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Southeast University School of Science and Engineering Department of Computer Science &Engineering Program: B.Sc. in CSE Course Code: PHY1034 Course Title: Physics Laboratory Course Credit: 1.0, Prerequisite: None

Laboratory Experiment Sheet Course Teacher: Ishrat Jahan

Experiment #: 01 Experiment Title: Determination of the specific resistance of a wire using a meter bridge Objectives: 1. To understand Wheatstone bridge and verify Wheatstone bridge principle. 2. To correlate the principle of Wheatstone bridge with meter bridge experiment. Theory: A meter bridge is the practical application of Wheatstone bridge arrangement as shown in figure below. The four resistances are connected to each other as shown and if the bridge is in balanced state, i.e., there is no deflection in the galvanometer (G), P/Q = R/X

This relation is used to find the unknown resistance of the given material of wire. The unknown resistance 'X' can be found by meter bridge which uses the principle of Wheatstone bridge. The unknown resistance 'X' of the given wire is obtained by relation:

⇒

l X = R (100−l ) Rl X= (100−l) …. (1)

If L is the length of the experimental wire and r is the radius of the wire then, ρL X= πr 2

⇒ ρ=

Xπr 2 L …. (2)

List of Equipment: Apparatus 1. Metre bridge 2. DC power supply 3. Galvanometer 4. Resistance box 5. Jockey

6. One way key 7. A resistance wire 8. Screw gauge 9. Metre scale 10. Connecting wires

Circuit Diagram:

Procedure: ● Make the connections as per the circuit diagram. ●Connect the resistance wire in the left gap (between c & d) and resistance box in the right gap. ●Introduce some resistance in the circuit by taking out some resistance from the resistance box. ●Plug the key. Bring the jockey in contact with the end A first, and then with C. Note the deflection on the galvanometer.

●If the galvanometer deflects in the opposite direction, the connections are right and the null point is in between A and C. ● If not so, change the resistance in the resistance box and repeat the process so that the null point is somewhere between A and C. ●If the galvanometer deflected towards a single side, then check the connection. ●Now, slide the jockey slowly over the wire starting from one and (say, A) and note the galvanometer deflection. Continue the process till the balancing point is reached. ●Balancing point is the point at which the galvanometer shows zero deflection. Now, note the position of the jockey from end A. Take it as the balancing length (l) using the meter scale. ●Repeat the process for different values of R. The balancing length is measured each time. ●Calculate the unknown resistance of the resistance wire by using the equation (1). ●Measure the diameter of the given resistance wire using a screw gauge. Hence, its radius(r) can be found. Also measure the length (L) of the wire using a meter scale. From the measured values, the specific resistance (resistivity) of the given resistance wire can be calculated using the equation (2).

Data Collection: Table1: Determination of unknown resistance, X. No of observation s

Balance Point

Known Resistance

R (ohm)

l (cm)

Unknown Resistance 100-l (cm)

X=

Rl (100−l)

(ohm) 1 2 3

Mean Resistance, X 1+ X 2+ X 3 X= 3 (ohm)

Table2: Determination of the radius of the wire, r No of readings

Linear Scale Readings,

Circular Scale Division,

N

n

Least Count

(cm)

(cm)

Corrected circular Scale Reading (n ×L.C) (cm)

Total Reading (T.R=L.S.R+C.S. R) (cm)

Diameter,d Radius (Mean d r= reading) 2 (cm) (m)

1 2 3

Length of the wire, L= ……………m.

Calculation:

Specific resistance of the wire,

ρ=

Xπr 2 L

= …………… ohm-m. Result: The unknown resistance of the given resistance wire, X = ……...... Ω The specific resistance (resistivity) of the given resistance wire, ρ = ……...... Ω m. Experiment #: 02 Experiment Title: Determination of the resistance of a galvanometer by half-deflection method. Objectives: 1. To understand the various components used in the experiment. 2. To be able to construct circuits based on circuit diagrams. Theory: A galvanometer is a device used to detect feeble electric currents in a circuit. It consists of a coil suspended between the poles of a powerful magnet. As current passes through the coil, it deflects. It can be detected from the deflection on galvanometer needle. The deflection is proportional to the current passed through it.

Here, current will flows through the circuit when key K 1 is closed and K2 is open. The current flowing through the galvanometer is proportional to the deflection in it.

