phsycis manuals.docx

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1 Department of Mechanical Engineering Mohammad Ali Jinnah University

Lab Manual Applied Physics Lab

TABLE of ContentsLab 01 ................................................................................................................................. 6

Error Analysis and Graph Drawing ................................................................................ 6

Error analysis .............................................................................................................. 6

Graph drawing ............................................................................................................ 8

Lab 02 (a) .......................................................................................................................... 12Introduction to widely used components ...................................................................... 12

Resistors .................................................................................................................... 12

Capacitors ................................................................................................................. 13Diodes ....................................................................................................................... 14

Meters and Oscilloscope ........................................................................................... 15

Breadboard ................................................................................................................ 16

Strip board ................................................................................................................. 16Function Generator ................................................................................................... 18

Lab 02 (b) .......................................................................................................................... 19

To Find the Resistance by Color-Coding Techniques .................................................. 19

Objective ................................................................................................................... 19

Apparatus .................................................................................................................. 19

Tolerance................................................................................................................... 19Resistor short hand .................................................................................................... 22

Lab 02 (c) .......................................................................................................................... 23

To Study Resistors in Series and Parallel ..................................................................... 23

Objective ................................................................................................................... 23Resistors in Series: .................................................................................................... 23Series Resistor Circuit............................................................................................... 23

Series Resistor Equation ........................................................................................... 25

Resistors in Parallel................................................................................................... 25

Parallel Resistor Circuit ............................................................................................ 26

Parallel Resistor Equation ......................................................................................... 26

Lab 03 (a) .......................................................................................................................... 29Familiarization with Analog and Digital Multimeter ................................................... 29

Objective ................................................................................................................... 29

Apparatus .................................................................................................................. 29Theory ....................................................................................................................... 29

Multimeter................................................................................................................. 29

Lab 03 (b) .......................................................................................................................... 33

Ohms Law.................................................................................................................... 33

Objective ................................................................................................................... 33

Apparatus .................................................................................................................. 33

Theory ....................................................................................................................... 33

Ohms Law................................................................................................................ 33Lab 03 (c) .......................................................................................................................... 35

Voltage Divider and Current Divider ........................................................................... 35

Objective ................................................................................................................... 35Voltage Divider ......................................................................................................... 35


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Current Divider ......................................................................................................... 35

Experimental Setup ................................................................................................... 36

Observations & Calculations .................................................................................... 36Lab 04 ............................................................................................................................... 38

Kirchhoff's voltage law (KVL) ..................................................................................... 38

Objective ................................................................................................................... 38

Apparatus .................................................................................................................. 38Experimental Setup ................................................................................................... 39

Observations & Calculations .................................................................................... 39

Lab 05 ............................................................................................................................... 42Kirchhoff's Current law (KCL) ..................................................................................... 42

Objective ................................................................................................................... 42

Apparatus .................................................................................................................. 42

Statement................................................................................................................... 42Experimental Setup ................................................................................................... 43

Observations & Calculations .................................................................................... 43

Lab 06 ............................................................................................................................... 45

To Study the Variation of Photoelectric Current with Intensity of Incident Light ....... 45Objective ................................................................................................................... 45

Apparatus .................................................................................................................. 45

Photoelectric effect ................................................................................................... 45Photo Cell.................................................................................................................. 45

Experimental Setup ................................................................................................... 46

Observations & Calculations .................................................................................... 46Lab 07 ............................................................................................................................... 47

Magnetic lines of Force ................................................................................................ 47

Objective ................................................................................................................... 47

Apparatus .................................................................................................................. 47Magnetic lines of Force ............................................................................................ 47Characteristics of magnetic lines of force ................................................................. 48

Procedure .................................................................................................................. 49Lab 08 ............................................................................................................................... 51

Function Generator and Oscilloscope ........................................................................... 51

Objective ................................................................................................................... 51Apparatus .................................................................................................................. 51Procedure .................................................................................................................. 53

Lab 09 ............................................................................................................................... 54

Demonstration of Vectors ............................................................................................. 54Objective ................................................................................................................... 54Vectors ...................................................................................................................... 54

Resolution of Vectors ............................................................................................... 57

Dot Product: .............................................................................................................. 57Cross Product: ........................................................................................................... 58

Lab 10 ............................................................................................................................... 59

Motion of a simple pendulum ....................................................................................... 59Objective ................................................................................................................... 59


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Theory ....................................................................................................................... 59

Procedure .................................................................................................................. 60

Observation and Calculations ................................................................................... 61Analytical Solution ................................................................................................... 61Conclusion/Comments .............................................................................................. 61

Lab 11 ............................................................................................................................... 62

Using Vector Addition Method .................................................................................... 62Objective ................................................................................................................... 62

Apparatus .................................................................................................................. 62

Theory ....................................................................................................................... 62Procedure: ................................................................................................................. 64

Readings/Results: ...................................................................................................... 65

Observation and Calculations: .................................................................................. 65

Comments/Conclusions: ........................................................................................... 66Lab 12 ............................................................................................................................... 67

Resolution of a Vector .................................................................................................. 67

Objective: .................................................................................................................. 67

Apparatus: ................................................................................................................. 67Theory: ...................................................................................................................... 67

Procedure: ................................................................................................................. 68

Measurements and Calculations: .............................................................................. 69Results: ...................................................................................................................... 70

Conclusion/Observation:........................................................................................... 70

Lab 13 ............................................................................................................................... 71Value of g using spring mass system ......................................................................... 71

Objective: .................................................................................................................. 71

Apparatus: ................................................................................................................. 71

Theory: ...................................................................................................................... 71Procedure: ................................................................................................................. 71Observations and calculations: ................................................................................. 72

Lab 14 ............................................................................................................................... 73Coefficient of sliding friction........................................................................................ 73

Objective: .................................................................................................................. 73

Apparatus: ................................................................................................................. 73Theory: ...................................................................................................................... 73Procedure: ................................................................................................................. 75

