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PHYSICS 1 SPH 2170 A1PRECISION MEASUREMENTS- Objectives:

To study some of the instruments and methods used in precision measurements , and to compute the

volume and density of various items.

Apparatus: Metre rule, vernier calipers ,micrometer screw gauge ,electronic balance and traveling microscope

.Such items as copper cylinder , steel ball and glass capillary tube are also supplied.

METHOD: The experiment comprises e measurement of the various objects supplied with the

appropriate instruments. Where feasible, at least two instruments should be used for each measurement and

the precision obtained in each case compared. In this way, the volume and density of atleast two metal

objects weighings should be done on the electronic balance.

In the second part of the experiment, some electrical circuits have been set up for you to measure the current.

Measure the current using an ammeter, a milliammeter and a microammeter, and estimate the reading errors in

each case.

N.B. in all cases an estimate of the precision obtained should be, i.e. note the reading errors on all

measurements. Where appropriate note the zero error.

Record the data in work sheet 1,working out any calculations asked for. Answer the questions posed on the

sheet.

WORKSHEET 1 N.B. You must include in the table the units of any measurements you take.

ITEMS MEASURING INSTRUMENTS

Met

er

rule

Verni

er

calip

ers

Micromete

r Screw

Gauge

Bala

nce

Amm

eter

Milli

Ammet

er

µA

scope

Travelling

Microscope

X Y Z

Zero error

Reading

error

Copper

cylinder:

mass

height

Diameter

(external)

Diameter

(internal)


Steel Ball:

Diameter

Copper

wire: length

Diameter

glass rod:

diameter

length

Current

scope voltage

signal height

peak-peak height

peak height=

Analysis :

volume Density of the material

Copper cylinder: Internal volume

External volume

Steel bar

Glass rod

Calculation of voltage:

Instrument Value of Resistances

Calculated V= IR

From Ammeter

From Milli-Ammeter

From µA

scope voltage signal sensitivity= voltage = sensitivity x height

ERRORS Now work out the errors in volumes and densities and voltages calculated above using the reading errors of the

appropriate instruments. Refer to the section on errors in this manual for instructions on how to calculate errors.


volume Density of the material

Copper cylinder: Internal volume

External volume

Steel bar

Glass rod

Instrument calculated V= IR From Ammeter

From Milliammeter

From µA

from scope

QUESTIONS:Why is it appropriate to use the metre rule for measuring the length of the copper wire

but the micrometer screw gauge for he diameter?.What is the difference between accuracy and precision?

CONCLUSION:The volume of the copper cylinder was found to be --------------------------------------------

---------(units) ,and its density was found to be------------------------ ------------------- ------------ (units)Write

similar conclusions for the steel ball `and capillary tube , and give correct values for the densities of

copper and steel . The values may be found in the reference book Tables of physical and chemical

constants,15th Edition , G.W.C. Kaye.and Labye (Longman 1986 )


HARMONIC MOTION-A7

introduction:

If an object is strained and released (or if an impulse is delivered), it will oscillate periodically about its

equilibrium or rest position. Examples of such objects are a saw blade clamped at one end, a mass attached to a

spring, a mass attached to a rod (torsional oscillations), musical string instrument; drum head, spider’s web,

eardrum, and a car body (oscillates vertically on its springs).

If during the oscillation, the elastic restoring force has a magnitude, which is proportional to the

displacement from the equilibrium position and a direction such as to restore the object to that equilibrium

position, then the motion is simple harmonic.

In this exercise you are going to perform a set of experiments to illustrate simple harmonic motion using

a spiral spring.

Apparatus

Spiral spring to which a light pointer is attached by plasticine at its lower end, rigid stand and clamp, meter rule,

scale pan and weights, stop watch.

a) To find the spring constant

If a spring is stretched a distance x which is not too large then the Hooke’s law states that the spring exerts a

force F which is proportional to x:

F = -kx………(1)

Where k is the force constant of the spring.

Method

The spring, with scale pan attached, is firmly clamped and the meter scale placed vertically so that the pointer

moves slightly over it (Fig 1). Place weights on the scale pan and measure the stretch produced in each case.

The scale readings are also taken when unloading the spring and the mean stretch thus obtained. Loads less than

1kg should be used as more may permanently deform the spring. Plot the magnitude of the spring force (load)

versus the stretch of the spring.

Fig.1


Question 1:

Is your graph describable by Hooke’s law? If so, determine the spring constant k.

Question 2:

Does your graph pass through the origin? If not, explain why.

Question 3:

From your graph what is the change in elastic potential energy of the spring when the load is increased from

0.5kg to 0.7kg?

b) To determine the acceleration of gravity (g) and the effective mass if the spring

Theory:

If a mass m is attached to a spring and the spring is extended by a further distance x a restoring force kx

is called into play. The spring on being released executes vertical oscillations the motion of the mass being

Md2x/dt2 = -kx

i.e. d2x/dt2 + kx/M =0…. (2)

The motion is thus simple harmonic with periodic time T given by

T = 2π√ M/k…(3)

The above analysis assumes the spring to be weightless. In practice the spring has a mass and therefore a

correction has to be made to equation (3) to include the ‘effective’ mass of the spring.