Where, E =emf of the cell R = resistance from the resistance box G = galvanometer resistance for current I θ = galvanometer deflection for current I k = proportionality constant. When K2 is closed and by adjusting the shunt resistance S, we can make galvanometer deflection as θ/2. Then the current in the circuit is;

Now, a fraction, S/ (G+S) of the current in the circuit is flows through the galvanometer, which is given by,

Now, from the above relations, we can get the resistance of the given galvanometer as,

List of Equipment: Apparatus 1. Zero centre galvanometer 2. DC power supply 3. Two resistance boxes 4. Two one way keys.

5. Connecting wires, Procedure:          

Make the connections accordingly as shown in the circuit diagram. Make sure that plugs of the resistance boxes are tight. Take out a high resistance (say2000 ohm) from the resistance box 1 and insert the key k1. Adjust the resistance from this resistance box to get maximum galvanometer deflection. Note the deflection and record it as θ in the tubular column. Insert the key K2 also, without changing the value on the resistance box. Now, adjust the resistance from the low resistance box such that galvanometer shows deflection which is exactly half of the previous reading. Record the value of low resistance box. We can repeat the experiment by changing the value of high resistance R and adjusting low resistance S. The resistance of the given galvanometer can be calculated each time by using the relation G= RS/(R-S)

Data Collection: 

Table1: Determination of resistance of the galvanometer. No.

of obs.

Resistanc e R (ohm)

Deflection in the galvanometer, θ

Shunt resistance

Half deflection

Galvanomete r

S (ohm)

θ/2

Resistance

G=

RS ( R−S )

(ohm) 1

2 3

Mean G (ohm)

Calculation: 

Calculate the value of G in each case and record it in the tabular column. The mean of these calculated values will give the resistance of the given galvanometer.



Result:



The resistance of the galvanometer is……...... Ω

Experiment #: 03 Experiment Title: Determination of acceleration due to gravity (g) by a compound pendulum. Objectives: 1. To understand gravitational acceleration by means of a compound pendulum. Theory: Compound pendulum is a rigid body of any shape free to turn about a horizontal axis. When the body oscillates about a hole from one end or the corresponding hole from the other end, then the time periods are the same. Then the time period of oscillation T is found from the following relation,

T =2 π √ L/g L ⇒ g=4 π 2 2 T By finding L graphically, and determining the value of the period T, the acceleration due to gravity ‘g’ at the place of the experiment can be determined. List of Equipment: Apparatus 1. A bar pendulum 2. A precision stop watch 3. A meter scale Procedure: ● Find out the centre of gravity G of the bar. ●Insert a metal wedge in the first hole in the bar towards A and place the wedge on the support S1S2 so that the bar can turn round S. ●Set the bar to oscillate taking care to see that the amplitude of oscillations is not more than 5◦. Note the time for 20 oscillations. ●Measure the length from the end A of the bar to the top of the first hole i.e., up to the point of suspension of the pendulum.

●In the same way, suspend the bar at holes 2, 3, ……… and each time note times for 50 oscillations. Also measure distances from the end A for each hole. ● When the middle of the bar is passed, it will turn round so that the end B is now on the top. But continue measuring the distances from the point of suspension to the end A. ●Now calculate the time period T from the time recorded for 20 oscillations. ●On a graph paper, plot a curve with length as abscissa and period T as ordinate with the origin at the middle of the paper along the abscissa. Data Collection: Table1: Determination of time period, T Position

Hole No.

End A

1

Distance from end A

Time for 20 Oscillations

Time Period

2 3 4 End B

1 2 3 4

Calculation: From the graph, AC= …………………. cm BD= ………………….. cm

AC + BD 2 Mean length, L =

= ……………….cm Corresponding time period, T =………………….. s

g=4 π 2 Acceleration due to gravity

L T 2 = …………… cm s-2 = …………….. m s-2

Result: cceleration due to gravity, g= ……….. ms-2 Experiment #: 04 Experiment Title: Determination of the moment of inertia of a fly wheel about its axis of rotation. Objectives: 1. To measure the angular velocity of a flywheel. 2. To use the conservation of energy to calculate its moment of inertia.