Observations and calculations ................................................................................... 75


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PH 1012 Applied PhysicsSyllabusCourse Designation: Core (Natural Sciences)

Credits: 1

No. of Sessions per week: 1

Session Duration: 180 minSemester: Fall 2012

Applied Physics Course Instructor

Muhammad Numan

Office : Engineers Room, 3rd floor , Block (B)E-mail:[email protected]

Office Hours

Monday 11:15 am to 4:00 pm

Tuesday 11:15 am to 4:00 pmWednesday 11:15 am to 4:00 pm

Textbook

Applied Physics Manual

Applied Physics - Course Outline

Lab No. 01Error Analysis and graph drawing Week 02

Lab 02 (a)Introduction to widely used components Week 03

Lab 02 (b)To Find the Resistance by Color-Coding Techniques Week 03

Lab 02 (c)To Study Resistors in Series and Parallel Week 03

Lab 03 (a)

Familiarization with Analog and Digital Multimeter Week 04

Lab 03 (b)

Ohms Law Week 04
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Lab 03 (c)

Voltage Divider and Current Divider Week 04

Lab 04Kirchhoff's voltage law (KVL) Week 05

Lab 05Kirchhoff's Current law (KCL) Week 05

Lab 06To Study the Variation of Photoelectric Current with Week 06Intensity of Incident Light

Lab 07Magnetic lines of Force Week 07

Lab 08Function Generator and Oscilloscope Week 08

Lab No. 09Demonstration of vectors Week 10

Lab 10Simple pendulum Week 11

Lab 11

Using vector addition method Week 12

Lab 12

Resolution of vectors Week 13

Lab 13

Value of g using spring mass system Week 14

Lab 14

Coefficient of sliding friction Week 04


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Lab 01

Error Analysis and Graph Drawing

Error analysis

It is impossible to do an experimental measurement with perfect accuracy. Before we go into

details of error analysis it is important to understand the meaning of error in science.

Error in a scientific measurement usually does not mean a mistake or blunder. Instead,

the terms "error" and "uncertainty" both refer to unavoidable imprecision in

measurements. Of course, not all measurements have errors. If asked how many people

there are in a room, one can usually give an exact number as an answer. However, if we

want to know how many atoms there are in a room, giving an exact answer is nearly

impossible. There is always an uncertainty associated with any measured quantity in an

experiment even in the most carefully done experiment and despite using the most

sophisticated instruments. This uncertainty in the measured value is known as the error in

that particular measured quantity. There is no way by which one can measure a quantity

with one hundred percent accuracy.

When a measurement of a physical quantity is repeated, the results of the variousmeasurements will, in general, spread over a range of values. This spread in the measured

results is due to the errors in the experiment. Errors are generally classified into two types.

Systematic (or determinate) error

A systematic error is an error, which is constant throughout a set of readings. Systematic

errors are errors associated with a flaw in the equipment or in the design of theexperiment. Systematic errors cannot be estimated by repeating the experiment with the

same equipment.


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Example

If a voltmeter is not connected to anything else it should, of course, read zero. If it does

not, the "zero error" is said to be a systematic error. All the readings of this meter are too

high or too low. The same problem can occur with stop-watches, thermometers etc. Evenif the instrument cannot easily be reset to zero, we can usually take the zero error into

account by simply adding it to or subtracting it from all the readings. (It should be noted

however that other types of systematic error might be less easy to deal with.) Similarly, if

10 ammeters are connected in series with each other they should all give exactly the same

reading. In practice they probably will not. Each ammeter could have a small constant

error. Again this will give results having systematic errors.

For this reason, note that a precise reading is not necessarily an accurate reading. A

precise reading taken from an instrument with a systematic error will give an inaccurate

result.

Random (or indeterminate) error

Errors that can be reliably estimated by repeating measurements are called random errors.

These errors can be both positive and negative and lead to a dispersion of the measurements

around a mean value.

Example

Connect a voltmeter into a circuit, take a reading, disconnect the meter, reconnect it and

measure the same voltage again. There might be a slight difference between the readings.

These are random (unpredictable) errors. Random errors can never be eliminated

completely but we can usually be sure that the correct reading lies within certain limits.

To indicate random error, the results of measurements should be written as

Result Uncertainty

For example, suppose we measure a length, to be 25cm with an uncertainty of 0.1cm.


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We write the result as

= 25cm 01cmBy this, we mean that all we aresure about is that

is somewhere in the range 24.9cm to

25.1cm.

In a time period measurement, errors in starting and stopping the clock will lead to random

errors, while a defect in the working of the clock will lead to systematic error.

Random errors are handled using statistical analysis. Assume that a large number (N)

of measurements are taken of a quantity Q giving values Q1, Q2, Q3QN. Let Q be

the mean value of these measurements

and let 'd' be the deviation in the measurements

( )

The result of the measurement is quoted (assuming systematic errors have been eliminated

as)

Graph drawing

In practical analysis the graph of experimental data is the most important in improvingthe understandings of experimental results .Moreover one can calculate unknowns related

to the experiments and compare the experimental data with the theoretical curves.


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Example

Let us take the example of ohm law in which using the following circuit we can easilymeasure voltage and current to plot the respective graphs.

From this circuit we take readings of voltage and current plotting them as a graph called a

VI characteristic.

We normally put the voltage on the y-axis and current on the x-axis. This allows us to

determine the resistance from the gradient. This is a voltage current graph for an ohmic

conductor.

The straight line in Figure 1 shows a constant ratio between voltage and current, for both

positive and negative values. So when the voltage is negative, the current is negative, i.e.flowing in the opposite direction. Ohms Law is obeyed.

Figure 1


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For a filament lamp we see in Figure 2 that the resistance rises as the filament gets hotter,

which is shown by the gradient getting steeper.

A thermistor (a heat sensitive resistor) behaves in the opposite way as shown in Figure

3. Its resistance goes down as it gets hotter. This is because the material releases more

electrons to be able to conduct.