Method:

A load is added to the pan, which is set in vertical vibration by giving it a small additional displacement. The

periodic time T is obtained by timing 20 oscillations. Repeat the experiment with different loads. Plot a graph of

T2 versus load and then find the values of g and m from it. Note that the mass of the scale-pan should be

included in the load in this experiment. Experimental errors must also be included.

Question 4:

Weigh the spring using a balance. What would you expect the effective mass of the spring to be using this

measured value? Compare it with the one obtained from the graph.

Question 5:

What is the percent discrepancy between your value of g and the expected value?

Damped Simple harmonic motion:

Theory:

For a real mechanical system the amplitude decreases with time and the motion is called damped simple

harmonic. The decrease in amplitude is due to friction and the energy of oscillations eventually dissipated as

thermal energy. The damping force is often proportional to the velocity of the mass but in the opposite

direction. Newton’s second law applied to the oscillator yields the equation of motion for the mass M:

F = -kx – bdx/dt = Md2x/dt2

So that, d2x/dt2 + b/M X dx/dt + kx/M = 0 …(5)

Where b is a positive constant, called the damping constant (Fig.2)

For a lightly damped harmonic oscillator the equation of motion is given by


X (t) = Ao e-bt/2M cos (ωt - Φ)…(6)

Where the periodic of oscillation is given by

T = 2π/W = 2π ……(7)

√ (k/m – (b/2M) 2)

Amplitude is A = Aoe-bt/2M…(8)

Method

Hang a medium size mass from the spring. Displace the mass from its equilibrium position by a

fairly large amount but do not exceed the linear portion of the spring. Release the mass and simultaneously start

the timer, then measure the amplitude and the time for after every 10 complete oscillations. Obtain 10 or more

measurements and be sure to keep the timer running; hence you will measure amplitude as a function of time.

Using equation (8) plot a suitable graph connecting amplitude and time such that a straight line

would be expected.

Calculate the damping constant b from your graph.

Note

Remember to include the effective mass of the spring. If the scale pan was used include its mass in the load.

Question 6:

From equation (7) calculate T’ and its error.

Question 7:

In exp 5.1 it was assumed that damping was absent or at worst negligible. Obtain from the results of that

experiment the value for the period corresponding to the mass that was used in exp 5.3. Call it Texp

(experimental period). Now, calculate the theoretical periods T and T’ from equations (3) and (7) respectively.

Compare the values of Texp, T and T’. Which theoretical period, T or T’, yields the smaller percent discrepancy?

Discuss your results.

Question 8:

What is the percent discrepancy between T and T’. Is damping important with regard to the period?

Fluid

Fd V Fs

K


REFRACTIVE INDEX- B9 LAWS OF REFRACTION

Aim: 1. Determination of refractive index of glass and water by

plotting (graphical method) (glass)

apparent depth method (water)

A. PLOTTING (GRAPHICAL METHOD)

APPARATUS

ABCD is a rectangular glass block.P1, P2, P3 and P4 are pins on a drawing board and paper.

P

E B

C D

A

F

P1

r

i

i


Method

1. Place a rectangular glass block on a paper on the drawing board.

2. Draw line P as shown in the figure.

3. Look in along the direction of P1 and P2 until the image of line P through the glass is in line with the pins.

4. Remove the pins and mark their positions on the paper.

5. Repeat the procedure for 5 more lines namely Q, R, S, T, and U. To get pins P3 and P4, P5 and P6, P7 and P8

P9 and P10 and P11 and P12. Make sure you mark the positions of the pins precisely.

6. Draw the outline of the glass block on the drawing paper.

7. Remove the glass block and pins from the paper.

8. Draw the normals at points E and F and join E&F.

9. Measure the angles i and R with a protractor, and calculate the refractive index. Repeat this for 5 more times

and plot a graph of sin i/sine r and get the refractive index of glass. Also calculate for each set of data sin

i/sin r and get their average value. Compare this with the one obtained from plotting.

i Sin i r Sin r Sin i/sin r

B. APPARENT DEPTH METHOD

Apparatus

Glass or Perspex block B, traveling microscope M, lycopodium powder L and beaker.

(fig (a)). fig (b)).

r1

r2

r3


Method

Place the beaker B on a sheet of paper P and arrange the travelling microscope so that the microscope M and the scale s are vertical . Put a pin on the

bottom of the beaker. Focus the microscope M on the pin. Having achieved a sharp focus using the fine adjustment screw take the reading r3 (fig (c)).

of the vertical scale of the microscope.

NOW almost fill the beaker B with water. Move the microscope down until the pin seen through the water is in sharp focus. Take the reading r2

fig

(b)). of the vertical scale of the microscope.

Focus the microscope M on the upper surface of the water which is sprinkled using a little lycopodium powder L or chalk dust if necessary Having

achieved a sharp focus using the fine adjustment screw take the reading r1

(fig (a)). Of the vertical scale of the microscope.

Repeat the procedure above for 5 more different depths of water and fill the table below.