Theory: The flywheel consists of a heavy circular disc/massive wheel fitted with a strong axle projecting on either side. The axle is mounted on ball bearings on two fixed supports. There is a small peg on the axle. One end of a cord is loosely looped around the peg and its other end carries the weight-hanger. Let a mass M, attached by means of a string to the axle of a fly-wheel of radius r, the moment of inertia of which, about its axis of rotation is I. The length of the string is such that it becomes detached from the axle when mass strikes the floor. In falling a distance h, the potential energy of the mass has been converted into kinetic rotational and translation energy. If ω be the maximum angular velocity of the wheel, F the amount of work done against friction per revolution and n1 the number of revolutions made while the mass falls the distance h, the loss in potential energy of M=gain in kinetic energy of M+ gain in K.E. of fly wheel+ work done against friction. Mgh=1/2 Mr2ω2+1/2 I ω2+n1F……… (1) After the mass strikes the ground the wheel executes a further n 2 revolutions and the angular velocity gradually decreases to zero. The rotational kinetic energy Iω 2 has been used up in overcoming frictional forces, hence Fn2=1/2 I ω2………. (2)

If n2 revolutions take a time t, then the average angular velocity ωa is given by

ωa=

2 πn 2 t

Since the angular velocity decreases uniformly from a maximum ω to minimum of zero, the average angular velocity ωa is also given by

Also the motion is uniform, hence

ω= i.e.

4 πn2 t

ω 2 πn2 = t 2

.. .. .. . .. .(3)

From equations (1), (2) and (3) it follows that

I=

2 Mgh− Mω 2 r 2 n1 ω 2 ( 1+ ) n2 ……….. (4)

List of Equipment:

ωa=

ω +0 ω = 2 2

Apparatus 1. Flywheel 2. Weights 3. Cord 4. Stop-watch 5. Meter scale 6. Slide calipers Diagram:

Procedure: ● Put the loop at one end of the cord round the peg P on the axle a weight Mg at the other end. Wrap the cord round the axle by rotating the wheel until the weight is at A just below the rim. ● Mark a point H on the rim of the wheel in order to count the number of revolutions of the wheel. ● Allow the weight to go down till it rests on the upper surface B of the floor on the ground. Adjust the length of the cord in such a way that at this position of the weight the cord just slips off the peg P. Thus the weight will fall from A to B trough a height h=A’B’ just before the gets detached from the peg p. ●Rotate the wheel again till the weight is raised to the position A. Allow the weight to fall and count the rotation n1 made by the wheel by observing the mark H on its rim while the weight falls from the position A to B. ●Wind up the thread again till the weight is at the position A. Allow the weight to descend. Start a stop-watch just when the cord slips off the peg and count the number of rotations n2 made by the wheel before it comes to rest and record the time t taken for the purpose. ● Use two different masses and take three observations in each case.

vii) Measure the diameter of the axle at two mutually perpendicular directions and determine the radius r. 4 πn2 ω= t ●Use equation for determining the angular velocity and equation 2 2 2 Mgh − Mω r I= n1 ω 2 ( 1+ ) n2 for calculating moment of inertia.

Data Collection: Table1: Determination of n1, n2 and t No of obs.

Mass M (g)

Height H (cm)

No. of revolution s n1

Mean n1

No. of revolution s n2

Mean n2

Time t (s)

Mean t (s)

Table2: Determination of the radius, r Position of scale

Horizonta l reading Vertical reading Calculation:

No. of obs.

M.S. V.S. reading reading (cm)

V.C (cm)

Excess by Vernier (cm)

Total for the Diamete rD (cm)

Radius Mean r=D/2 Radius (cm) r (cm)

Mean Radius r (cm)

For the mass of ----------------------g

ω=

4 πn2 t

I1 =

2 Mgh − Mω 2 r 2 n1 ω2 (1+ ) n2

For the mass of ----------------------------g

ω=

4 πn2 t

I2 =

2 Mgh − Mω 2 r 2 n1 ω2 ( 1+ ) n2

For the mass of ----------------------------g

I3 =

2 Mgh−Mω2 r 2 n1 ω2 (1+ ) n2

I= The moment of inertia of the fly wheel is,

I 1+ I 2+ I 3 3

g-cm2

Result: The moment of inertia of the given fly wheel is ------------------- g-cm2

Experiment #: 05 Experiment Title: Calibration of a polarimeter and determination of the specific rotation of a sugar solution by means of a polarimeter. Objectives: 1. To understand the interaction of plane polarized light with solutions of chiral substances. 2. To understand various processes and techniques involved in measuring the optical activity of sugar solutions using polarimeter. 3. To understand the step-by-step procedure including most details from preparing the sample to identification of sugar solution used as part of the experiment. Theory: The angle of rotation produced to the plane of vibration by an optically active substance, in solution or otherwise, is proportional to (i) The thickness of the medium (solution) (ii) The concentration of the solution or the density of the active substance in the solvent and (iii) The nature of the substance.