Exercise

Q1 What is the general classification of errors? Give an example of each. How are they

taken care of?

Figure 2

Figure 3


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Q 2 Consider an experiment to measure the gravitational acceleration g by measuring

the time period of a simple pendulum. What are the possible sources of systematic

error in this experiment?

Q2 What is the meaning of standard error? Calculate the standard error? Calculate the

standard error for the hypothetical data given in the table?

Q4 If there are always errors in any measurement then there is nothing like the true

value of any measured quantity . Comment on this statement.

Q3 Let Q = x - y, where x= 100 2 and y = 96 2 .Calculate Q (express the result with

the error included)

Radius of curvature(cm)130.121

130.126

130.139

130.148

130.155

130.162

130.162

130.169


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Lab 02 (a)

Introduction to widely used components

Resistors

Component Circuit Symbol Function of Component

Resistor

A resistor restricts the flow of current,

for example to limit the current passing

through an LED.

It is measured in ohm ()Variable Resistor

(Rheostat)

The variable resistor as a rheostat is

usually used to control current.

Examples includes: adjusting lamp

brightness, adjusting motor speed.

Variable Resistor

(Potentiometer)

The variable resistor as a potentiometer

is usually used to control voltage. It can

be used as a transducer.

Variable Resistor(Preset)

The variable resistor as a preset is

operated with a small screwdriver. It is

designed to be set when the circuit is

made and then left without further

adjustment. For example to set the

frequency of an alarm tone
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Capacitors


Capacitor

A capacitor stores electric charge. A

capacitor is used with a resistor in a

timing circuit. It can also be used as a

filter, to block DC signals but pass

AC signals. It is measured in farad

Capacitor,polarized

A polarized capacitor is one which

has a polarity, positive on one

terminal, negative on the other. This

makes it superficially look like a

battery. In use, the capacitor has its

positive voltage always higher than

that on the negative terminal. This

sort of capacitor is commonly found

in power supply filters.

sVariable CapacitorA variable capacitor is used in a radio

tuner.

Trimmer Capacitor

This type of variable capacitor (a

trimmer) is operated with a small

screwdriver or similar tool. It is

designed to be set when the circuit is

made and then left without further

adjustment.
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Diodes

Component Circuit SymbolFunction of

Component

Diode

A device which only

allows current to

flow in one

direction.

LED

Light Emitting Diode

A transducer which

converts electrical

energy to light.

Zener Diode

A special diode

which is used to

maintain a fixed

voltage across its

terminals.

PhotodiodeA light-sensitive

diode.
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Meters and Oscilloscope


Voltmeter

A voltmeter is used to measure voltage.

The proper name for voltage is 'potential

difference', but most people prefer to say

voltage.

Ammeter An ammeter is used to measure current.

Galvanometer

A galvanometer is a very sensitive meter

which is used to measure current in .Ohmmeter

An ohmmeter is used to measure

resistance. Most multimeters have an

ohmmeter setting.

Oscilloscope

An oscilloscope is used to display the

shape of electrical signals and it can be

used to measure their voltage and time

period.
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Breadboard

A breadboard is used to make up temporary circuits for testing or to try out an idea. No

soldering is required so it is easy to change connections and replace components. Parts

will not be damaged so they will be available to re-use afterwards.

Almost all the Electronics Club projects started life on a breadboard to check that the

circuit worked as intended.

The photograph shows a typical small breadboard which is suitable for beginners

building simple circuits with one or two ICs (chips). Larger sizes are available and you

may wish to buy one of these to start with.

Strip board

Strip board has parallel strips of copper track on one side. The tracks are 0.1" (2.54mm)

apart and there are holes every 0.1" (2.54mm).


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Strip board is used to make up permanent, soldered circuits. It is ideal for small circuits

with one or two ICs (chips) but with the large number of holes it is very easy to connect a

component in the wrong place. For large, complex circuits it is usually best to use a

printed circuit board (PCB) if you can buy or make one.

Oscilloscope

An oscilloscope is easily the most useful

instrument available for testing circuits

because it allows you tosee the signals at

different points in the circuit. The bestway of investigating an electronic system

is to monitor signals at the input and

output of each system block, checking

that each block is operating as expected

and is correctly linked to the next. With a

little practice, you will be able to find and

correct faults quickly and accurately.

The function of an oscilloscope is

extremely simple: it draws a V/tgraph, a

graph of voltage against time, voltage on

the vertical or Y-axis, and time on the

horizontal or X-axis.


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Function Generator

A function generator is a device that can

produce various patterns of voltage at a

variety of frequencies and amplitudes.

Most function generators allow the user

to choose the shape of the output from a

small number of options.

Square wave - The signal goesdirectly from high to low

voltage.

Sine wave - The signal curveslike a sinusoid from high to low

voltage.

Triangle wave - The signal goesfrom high to low voltage at a fixed rate.

The amplitude control on a function generator varies the voltage difference between the

high and low voltage of the output signal. The direct current (DC) offset control on a

function generator varies the average voltage of a signal relative to the ground. The

frequency control of a function generator controls the rate at which output signal

oscillates.


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Lab 02 (b)

To Find the Resistance by Color-Coding Techniques

Objective

To understand the color code techniques of resistors

Apparatus

Resistors of different values Multimeter

Theory: While working with electronic

circuits and sorting of components

resistors are color coded for their easy

selection of junk and enhanced working.

Color bands are on the resistors associated

with worldwide known numerical values

.Resistors are having different color

coding schemes which are given below.

The 4-band Resistor Code:

The first band gives the first digit. The second band gives the second

digit.

The third band indicates thenumber of zeros.

The fourth band is used to showsthe tolerance (precision) of theresistor.

Tolerance


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Gold 5%

Silver 10%

No color 20%


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Examples

Green, blue, red, with silver tolerance band: 56 x 100 = 5.6 kohms, with a

tolerance of 10% .