Measurements r

1 (mm) r

2 (mm) r

3 (mm) (r

1-r

2) (mm) (r

1-r

3) (mm)

1.

2.

3.

4.

5.

6.

Draw a graph of (r1-r3) (mm) versus (r1-r2) (mm) and find n for water graphically.

Conclusion:

The refractive index of water is: Apparent method:…………+ ….%.

The refractive index of glass is: Plotting method:…………+ ….%.

H18HEAT CAPACITY OF METAL BLOCK & SPECIFIC HEAT CAPACITY OF OIL

BY MIXTURES

i. HEAT CAPACITY OF A METAL BLOCK

ii. SPECIFIC HEAT CAPACITY OF OIL, BY MIXTURES

APPARATUS

Large mass of metal (about 0.2kg) A, beaker B, copper calorimeter C in insulating jacket D, copper stirrer E,

tripod, gauze, burner, chemical balance, weights, oil (e .g paraffin or castrolite), thread, stop-watch,

thermometer 0-100oC

(fig (c)).

heat

A

C

D

E


i. HEAT CAPACITY OF METAL

METHOD

Fill the beaker B with some water, place the metal A inside it, and boil the water, meanwhile, weigh the

calorimeter and stirrer, fill it a bout one-half with tap water, and re-weigh. Take the temperature of the water in

the calorimeter. Take the temperature of the boiling water, and then quickly transfer metal A to the water in the

calorimeter C. Observe the water temperature every 10s until it reaches a maximum and then drops several

degrees below the maximum reached.

MEASUREMENTS

Mass of calorimeter + stirrer m1 (c1 =… Jkg-1K-1) =…kg

Mass of calorimeter + stirrer + water m1 + mass of A =…kg

Initial water temperature t1 =…0C

Final temperature observed =…0C

Final temperature, corrected for cooling t2 =…0C

Temperature of boiling water t =…0C

COOLING CORRECTION

This may be obtained by a graphical method, as explained 0n p. 49. An alternative method is as follows:

Suppose it took a time x for the water to reach its final temperature when the hot metal was dropped in; then,

approximately, the cooling correction is the temperature drop from the maximum temperature in a time x/2.

Since a metal is a good conductor, it gives up its heat quickly, and the cooling correction may therefore be

negligible.

CALCULATION

Heat lost by metal = Heat gained by water and calorimeter + stirrer. If C is the heat capacity of the metal and m

the mass of water of specific heat capacity

Cw(=4200Jkg-1K-1), then

CONCLUSION

The heat capacity of the metal was…JK-1

ERRORS

1. Heat lost by the hot metal on transferring it to the calorimeter;

2. Some hot water is carried over with the metal;

3. Observations of the temperature (e. g. 16.4+ 0.20c) and mass (e. g 194+ 194.6+ 0.1 x 10-3kg )

ORDER OF ACCURACY

ii. SPECIFIC HEAT CAPACITY OF OIL

METHOD


Add some water to the beaker, place the metal A inside it, and heat the water until it boils. Meanwhile weigh the

calorimeter, fill it about one-half with the oil, and re-weigh. Observe the oil temperature. Take the temperature

of the boiling water, and then quickly transfer A to the oil. Observe the time taken for the oil to reach its

maximum temperature, and then find the temperature drop c, in half this time. This is the cooling correction

MEASUREMENTS

Mass of calorimeter m1+ stirer (c1 =…Jkg-1K-1) =…kg

Mass of calorimeter + oil m1 + stirrer +Mass of A =…kg

Initial oil temperature t1 =…0C

Final temperature, corrected for cooling t2 =…0C

Temperature of boiling water t =…0C

Heat capacity of metal (C) ~ from previous experiment =…JK-1

CALCULATION

Heat loss by metal = Heat gained by oil and calorimeter. If c is the oil’s specific heat capacity and m is the mass

of the oil, then with m and m1 in kg, calculate c from

H x (t-t1) = (mc + m1c1) (t2 – t1)

CONCLUSION

T he specific heat capacity of the oil was…Jkg-1K-1.ERRORS AND ORDER OF ACCURACY

W4 THE RIPPLE TANK

AIMS: The aims of this experiment are:

1. To observe the characteristics and behavior of water waves.

2. To show the analogy between water waves and light waves.

APPARATUS

Water ripple tank, Metal reflectors , Low voltage power unit (3.0 V D-C) ,Ammeter ,Variable resistor, Motor

Vibrator, Lamp, Level.

INTRODUCTION

The ripple tank is an apparatus for studying the phenomena of water waves. The wave generator is a vibrator set

into motion by a 3V.D.C Motor. A variable resistor in series with the motor varies its speed and therefore the


frequency of vibrations. A lamp illuminates the wave pattern. The wave pattern is projected on the table through

the transparent bottom of tank. If one wishes to copy a wave pattern on paper the paper can be spread out on the

table under the ripple tank. When measuring wavelengths or other distances remember to measure these lengths

as they are in the ripple tank. For calibration place an object of known length on the bottom of the ripple tank

and measure the length of its image.The ripple tank should be leveled using the spirit level. Use so much water

that it stands midways on the sloping walls. The wave generator with wooden plate and motor has to be raised

or lowered so that the wave source just touches the water surface. The wave pattern can be ‘stopped’ by viewing

through stroboscope.