Thus θ ∞ l.c or θ= s l.c

s=

θ lc

where θ is the angle of rotation produced, l is the length (or thickness) of the substance in decimeter, c is the concentration in gm/cm3 of the solution and s is a constant called specific rotation and depend upon the nature of the substance. If =1decimeter and c=1gm/cm3 then specific rotation may defined as the rotation produced while traversing a path of one decimeter (10 cm) length in the solution containing 1 gm of the optically active substance per cm3 of the solution (density in unity). Then, Rotation produced by1decimeter length of the solution Specific Rotation= -------------------------------------------------------------------Density of the solution in g/cc

θ 10 θ l/10 = = c lc where the length l is expressed in centimeters. The amount of rotation also depends upon (a) the temperature and (b) the wavelength of the light used. So for a given temperature and a given wavelength

S tλ =

10 θ lc …………. (1)

The specific rotation of dextrorotatory substance is taken as positive while that of a laevorotatory substance is considered negative. Now the angle of rotation (θ) for different values of known concentrations (c) of a solution can be measured with the help of a polarimeter. If a graph is plotted with θ against c, then the graph will be a straight line. The polarimeter is thus calibrated. Taking then the solution of an unknown concentration, the rotation of the plane of polarization produced by the solution can be measured and from the graph, its concentration can be determined. Again, using equation (1), the value of the specific rotation of the solution can also be determined.

List of Equipment: Apparatus 1. Polarimeter 2. A balance 3. Measuring cylinder 4. Sugar 5. Sodium lamp

Diagram:

Procedure: ● Examine the circular scale in contact with the analyzer and find its vernier constant. Obtain the zero reading of the instrument. ● Carefully weight out 20 g of sugar in a watch glass; dissolve it 100 g or 100 c.c. of distilled water. Make up the solution of 20%.During the dissolving do not apply any heat just pour the solution from one vessel to another so that the solution has a uniform concentration. ● Carefully measure the length of the tube. Clean the tube as well as the glass plates used to close its ends. Filter some distilled water so that it becomes free from dust and fill the tube with it. Take care so that no air bubble is introduced. Close the tube. ● Place the tube with its contents horizontally on two V supports between the analyzer and polarizer so that it is coaxial with the telescope. Focus the eye piece of the telescope so that on the field of view of the polarizer any line dividing it may be seen clearly. Rotate the analyzer so that the field of view is completely and uniformly bright. Read the position of the analyzer of the circular scale. Repeat the operations for at least three times and take the mean of these three readings. Call these readings P. ● Remove the tube, empty it and rinse it with a little of the prepared solution. Carefully fill the tube completely with the solution. Take care not to have any air bubble inside the tube. Clean the ends and replace the tube in the position and allow it to stand there for sometimes so that the temperature becomes uniform all throughout the solution. See through the telescope, the uniform brightness is disappeared. Rotate the analyzer till the uniform brightness is appeared as like before. Repeat the operation for at least three times and take the mean of these three readings. Call it Q. (Q~P) is the angle through which the polarization has been rotated. Calculate the specific rotation. ● Next repeat the operation for with 15% and 10% sugar solution respectively and collect the corresponding data which has been described previously. ● Draw a graph between the percentages (strengths) of the solution and the corresponding angle of rotations. This should be a straight line. Take a point P on the graph well away from the origin. Find the values of θ and c corresponding to this point. Calculate the specific rotation of the solution using equation (1). The unknown strength of a solution can also be determined from the graph by noting the angle of rotation produced by the unknown solution.

Data Collection: V.C. of the circular scale =0 .1 mm Length of the tube,l = ………………………….cm Table1: Determination of angular rotation strength of No. of obs. sugar solution (percent)

First reading with water (p)

Second ...