Brown, black, orange, gold tolerance band: 10 x 1000 = 10000 ohms (or

10K ohms), with a tolerance of 5% .

The 5-band Resistor Code: The 5 band code is used for marking high quality, precision

resistors with 2%, 1% or lower tolerances. The rules are similar to the previous system;

the only difference is the number of digit bands. The first 3 bands will represent the

value, the 4th band will be the multiplier and the 5th stripe will give us the tolerance.

Examples

Blue, brown, white, brown, red tolerance band: 619 x 10 = 6190 ohms

(6.19K ohms), with a tolerance of 2% .

Red, red, brown, black, with a brown tolerance band: 221 x 1 = 221 ohms,

with a tolerance of 1% .

The 3-band Resistor Code or Small value resistors:

The standard color code cannot show values of less than 10. To show these small values

two special colors are used for the third band: gold which means (multiply by 0.1) and

silver which means (multiply by 0.01). The first and second bands represent the digits as

normal.

Examples

Red, violet, gold bands represent 27 0.1 = 2.7

Green, blue, silver bands represent 56 0.01 = 0.56


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Resistor short hand

Resistor values are often written on circuit diagrams using a code system which avoids

using a decimal point because it is easy to miss the small dot. Instead the letters R, K and

M are used in place of the decimal point. To read the code: replace the letter with a

decimal point, then multiply the value by 1000 if the letter was K, or 1000000 if the letter

was M. The letter R means multiply by 1.

For example

560R means 560ohm

2K7 means 2.7 k= 2700

1M0 means 1.0 M= 1000 k

Measurements

Serial # 1st

band 2nd

band 3rd

band Tolerance % Calculated Measured Difference

1

2

3

45

Exercise

Q1 How a variable resistor is used as potential meter or rheostat?

Q2 what does it mean that when the third band of a resistor is gold or silver?


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Lab 02 (c)

To Study Resistors in Series and Parallel

Objective

To understand different combinational circuits of resistorsResistors Combinations

Resistors can be connected together in either a series connection, a parallel connection or

combinations of both series and parallel together, to produce more complex networks

whose overall resistance is a combination of the individual resistors. Whatever the

combination, all resistors obey Ohm's Law andKirchhoffs Circuit Laws.

Resistors in Series:

Resistors are said to be connected in "Series", when they are daisy chained together in a

single line. Since all the current flowing through the first resistor has no other way to go

it must also pass through the second resistor and the third and so on. Then, resistors in

series have a Common Current flowing through them, for example:

IR1 = IR2 = IR3 = IAB = 1mA

In the following example the resistors R1, R2 and R3 are all connected together in series

between points A and B.

Series Resistor Circuit
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As the resistors are connected together in series the same current passes through each

resistor in the chain and the total resistance, RT of the circuit must be equal to the sum of

all the individual resistors added together.


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RT = R1 + R2 + R3

and by taking the individual values of the resistors in our simple example above, the total

resistance is given as:

RT = R1 + R2 + R3 = 1k + 2k + 6k = 9k

Therefore, we can replace all 3 resistors above with just one single resistor with a value

of 9k.

Where 4, 5 or even more resistors are all connected together in series, the total resistance

of the series circuit RT would still be the sum of all the individual resistors connected

together. This total resistance is generally known as the Equivalent Resistance and can be

defined as "A single value of resistance that can replace any number of resistors without

altering the values of the current or the voltage in the circuit". Then the equation given

for calculating total resistance of the circuit when resistors are connected together in

series is given as:

Series Resistor Equation

One important point to remember about resistors in series circuits, the total resistance

(RT) of any two or more resistors connected together in series will always be GREATER

than the value of the largest resistor in the chain and in our example above RT = 9 k

were as the largest value resistor is only 6 k.

Resistors in Parallel

Resistors are said to be connected

together in "Parallel" when both of

their terminals are respectively

connected to each terminal of the

other resistor or resistors. The voltage

drop across all of the resistors in


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parallel is the same. In the following circuit the resistors R1, R2 and R3 are all connected

together in parallel between the two points A and B.

Parallel Resistor Circuit

In the previous series resistor circuit we saw that the total resistance, RT of the circuit was

equal to the sum of all the individual resistors added together. For resistors in parallel the

equivalent circuit resistance RT is calculated differently.

Parallel Resistor Equation

Here, the reciprocal

value of the individual resistances is all added together instead ofthe resistances themselves. This gives us a value known as Conductance, symbol G with

the units of conductance being the Siemens, symbol S. Conductance is therefore the

reciprocal or the inverse of resistance, (G = 1/R). To convert this conductance sum back

into a resistance value we need to take the reciprocal of the conductance giving us then

the total resistance, RT of the resistors in parallel.

Example No1

For example, find the total resistance of the following parallel network

Then the total resistance RT across the two terminals A and B is calculated as:


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This method of calculation can be used for calculating any number of individual

Exercises

What is the equivalent resistance of these resistance combinations?

. .

. .


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.ExerciseQ1 what will be the current through a series circuit when applied voltage is 10 volts and

circuit resistance is 5Ohm?

Q2 what will be the amount of current of each bulb when 12 bulbs are connected in

series?


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Lab 03 (a)

Familiarization with Analog and Digital Multimeter

Objective To understand and learn the practical use of analog and digital

multimeter

Apparatus

Analog multimeter Digital multimeter Ac / Dc power source Resistors

Theory

The perfect use of prcised measuring of equipment is very important before start

working with electrical and electronics circuits. Analog meter consists of a galvanometer

and a pointer for showing electrical quantities while digital meters use electronics devices

like A/D (analog to digital) converter and seven segment display for reading electrical

quantities.