Single point source

1. Screw the bent metal rod onto the front of the place of the wave generator so that the rod points

forwards. Switch on the power and let the motor run slowly observe and draw a fig.1.Place small pieces

of paper on the water and see if they move. Are the pieces of paper displaced at the wave speed? If not

explain your observations.Switch off the power and remove the bent metal rod. Lower the plane

generator to touch just touch the water surface. Place the plane reflector at a small distance in front of

the generator. Observe the reflected pulse and draw a fig.2. Where is the center from which the reflected

pulse seems to diverge? Compare your observations with the plane mirror image of a light source.

2. Repeat step (3) using the two reflectors with a gap of 1-2cm between them observe and draw a fig.3 .

Where is the source from which the transmitted pulse seems to diverge? Compare your observation with

Huygen’s principle.Place the metal parabolic reflector (convex side) so that the point source is at its

focus. Give a single push to the generator to produce a wave pulse. Observe (and draw a fig.4 ) the

reflected pulse and compare with the effect of a parabolic mirror when a light source is placed at its

focus.Repeat 7 metal parabolic reflector (concave side) observe and draw a fig.5

Two Synchronous point sources

Attach the two bent metal rods to the plate of the wave generator. Start the vibrator. Observe and observe and

draw a fig.4 the curves where the two waves interfere so that the water is at rest. Vary the frequency of the

waves by increasing the speed of the vibrator and observe observe and draw a fig.6 then explain the effect on

the interference pattern.

A Plane Wave

1. Use the plate of the wave generator itself as a source of waves. Produce waves with a wavelength about

2.5cm or to do this move the plate to and fro by hand.

2. Place the long reflector diagonally in the tank and observe reflected waves. Compare your observation

with the law of reflection for light observe and draw a fig.7.

3. Replace the long reflector by the two shorter reflectors parallel to the wave fronts 5-6cm away from the

wave generator and as far as possible from each other. Generate waves by hand or with the motor (about

2cm)observe observe and draw a fig.8. Decrease the distance between the two reflectors until about

1cm. Observe the wave fronts observe and draw a fig.9 then compare this with Huygen’s principle.

4. Place the very short reflector between the two reflectors so that two open spaces of 1cm or less are left

between the reflectors. Observe (and draw a fig.10) the interferences pattern and compare with the

results of experiment W4.2 and the experiment of Young.

5. Now remove the reflectors and put the rectangular plane block in the ripple tank at about 5cm from the

plane wave generator. The length of the block should parallel to the wave fronts observe and observe

and draw a fig.11.

6. Repeat 5 above with the block length about 450 to the wave front observe and draw a fig.12

The Report

The report should include the observations with carefully drawn neat figures and explanation where applicable

as well as answers to every question.


SPH 2171 PHYSICS 11

C18

CHARGING CURVES OF A CAPACITOR AND OSCILLOSCOPE

AIM:

1. To learn how to use the oscilloscope

2. To find out the values of capacitors given.

3. To find out of the formulas for capacitors in 1. Series 2. Parallel are collect

4. Explain how the current of capacitor voltage in a series C-R circuit which is connected to a D.C source varies with time.

5. Draw graph for variation of voltage with time for each of the component in C-R circuit when the capacitor is

Charging

Discharging

6. Define the time constant of a C-R circuit

7. Determine the growth and decay of the component voltage on current in a series C-R circuit, seconds after the commencing of

Charging

Discharging

THEORY:

heated filament cathode

Focussing anode

electron beam

accelerating X-plates Y-plates

anode

NB. Disposition of control varies depending on the make of oscilloscope.

Operation of oscilloscope

The oscilloscope can be used to give an image of a repetitive signal as a function of time. The signal as a

voltage, is applied to the Y-plates (vertical movement) and internally generated wave sweeps the electron

beam (seen as a spot on the screen) horizontally at some pre-determined rate. This rate is set using the

“time/division” control.

The “time/division” control is calibrated such that when it is operating at 50 cps, 1 cycle occupies 20 ms.

All the other ranges on the switch are direct multiples of this. The time calibration is only valid at the

minimum setting of the “X-pos” control. The X-shift control moves the whole trace horizontally

The trace may also be controlled vertically using the “volt/div” control. This switch inserts a series of

resistances between the input socket and the vertical amplifier. It is used either to obtain a picture of

convenient height or to obtain direct readings of the input voltage (provided the “Y-pos” control is at its

minimum setting).

To take measurements, a steady trace is required, and the “trig-level” control may be adjusted. You will

be using the internal trigger where the applied, i.e. unknown, signal is used to start the time base. The

“trig-level” switch controls the signal level at which the time base is triggered. The “d.c. /a.c.” switch is normally set to the a.c. position. This inserts a block capacitor in series with the input of the vertical amplifier to remove the d.c. Component of

the signal.

Method A

1. Connect the signal generator up to the oscilloscope. Set the generator to output sine waves at a

frequency of 500 Hz


2. You should see a steady sine wave on the screen. If not, press in the trigger level button. Adjust the

intensity and focus controls to give a sharp, but not too bright image.

