/cm
Results: Frequency of the AC mains is found to be = cycles/sec or Hertz.Standard value = 50 HzPercentage error = ...... %
Precautions and sources of error:
1. The wire from which the pan is suspended should not be in contact with any surface.2. Use choke to limit the current or wire may burn out.3. The wire may be uniform and free from kinks and joints.
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4. The magnetic field should be at center of vibrating loop and must be perpendicular to the length of the wire.
5. The material of the sonometer wire should be non magnetic.6. The bridges used should give sharp edges to get the well defined nodes.7. The weights should be removed from the wire otherwise the wire may develop elastic fatigue.8. In order that the tension in the cord may be exactly equal to the weight suspended, there should be
no friction at the pulley.
Lab 16
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To Convert a Galvanometer into a Voltmeter
OBJECTIVE:
We are going to convert galvanometer into voltmeters of different ranges which can be used to measure the potential differences in electrical circuits.
DESCRIPTION:
A galvanometer can be converted in to a voltmeter by connecting a high resistance (R) in series with the galvanometer as shown in the figure. The value of resistance (R) connected in series decides the range of the voltmeter. The scale is calibrated in volts, so as to read the potential difference directly. To measure the potential difference between two points, the voltmeter must be connected in parallel across those two points in the circuit. When a high value of resistance is connected in series to the galvanometer, only a small fraction of the total current will flow through the galvanometer. So, this does not cause any damage to the galvanometer. More over, as the current flow in the galvanometer, which is connected in parallel in the circuit, is very small, it causes no effect in the current of the main circuit.
Figure: Galvanometer Conversion into Voltmeter
Procedure: -
1. Connect the circuit as shown in the above figure. The variable power supply connected gives the required potential difference to the circuit.
2. Now select and connect the required resistance (R) in series with the galvanometer, to convert the galvanometer into voltmeter of required range.
3. The selection of the resistance that should be connected in series to the galvanometer is in such away that the galvanometer shows full deflection for the required range.
4. By increasing the supply voltage, the galvanometer reading is increased in steps of 5 divisions, starting from zero, the corresponding voltmeter readings are noted, in the table.
TableVoltmeter range = VValue of resistance connected in series to galvanometer = _
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S. No.Galvanometer reading
(n divisions)Volt Meter Reading
(V)
1
2
3
4
Precautions: -
1. The series resistance should be so selected such that for the required range of voltmeter, the galvanometer shows full the deflection with in the scale.
2. The continuity of connecting terminals should be checked before going to the experiment.
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