Multimeter

A multimeter or a multitester, also known as a volt/ohm meter or VOM, is an electronic

measuring instrument that combines several measurement functions in one unit. A typical

multimeter may include features such as the ability to measure voltage, current and

resistance
http://en.wikipedia.org/wiki/Electronicshttp://en.wikipedia.org/wiki/Measuring_instrumenthttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Measuring_instrumenthttp://en.wikipedia.org/wiki/Electronics


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Digital Multimeter Analog Multimeter

How meters are connected?

Using as a AmmeterIt is important for you to have a clear idea of how meters are connected into circuits.

DiagramsA andB below show a circuit before and after connecting an ammeter. To

measure current, the circuit must be broken to allow the ammeter to be connected in

series and ammeters must have a LOW resistance.

Figure A Figure B

Think about the changes you would have to make to a practical circuit in order to include

the ammeter. To start with, you need to break the circuit so that the ammeter can be

connected in series. All the current flowing in the circuit must pass through the ammeter.

Meters are not supposed to alter the behavior of the circuit, and it follows that an

ammeter must have a very LOW resistance.

Using as a VoltmeterTo measure potential difference (voltage), the circuit is not changed. The voltmeter is

connected in parallel between the two points where the measurement is to be made. Since

the voltmeter provides a parallel pathway, it should take as little current as possible. In

other words, a voltmeter should have a very HIGH resistance. Diagram A and Cbelow

show a circuit before and after connecting a voltmeter:


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Figure A Figure C

Circuit Diagram

R1=1k,R2=2.2k,R3=4.7k

No of

Observations

Vdc

(Battery)

Voltage

Across R1

(Volts)

Voltage

Across R2

Voltage

Across R3

Current

Across

R1,R2,R3

1 5V

2 8V

3 12V


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Questions

Q.1 Can we measure power with a multimeter?

Q.2 How a multimeter is connected in a circuit by measuring current through that

circuit?

Q.3 Is ohmic scale on analog meter is linear or non linear?


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Lab 03 (b)

Ohms Law

Objective

To verify Ohms Law using different CircuitsApparatus

Multimeter Resistors of different values Connecting wires

Theory

Current (I) is same in all parts of a series circuit Total resistance (R) equals the sum of all series resistance Total resistance is reciprocal of the sum of all the resistances The applied voltage (V) is the same across the parallel resistors Each branch current (I) equals the sum of the Branch currents

Ohms Law

Ohm's law states that the current through a conductor between two points is directly

proportional to the potential difference or voltage across the two points, and inversely

proportional to the resistance between them .The mathematical equation that describes

this relationship is

Where I is the current through the resistance in units of amperes, V is the potential

difference measured across the resistance in units ofvolts, andR is the resistance of the

conductor in units ofohms.
http://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Proportionality_%28mathematics%29http://en.wikipedia.org/wiki/Potential_differencehttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Amperehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Ohmhttp://en.wikipedia.org/wiki/Ohmhttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Amperehttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Voltagehttp://en.wikipedia.org/wiki/Potential_differencehttp://en.wikipedia.org/wiki/Proportionality_%28mathematics%29http://en.wikipedia.org/wiki/Electric_current


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Precautions

No loose connections should exist. Always insert Ammeter in series. Always insert Voltmeter in parallel.

Circuit Diagram

Table 1: Observation and calculations from the above circuit:

No. of

observations

Vs

(Applied

Voltage)

VR(Volts)

R I

1

2

3

IV- Graph from the Above Experimental Results

I (mA)

V


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Lab 03 (c)

Voltage Divider and Current Divider

Objective

To study Voltage Divider rule and Current DividerVoltage Divider

The voltage divider rule is a simple rule which can be used in

solving circuits to simplify the solution. The voltage divided

between the resistors in directly proportional to their resistance.

Applying Ohm's Law in the diagram the relationship between

the input voltage, Vin, and the output voltage, Vout, can be found:

Current Divider

Current divider is a simple linear

circuit that produces an output

current (IX) that is a fraction of its

input current (IT).

A general formula for the current

IX in a resistor RX that is in parallel

with a combination of other

resistors of total resistance RT asshown by Figure .where IT is the

total current entering the combined

network of RX in parallel with RT.

Notice that when RT is composed
http://en.wikipedia.org/wiki/Ohm%27s_Lawhttp://dictionary.sensagent.com/Linear/en-en/http://dictionary.sensagent.com/Electrical_network/en-en/http://dictionary.sensagent.com/Electric_current/en-en/http://dictionary.sensagent.com/Electric_current/en-en/http://dictionary.sensagent.com/Electrical_network/en-en/http://dictionary.sensagent.com/Linear/en-en/http://en.wikipedia.org/wiki/Ohm%27s_Law


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of a parallel combination of resistors, say R1, R2 and R3, then the reciprocal of each

resistor must be added to find the total resistance RT:

Experimental Setup

Observations & Calculations

R1 R2 R3 R4

Calculated

Measured

ITotal V1 V2 V3 V4 VTotal= V1+ V2+ V3+ V4

Calculated

Measured
http://en.wikipedia.org/wiki/Series_and_parallel_circuits#Parallel_circuitshttp://en.wikipedia.org/wiki/Series_and_parallel_circuits#Parallel_circuits


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Lab 04

Kirchhoff's voltage law (KVL)

Objective

Understanding and performing Kirchhoffs voltage lawApparatus

Resistors DMM

Statement

The directed sum of the electrical potential differences (voltage) around any closed

circuit is zero, or:

More simply, the sum of the emfs in any closed loop is equivalent to the sum of the

potential drops in that loop, or:

The algebraic sum of the products of the resistances of the conductors and the currents in

them in a closed loop is equal to the total emfavailable in that loop.
http://en.wikipedia.org/wiki/Potential_differencehttp://en.wikipedia.org/wiki/Electromotive_forcehttp://en.wikipedia.org/wiki/Electromotive_forcehttp://en.wikipedia.org/wiki/Electromotive_forcehttp://en.wikipedia.org/wiki/Electromotive_forcehttp://en.wikipedia.org/wiki/Potential_difference


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Experimental Setup


Calculated values

voltage V1 V2 V3 VTotal= V1+ V2+ V3+ V4

5 V12 V

15 V

20 V

Measured values


5 V

12 V

15 V

20 V


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Replace the values of resisters


Calculated values


5 V

12 V

15 V

20 V

Measured values


5 V

12 V

15 V

20 V


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Lab 05

Kirchhoff's Current law (KCL)

Objective Understanding and performing Kirchhoffs current law

Apparatus

Resistors DMM

Statement

At any node (junction) in an electrical circuit, the sum ofcurrents flowing into that node

is equal to the sum of currents flowing out of that node, ors

The algebraic sum of currents in a network of conductors meeting at a point is zero.