3. Now try the effect of the following controls: X pos Y pos time/div volts/div

4. Measure the wavelength of the wave seen on the screen and calculate the frequency of the wave.

5. The oscilloscope can also be used to measure voltage, the voltage output of generator to 2.

6. Measure the voltage from the oscilloscope screen.

7. Now set the generator to give out square waves at 500 Hz and voltage output setting 2.

8. Measure the frequency and voltage of the wave.

9. Record all data on the worksheet. Comment and compare your results from the sine and square

waves.

Method B:

1. When a capacitor is charging through a Resistor R1 ; The rate of charge of I or voltage VC at a

particular instant depends on the value of I or voltage VC at that instant. Follows an exponential curve

and the mathematical equation is

VC = E (1-e-t/CR1) and I = (E/R1)e-t/CR1

2. When the capacitor is discharging the current I flows opposite to the charging

Current I through R2. VC starts to decay. The curve is an exponential as above

VC = Ee-t/CR2 And I =-(E/R2) e-t/CR2

3. The rate of charging or discharge at any particular time is shown by gradient or Slope of VC /time

graph at that time. A tangent drawn on the graph at any

Point indicates the slope and thus the rate of charge or discharge. If the rate of

Charge /discharge were not to charge but remain constant then the capacitor

Were to charge/discharge in a time = CR in seconds. This is called time constant T.

T = CR

APPARATUS:

1. Power supply

2. High resistance values R1

3. 5 unknown capacitors C1, C2, C3, C4, and C5

VC

Discharge I

E/R2

t1

Charge

E/R1


4. Discharging resistors RO

PROCEDURE I

Using the lowest value of C1; connect the circuit as shown in the above figure

Use the oscilloscope to determine the P.d across the capacitor as it charge through R1 with time.

Table this in a suitable table C1.

Make the capacitor to discharge through R2 and record the P.d across it with time.

Table this in table C1.

Repeat this for other values of capacitor C2, C3, and each time record P.d across the capacitor with time

in a suitable table.

Draw on the same axis the graphs of P.d across capacitor against time (charging and discharging) for all

the capacitors.

Worksheets

Sine wave

Generator

Frequency (Hz)

Length on

Screen (cm)

Time / div

(secs)

Time (secs) Oscilloscope

Frequency (Hz)

500

Voltage setting Height on screen

(cm)

Volt / div (volts) Voltage (volts)

2

TP1

+ E10V

S2

R11M

R2100

C110uF


Table C1 E = ______________ R1 = ___________ R2 = _________________

Charging V (volts) Time in s Voltage in v

Discharging V

(volts)

Time in s Voltage in v

Table C2 E = ______________ R1 = ___________ R2 = _________________


Discharging V

(volts)


Table C3 E = ______________ R1 = ___________ R2 = _________________


Discharging V

(volts)


Table C1 and C2 series E = ______________ R1 = ___________ R2 = _________________


Discharging V

(volts)




Discharging V

(volts)




Discharging V

(volts)


Table C1 ,C2 and C3 series E = ______________ R1 = ___________ R2 = _________________


Discharging V

(volts)


Table C1 and C2 parallel E = ______________ R1 = ___________ R2 = _________________



Discharging V

(volts)




Discharging V

(volts)




Discharging V

(volts)


Table C1 ,C2 and C3 parallel E = ______________ R1 = ___________ R2 = _________________


Discharging V

(volts)


Work to do:

1. Determine the value of the capacitors from the graph

C1 =

C2 =

C3 =

C1 and C2 series

C1 and C3 series

C2 and C3 series

C1 and C2 parallel

C1 and C3 parallel

C2 and C3 parallel

C1 ,C2 and C3 series

C1 ,C2 and C3 parallel

2. What can you deduce from the graphs?

Questions:

1. A 0.5µF capacitor is connected to a 200V supply via a supply a 150 capacitor. Ignoring lead

resistance, calculate the circuit time constant and the capacitor and the capacitor voltage after a time

equal to the time constant.

2. A 10µF capacitor is fully charged via a total resistance of 22KV to 250V.

Calculate the capacitance voltage 10ms after charging commenced. How long did it take for the

capacitor to be fully charged.


3. Determine the value of time constant when charging for each capacitor.

4. A capacitor is fully charged to a p.d of 200V. when discharged through a 250 resistor the capacitor

voltage falls to 45V in 0.3s. calculate the

Capacitance of a capacitor and the time constant.

C11: OHM’S LAW

Objectives To verify or prove experimentally that these statements are true

a) Ohm’s law for a metallic conductor

b) R = R1 + R2 + R3 for resistances in series

c) 1/R = 1/R1 + 1/R2 + 1/R3 for resistances in parallel

d) Ohm’s law is not obeyed by a semiconductor

Apparatus

Theory Ohm’s law for a metal conductor states that potential difference, V, between two ends of the conductor is

directly proportional to the current, I, flowing through it, at a constant temperature. i.e. V = RI, where R is a

constant known as resistance (in ohms)

Method A

1. Determine the resistances R1, R2 and R3 separately as above.

2. Determine the resistances R1, R2 and R3 in series.

3. Determine the resistance of the three (R1, R2 and R3) resistors in parallel.

Record all values on the worksheet and test to see if the relationships for resistors in series and in parallel hold.