Here,

I = IA + IB + IC
http://en.wikipedia.org/wiki/Electrical_circuithttp://en.wikipedia.org/wiki/Current_(electricity)http://en.wikipedia.org/wiki/Current_(electricity)http://en.wikipedia.org/wiki/Electrical_circuit


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Experimental Setup


Calculated values

R1 R2 R3 total

Voltage

Current

Resistance

Measured values

R1 R2 R3 total

VoltageCurrent

Resistance


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Replace the values of resisters


Calculated values

R1 R2 R3 total

Voltage

Current

Resistance

Measured values

R1 R2 R3 total

Voltage

Current

Resistance


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Lab 06

To Study the Variation of Photoelectric Current with Intensity

of Incident Light

Objective

Understand the phenomena of Photoelectric effect and working of photocell

Apparatus

Photocell Resistors DMM

Photoelectric effect

The photoelectric effect refers to the emission, or ejection, of electrons from the surface

of, generally, a metal in response to incident light.

Photo Cell

Introduction: A photocell is a practical application of the phenomenon of photoelectriccell.

Construction: A photocell consists of an evacuated sealed glass tube containing a wire

anode and a concave cathode of suitable emitting material such as Cesium (Cs) The

material of cathode responds to a given frequency range.

Working: When light of frequency greater than the threshold frequency of the cathode

material falls on the cathode, photoelectrons are emitted. These electrons are collected by

the anode and an electric current starts flowing in the external circuit. The current

increases with the increase in the intensity of light. The current would stop, if the light

does not fall on the cathode.


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Experimental Setup


No of

ObservationsDistance(d)

Square of d Intensity Current (I)A1

2

34

5

6


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Lab 07

Magnetic lines of Force

Objective To understand the properties of magnetic field. To draw the line of force or flux and to understand and utilize electromagnet.

Apparatus

Magnet Bars Multimeter Compass Needle Electromagnet

Magnetic lines of Force

Introduction

Magnetic line of force is continuous curve in a magnetic field. Any point in the magnetic

lines of force represents the direction of the magnetic field at that point. This force of

lines can be drawn by using the compass needle and the iron fillings. Magnetic lines of

force provide the direction of magnetic field.


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Characteristics of magnetic lines of force

Magnetic lines of force have a travel path from north to South Pole of a magnetfor outside and for inside it have a travel path from south to North Pole of the

magnet.

Magnetic line of force is continuous curve and closed. The strength of the magnetic field should be calculated by measuring the number

of lines per unit area.

The lines of force are closer at the poles of the magnet and they are wider when itmoves away from the poles of the magnet. Thus the magnetic field is stronger at

the poles and it is reduces when it is move away from the poles.

At any point the tangent of the lines of force provides the magnetic field directionalso at the same point.

It is impossible that the magnetic lines of force can intersect.


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Procedure

1. Set the bar magnet on the table as shown in figure.2. Place compass around the magnet for at least 15 positions and record the directions

printed by the compass needle.

3. Plot your observed directions and draw the smooth curve to show the lines of forcebelow.

What do the lines around the bar magnet indicate?

The lines that we have mapped out around the magnet, called the magnetic lines of force,

indicate the region in which the force of the magnet can be detected. This region is called

the magnetic field. If an iron object is near a magnet, but is not within the magnetic field,

the object will not be attracted to the magnet. When the object enters the magnetic field,


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the force of the magnet acts, and the object is attracted. The pattern of these lines of force

tells us something about the characteristics of the forces caused by the magnet. The

magnetic lines of force, or flux, leave the north pole and enter the south pole.

How is the earth like a magnet?

Since the earth is a huge magnet with a magnetic north and south pole, the lines of

magnetic force around the earth look like there is a huge vertical bar magnet running

through the center of the earth. We will see in the next experiment how the magnetic

lines of flux around a magnet can be seen. The next page will tell you more about how

you can observe the magnetic field of a magnet and what you can learn from reading the

patterns of the magnetic lines of force.

Questions

1. What happened when you placed the circular piece of metal in the magnetic linesof flux? Outside the lines?

2. What do the lines around the bar magnet indicate?

3. If the earth is like a huge magnet, with a magnetic pole at the north end andanother magnetic pole at the south end, what might these imaginary lines look like

around the earth?


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Lab 08

Function Generator and Oscilloscope

Objective

To understand the working of Function generator to generate a desired outputsignal.

To understand the working of Oscilloscope to Visualize the Desired output SignalGenerated by Function Generator.

Apparatus

Function Generator Oscilloscope Function generator and Oscilloscope probes

Theory

A function generator is a device that can produce various patterns of voltage at a variety

of frequencies and amplitudes. It is used to test the response of circuits to common input

signals. After powering on the function generator, the output signal needs to be

configured to the desired shape. Typically, this means connecting the signal and ground

leads to an oscilloscope to check the controls. Adjust the function generator until the

output signal is correct, then attach the signal and ground leads from the function

generator to the input and ground of the device under test. For some applications, the

negative lead of the function generator should attach to a negative input of the device, but

usually attaching to ground is sufficient.

The function of an oscilloscope is extremely simple: it draws a V/t graph, a graph of

voltage against time, voltage on the vertical or Y-axis, and time on the horizontal or X-

axis.