Use your experimental values of V and I to plot graphs of V versus I. A straight-line graph proves ohm/s law.

Find Rs from the slope of your graphs.

Method B

Repeat the first part of the experiment using a semiconductor and draw the graph of V against I. Set the

potentiometer R so that the voltage in V and the current in A are zero. Adjust R so that voltage V increases in

suitable small steps such as 0.2V from 0 to the maximum such as IV, and record the values of V and I from the

meters. Reverse the diode D in the circuit. Record the value of I at a reverse voltage of IV.

R1 R2 R3 Series Parallel

V (v) I (A) V (v) I (A) V (v) I (A) V (v) I (A) V (A) I (A)

1.0 0.049 2.0 0.66 5.0 0.125 10.0 0.11 1.0 0.10

2.0 0.099 3.0 0.01 6.0 0.15 12.0 0.40 6.0 0.65

3.0 0.150 4.0 0.13 7.0 0.175 15.0 0.166 12.0 1.30

4.0 0.201 5.0 0.166 8.0 0.20 20.0 0.22 15.0 1.63


5.0 0.25 6.0 0.2 9.0 0.225 24.0 0.66 18.0 1.95

From graphs From formula % Difference

R (series)

R (parallel)

Compare your experimental results with those obtained using the formula. Discuss the sources of errors in these

measurements on resistance. Is this the most accurate way of measuring resistance? If not, what would you use

and why? Comment on your graph. Is ohm’s law verified?

What other methods can you use as trainee to verify the value of a resistor?

color 1st – significant

figure

2nd – significant

figure

3rd - multiplier 4th - tolerance

Black 0 0 100 + 0%

Brown 1 1 101 + 1%

Red 2 2 102 + 2%

Orange 3 3 103 -

yellow 4 4 104 + 5%

Green 5 5 105 + 0.5%

Blue 6 6 106 + 0.25%

violet 7 7 107 + 0.1%

Grey 8 8 108 + 0.5%

(+10%)

white 9 9 109 -

Gold - - 10-1 + 5%

Silver - - 10-2 +10%

None - - - +20%

Use now the resistance meter to determine the actual values of the resistances.

Conclusion: For comparison plot your six graphs on the same axis. Discuss the resistance of the junction diode

in forward and reverse bias and whether the diode is an ‘ohmic’ or ‘non-ohmic’ component.


C12- WHEATSTONE BRIDGE Aim: to find the values of resistances

Aim: to find the values of resistances

X1

, X2

and X3

To find out whether the formulas of 1. Resistances in series 2. And parallel are true.

To find the resistivity of the material of the wire given

Theory

When resistances are connected as shown in Fig. 2 below, they constitute a wheatstone network. If P, Q and R are known resistances adjusted in such away that the galvanometer G reads zero, the points B

and D will be at the same potential and no current flows between them. The network is said to be balanced. Thus:If the current through the meter is Ig = 0 , I

1 =I

3 and I

2=I

4.Or I

2/I

1=I

4/I

3 also PI

1/RI

2 =QI

3

=XI4

. Hence X = QR/P. If the above condition is satisfied then it is possible to use the network to determine the value of the unknown resistance X

Apparatus: Decade resistance box, wheat stone bridge, dry cell, three assorted resistors, galvanometer, resistivity wire, galvanometer and assorted wires.

Procedure/method: In Fig. below , P and Q are resistances of the portions AB and BC respectively, of a wire of uniform resistance. Commonly, this wire is 50 or 100

cm long. The point B on the wire is where the galvanometer G shows no deflection. P and Q will be proportional to the lengths AB and BC of the wire, respectively. R is a

standard resistance (decade resistance box). Set up the circuit as shown in Fig. 1 above. Find an approximate balance point with the protective resistor in the circuit (NB: this resistor limits current flowing

in the galvanometer). Now obtain the accurate balance point by shorting this protective resistor. Reverse the terminals of the accumulator E and repeat the measurement. Interchange R and X, and repeat the

procedure. How does the balance point change? Repeat the experiment for two other resistors X and tabulate your results with errors.Measure the resistances of the unknown resistor X and compare the values with

those from your experiment.

Use the chart below to determine the values of the resisances using the colour bands or codes.

Color 1st – significant figure 2nd – significant figure 3rd – multiplier 4th – tolerance

Black 0 0 100 + 0%

Brown 1 1 101 + 1%

Red 2 2 102 + 2%

Orange 3 3 103 -

yellow 4 4 104 + 5%

Green 5 5 105 + 0.5%

Blue 6 6 106 + 0.25%

violet 7 7 107 + 0.1%

Grey 8 8 108 + 0.5% (+10%)

white 9 9 109 -

Gold - - 10-1 + 5%

Silver - - 10-2 +10%

None - - - +20%

Part 2: Resistivity of the wire

Now use the bridge to measure the resistance of each of the wire given. Before connecting the battery to the

bridge, carefully check that all the connections are correct. Get the wire, attach it to the bridge, and set the


decade box resistance Rk to be as near to Rx as possible(you know Rx roughly from your DMM measurements).

Balance the bridge by moving the sliding contact along the wire while watching the galvanometer. With the

bridge balanced, measure L1 and L2, and compute

(11) .

Repeat this procedure as the table below shows.

From the results from the table , compute the average resistivity, and the uncertainty of the average ( ).

Compare your average value with the known value.

Now use the resistance meter to determine the actual values of the resistances.

TABLE OF RESULTS :

LENGTHS DUE TO TERMINALS UNREVERSED TERMINALS REVERSED Actual resistance (meter)

P Q P Q

X1

X2

X3

X1 and X2 series

X1 and X3 series

X2 and X3 series

X1 , X2and X3 series

X1 and X2 parallel

X2and X3parallel

X1 and X3parallel

X1 , X2and X3parallel

Wire given length= ...………cm Diameter= …………. mm

AFTER INTERCHANGING R AND X:

LENGTHS DUE TO TERMINALS UNREVERSED TERMINALS REVERSED Actual resistance (meter)

P Q P Q

X1

X2

X3

X1 and X2 series

X1 and X3 series

X2 and X3 series

X1 , X2and X3 series

X1 and X2 parallel

X2and X3parallel

X1 and X3parallel

X1 , X2and X3parallel

Wire given length= ...………cm

Diameter= …………. mm

Ig

I1 I

3

I4 I

2


Questions: How would the resistance per unit length change if you used: A) a shorter wire B)a thicker wire, than that used in

Q. 2 above.What are the possible sources of error in the experiment

C20 ~

KIRCHHOFF’S LAWS C20

Objective:

To verify Kirchhoff’s Laws by comparing voltages and currents obtained from a real circuit to those

Predicted by Kirchhoff’s Laws.

Introduction:

A simple circuit is one that can be reduced to an equivalent circuit containing a single resistance and a single voltage source. Many circuits are not

simple and require the use of Kirchhoff’s Laws to determine voltage, current, or resistance values. Kirchhoff’s Laws for current and voltage are given by

equations 1 and 2. In this experiment, we will construct two circuits with 4 resistors and a voltage source. These circuits will not be simple, thus

Kirchhoff’s Laws will be required to determine the current in each resistor. We will then use a digital multi-meter to obtain an experimental value for the

voltage across each resistor in the circuits. Kirchhoff’s Laws will then be applied to the circuits

to obtain theoretical values for the current in each resistor. By applying Ohm’s Law, we can then obtain a theoretical value for the voltage across each

resistor. The experimental and theoretical voltages can then be compared by means of % error.

Equation 1: Σ junction

I=0 junction law

Equation 1: Σ loop

I=0 loop law

Equipment:

Proto-board

4 resistors: (R1=68kΩ, R2=47kΩ, R3=15kΩ, R4=1000kΩ)

Digital multi-meter Variable power supply Wire leads and alligator clips

Experimental Procedure Part 1: figure 1

1. Using the proto-board, the 4 resistors, the variable power supply, and the wire leads and alligator clips; construct the circuit shown in Figure 1. First

ascertain the values of the resistance of the resistor.

2. Turn on the power supply. Connect the multi-meter across the power supply and adjust the voltage to suitable D.C. voltages {Get guidance from the

lab INSTRUCTOR}

3. Connect the multi-meter across each of the 4 resistors Put the multi-meter in series to each resistor and record the current through each. Record

these 4 values of voltage and current in the data table.

4. Turn the power supply off and disconnect the circuit.

Experimental Procedure Part 2: figure 2

1. Add a second power supply to the circuit as shown in Figure 2.

2. Turn on the power supplies. Adjust the voltages V1 and V

2 to 4.0 volts.

3. Connect the multi-meter across each of the 4 resistors Put the multi-meter in series to each resistor and record the current through each. Record

these 4 values of voltage and current in the data table.


4. Turn the power supply off and disconnect the circuit.

Analysis:

1. For the first circuit, use equations 1 and 2 to write a system of linear equations that may be solved for the current in each branch of the circuit. Then,

solve the system to obtain a theoretical value for each current. Show your work!

2. Using the currents obtained in step 1 of the analysis; apply Ohm’s Law to determine the theoretical voltage across each resistor.

3. Compare the theoretical voltages obtained in step 2 of the analysis to those measured in the actual circuit in Figures 2 and 1.