As you can see in Figure 1, the screen of this oscilloscope has 8 squares or divisions on

the vertical axis, and 10 squares or divisions on the horizontal axis. Usually, these

squares are 1 cm in each direction.


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Many of the controls of the oscilloscope allow you to change the vertical or horizontal

scales of the V/tgraph, so that you can display a clear picture of the signal you want to

investigate. 'Dual trace' oscilloscopes display two V/t graphs at the same time, so that

simultaneous signals from different parts of an electronic system can be compared.

Figure 1


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Procedure

1. Turn on the oscilloscope. Check it for the reference signal provided i.e. 2Vp-pand . Is the output correct? If not calibrate until the desired signal iscalibrated. Ask your instructor for details.

2. Turn on the Function Generator .Connect its probes to channel 1 of oscilloscope.

3. Generate a Signal of F= . with 4Vp-p Sine Wave and Draw the observedsignal below.

Plot the Graph in the Following Figure and also mention V/Div and Time/Div.

Volt/Div=

Time/Div=


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Lab 09

Demonstration of Vectors

Objective

Introduction to Vectors and Forces

Vectors

Quantities that have direction as well as magnitude are called as vectors.Examples of vectors are velocity, acceleration, force, momentum etc.

The magnitude of a vector is denoted by absolute value signs around the vectorsymbol: magnitude of vector = ||

I. Graphical representation of vector:The magnitude of a vector in a scaled vector diagram is depicted by the length of

the arrow. The arrow is drawn a precise length in accordance with a chosen scale. For

example, the diagram shows a vector with a magnitude of 20 miles. Since the scale used

for constructing the diagram is 1 cm = 5 miles, the vector arrow is drawn with a length of

4 cm. That is, 4 cm x (5 miles/1 cm) = 20 miles.

Using the same scale (1 cm = 5 miles), a displacement vector that is 15 miles will

be represented by a vector arrow that is 3 cm in length. Similarly, a 25-mile displacement

vector is represented by a 5-cm long vector arrow. And finally, an 18-mile displacement

vector is represented by a 3.6-cm long arrow See the examples shown below.

Fig. 1: Graphical display of vectors

4cm = 5 miles

3cm = 15 miles

5cm = 25 miles

3.6cm = 18 miles


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II. Unit vectorA vector whose magnitude is equal to 1 is called unit vector. Unit vectors are used to

represent the direction of vectors.

()( ) It is represented by placing a over the symbol of vector.For example , and are unit vectors along x, y and z axis respectively.Addition of vectors:

Vectors can be added and subtracted. Let

and

be two vectors. To get the sum of the

two vectors, place the tail ofonto the head ofand the distance between the tail ofand is

Fig. 2: Addition of Vectors

Some examples of vector addition

I. Parallel vectorsParallel vectors can be added simply adding the magnitudes of vectors while there

direction will remain same.

+ =

5N 5N 10


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II. Anti-parallel vectorsFor anti-parallel vectors magnitude are subtracted and direction of the result will

be that of vector that is bigger in magnitude.

+ = 0

III. Two vectors at right angleVectors that are perpendicular to each other their magnitude can be calculated

By using Pythagoras Theorem:

In right angle triangle as shown in Fig. 5: Squaring both sides Fig. 2: Right angle

triangle By solving equation we get the magnitude

||

------------------------ (1)

Now for finding the direction of Hypotenuse we use trigonometric law

Putting the values By solving we can get angle at which resultant lies

*+ -------------------------- (2)

5N -5N


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Resolution of Vectors

Splitting a vector into its components is called resolution of vectors.

The component of a vector which are at right angle are knows as rectangular components.

Lets consider a vector represented by line (as shown in Fig. 3) making an angle with the x-axis. If we draw projection from point on x-axis than the vector will beresolved into two components and ..As is along x-axis so it is called x-component of vector represented as Fx. Similarly is parallel to y-axis so this component of vector is represented as Fy.

||

And []

Fig. 1: Vector Components

Dot Product:

The dot product is the value expressing the angular relationship between two

vectors, also called the scalar product. The symbol for dot product is a heavy dot. ||||Example: work

Y-axis

X-axis

O B


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Cross Product:

The cross product of two vectors a and b is denoted by a b, the value obtained from

cross product is a vector quantity and is perpendicular to both vectors. |||| Example: Torque


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Lab 10

Motion of a simple pendulum

Objective

To determine the time period of simple pendulum

Theory

A simple pendulum consists of a mass m swinging back and forth along a circular

arc at the end of a string of negligible mass. The restoring force is the component of the

gravitational force that is tangent to the arc, and is given by:

Where is the angle of the string relative to the vertical, if the angle is less than about

15, the sine of is approximated by the angle , and therefore, the restoring force is

approximated by: The displacement x of the mass along the arc is given by

Where L is the length of the string, in the case where the angle is small, the motion is

nearly simple harmonic motion, and the force is given by an equation with the same form

as Hooke's law Where L is the length of the pendulum string and x is the displacement of the pendulum

mass m. Therefore, the period of oscillation T of the pendulum is given by


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Fig 1. Simple pendulum

Where g is the acceleration due to gravity, in this lab, you will use the motion of a simple

pendulum to determine a value for the acceleration due to gravity.

You set up a simple pendulum of known length and mass. Next, you will determine the average time interval it takes for the pendulum to

swing through one cycle.

Finally, you will use the data to determine a value for the acceleration due togravity.

Procedure

i. Setup the support stand and tie a mass to the end of a string. It should be attachedso that it hangs straight, with its 'flat' sides vertical. Cut the string to a free length

of approximately 0.5 m.

ii. Position the pendulum in order to allow it to swing freely.iii. Measure the length of the string from its pivot point at the top, to the 'center' of

the mass at the bottom. Record the length on the data sheet.

iv. Grab the pendulum mass with one hand, and hold the stopwatch in the other.v. Pull back the pendulum mass, keeping the string taut. Sighting through the

protractor, adjust the angle of the string to be 15 relative to vertical.

vi. Release the pendulum mass and simultaneously starts the stopwatch. Let thependulum swing through 5-10 cycles. Stop the stopwatch at the end of a cycle.