4. Repeat steps 1 to 3 for the second circuit.

5. Record the theoretical voltages, the experimental voltages, and the % errors in the results table.

Challenge: figure 3

Repeat experimental steps 1-4 and the analysis for the circuit in Figure 3 with resistors and a power supply:

(R1=68kΩ, R2=47kΩ, R3=22kΩ, R4=15kΩ, R5=1000kΩ)

C

I7

I8

I9

R1

R2

R3

R4

V

R1

R2

R3

R4

Vx

Vy

R1

B

I4

I5

I6

A

I1

I2

I3

G

H

Figure 1

Figure 2


Table of results:

Figure 1 V (theoretical) V (experimental) Percent error

R1

R2

R3

R4

Figure 1 I (theoretical) I (experimental) Percent error

R1 I

2 = I

2 =

R2 I

2 = I

2 =

R3 I

1 = I

1 =

R4 I

3 = I

3 =


R1

R2

R3

R4


R1 I

5 = I

5 =

R2 I

5 = I

5 =

R3 I

4 = I

4 =

R4 I

6 = I

6 =


R1

R2

R3


R4

R5


R1 I

8 = I

8 =

R2 I

12 = I

12 =

R3 I

11 = I

11 =

R4 I

9 = I

9 =

R5 I

10 = I

10 =

Now get the summation,Σ, of currents at the following junction:

At junction A, Σ (I1,I2,I3)=

At junction B, Σ (I4,I5,I6)=

At junctionC, Σ (I7,I8,I9)=

At junctionD , Σ (I11

,I10

,I7)=

At junction E, Σ (I10

,I12

,I8)=

At junction F, Σ (I11

,I9,I

12)=

At junction G, Σ (I4,I

5,I

6)=

At junction H, Σ (I1,I

2,I

3)=

now solve for v, vx, vy, vz and vw using appropriates loops. measure the actual input voltages and account

for the difference. Is the kirchoffs law verified? Comment and reccommend


C14- HORIZONTAL COMPONENT OF THE

EARTH’S MAGNETIC FIELD

Objectives : 1. To determine the horizontal component of earth’s magnetic field

2. Calculate the magnetic moment of the bar magnet

Apparatus: magnetometer and scale ruler

Theory

The horizontal component of the earth’s magnetic field Bo can be found from the measurement of mass, length

and time. A small magnet pivoted at it’s center to rotate in a horizontal plane will be deflected through an angle

when acted on by only one other field B at right angles to Bo. Thus from fig. 1 below

Bo

B

B=BOtanɵ

This is the principle behind the deflection magnetometer. For a magnet of moment M which is suspended at the

center in the earth’s horizontal field, it will experience a couple C if it is displaced by small angle from the

equilibrium position.

Thus C=M Bo (for small )

We can write the equation of motion as

I d2 / d t2 = - M B. ……………………...................................................................................................(1)


Where I is the moment of inertia of the magnet about an axis through it’s center. Equation (1) describes a

simple harmonic motion with a period T given as

T = 2 [ I / MBo]

This is the principle of the vibration magnetometer.

2a

m m

d

Calculation of the Horizontal component, Bo

The induction field B is calculated as follows

The bar magnet can be considered as a permanent dipole which can be replaced by two poles separated by a

distance 2a and having a pole strength m given by M= 2ma (where M is the magnetic moment of the dipole).

From the inverse square law and adopting sommerfield system, the induction field B at a point o distance d

from the magnet due to the bar magnet (dipole) is given by:

B={[ o/4] [m / (d-a)2 ] – [m / (d+a)2) ]}= {[o/4] [4mad /(d2-a2)2 ]}=[oMd / 2 (d2 –a2)2 ]

B= Bo tan , so (d2-a2)2/d =[M / Bo][o/2] cot

A graph of (d2-a2)2/d against cot is a straight line with slope (M / Bo) (o/2) from which (M / Bo) can be

calculated.(Note that a is half the magnetic length of the bar magnet. Thus the length 2a is

Approximately 7/8 of the physical length).

1. Experimental procedure:

The field B due to a bar magnet at various points along its axis is first determined from the deflections produced

in the deflection magnetometer. Remove the bar magnet and any other magnetic materials from the vicinity of

the magnetometer and adjust it until its arms are in the east-west direction and the aluminium pointer reads zero.

Place the magnet on one arm of the magnetometer to give a deflection of about 70. Read the distance, d, of the

center of the magnet on the arm (which is calibrated with the center of the magnetometer magnet as the zero

point) and note the deflection of the two ends of the pointer.Reverse the bar magnet and note the deflections

again.Repeat with the magnet on the other arm at the same distance. Determine the mean of the eight readings

of the pointer which give the deflection at the distance, d.

Repeat the experiment at least for 5 other different values of d so that varies between 30 and 70.

2. The vibration magnetometer

Suspend the bar magnet on a stirrup so that it can oscillate freely in a horizontal plane. Displace it by a

small angle from its equilibrium position and determine the time taken by 10 oscillations.

Repeat thrice and calculate the period. The period is given by

(M Bo) = [(42 I) / T)]

Where I is the moment of inertia of a bar magnet of length l and breadth b and is given by

I = [m (l2 + b2) / 12] m’ is the mass of the magnet)

From the value of M/Bo (in experiment 2) , the horizontal component of the earth’s magnetic field Bo can be

calculated. Calculate the magnetic moment of the bar magnet also.

Table of results:

ɵ

Eastern arm

Western arm

cotɵ

Mean

ɵ

d North pole facing east

North pole facing west

North pole facing east

North pole facing

west

300

ɵ


350

400

450

500

550

600

650

700

physics 1 sph 2170 - jomo kenyatta university of ... · method: the experiment comprises e...

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