L

x

T

O


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Record the number of cycles and the elapsed time on the data sheet. Measure the

time to the nearest 0.1 s.

vii. Repeat the measurement five times.Observation and Calculations

Radius of the bob =

Sr.

No

Length of the

stringTime on 10

Oscillations

Average

Time

[s]

Average

Time for

oneoscillation

[s]

Time period

T

[s]

S1 S2 S3

Analytical Solution

Conclusion/Comments


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Lab 11

Using Vector Addition Method

Objective

To find out the resultant by using vector addition

Apparatus

Weight hangers Pulleys Protector, scale Strings Vector board

Theory

The aim of the experiment is to understand the concepts of vector addition and

vector resolution. In the experiment three forces are applied at a point which is in static

equilibrium, the goal is to find out the resultant by using methods of vector addition such

as,

i. Head to tail methodOne of the forces is moved parallel to itself and they are drawn head to tail. Neither the

direction nor the length of the force is changed during this drawing. A third force isdrawn from the tail of first force to the head of the second force. Force represented thesun of the resultant of forces and .

ii. Component methodIt is always possible to resolve a force into two components along any given pair of

perpendicular directions. In order to resolve a force into its own components we need a

suitable co-ordinate system. We generally define the horizontal axis as

-axis and vertical

axis as -axis.the magnitude of these components is then found using the suitabletrigonometric equations.


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iii. Parallelogram methodThe forces are drawn from the same beginning point to the adjacent sides of

parallelogram. The parallelogram is then completed by drawing parallel lines to the two

forces and . The diagonal drawn from the beginning of the forces to the oppositecorner of the parallelogram is the force representing the sum ofand.

Fig.1. Two forces Fig.2. Head to Tail method

Fig.3. Parallelogram method Fig.4. Component method

Fig.5. resultant of and will be equal to

R

R

-axis

-axis


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Procedure:

1. Hang the weights on the pulleys.2. Balance the ring at the centre of apparatus.3. Measure the angles that forces are making with x and y axis.4. Find resultant of two forces by graphical as well as by trigonometric methods.5. Verify the results with the experimental values of the third force.

Fig.6. Vector addition apparatus setup.


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Readings/Results:

[N]

[N]

[N]

[deg]

[deg]

[deg]

For 1st reading:

For 2nd reading:

For 3rd reading:


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Observation and Calculations:

Calculate the values by using head to tail method and component methods. Compare the results with the experimental values.

Comments/Conclusions:


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Lab 12

Resolution of a Vector

Objective:

To show that the resolution of vector into components will have the same

effect as the original vector.

Apparatus:

Experiment Board, Force Ring, Mass Hangers, String, Degree Scale, Pulleys, Masses.

Theory:

Splitting a vector into its components is called resolution of vectors, and the

component of a vector along x and y axis are knows as rectangular components.

Lets consider a vector represented by line OA (as shown in Figure 1) making an angle with the x-axis. If we draw projection AB from point A on x-axis than the vector willresolve into two components and .As OB is along x-axis so it is called x-component of vector represented as. Similarly is parallel to y-axis so this component of vector is represented as . By usingPythagoras Theorem we can find the magnitude and direction of vector.

As in right angle triangle () , ()Since (from Fig.1)


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By putting values in (i) and (ii),

|| []

Fig.2. Vector Components

Procedure:

1.

Determine a force vector, F, by hanging a mass from the Force Ring over apulley. Use the Holding Pin to hold the Force Ring in place.

2. Set up the Spring Balance and a pulley so the string from the balance runshorizontally from the bottom of the pulley to the Force Ring.

3. Hang a second Mass Hanger directly from the Force Ring.4. Adjust the x and y components in this way until the Holding Pin is centered in the

Force Ring.

5. Calculate the components by using Head to Tail method or by componentmethod.

6. Calculate the readings of spring balance and the magnitude of force hanged toadjust the force ring at the centre.

7. Change the magnitude and direction ofF and repeat the experiment.

O


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Fig.2. Experimental setup

Measurements and Calculations:

Calculations for spring:

load extension K

Calculations for vector board:

Extension ||


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Results:

Conclusion/Observation:


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Lab 13

Value of g using spring mass system

Objective:

To determine acceleration due to gravity using mass spring system

Apparatus:

A spring fitted with pointer at its lower end Iron stand Meter rod Slotted weights Stop watch

Theory:From the previous section it is clear that time

period of a simple harmonic oscillator can be given by

Since mass spring system is a simple harmonic oscillator

other half of the formula can be used to find out the valueof acceleration due to gravity. Here we will use extension

in the spring x instead of length l. Fig 5.1: Mass spring system apparatus

This formula will be used for the calculation of acceleration due to gravity.

Procedure:

1. Take an iron stand, suspend the helical spring with pointer and attach a lighthanger to its lower end. Note that the spring is hanging freely and the pointer do

not touch the scale.


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2. Set the pointer at zero scale and when pointer comes to rest , note its position thiswill be the initial reading of pointer

3. Now add some weight and note the position of the pointer4. Pull the pointer down slightly and release it, so that springs make simple

harmonic oscillations. Record the time for 20 vibrations

5. Similarly take at least four sets of readings.Observations and calculations:

Load Pointer

reading

Extension Time for 10

vibrations

Average

Time

period for

20

oscillation

Time

period for

1

oscillation

Initial Final 1 2 3


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Lab 14

Coefficient of sliding friction

Objective:

To measure the static coefficient of friction between two surfaces using a

ramp.

Apparatus:

Inclined plane covering material for ramp Objects to slide down.

Theory:

The coefficient of friction between two surfaces is a number that determines howmuch force is required to move an object that is held back by friction when the two

surfaces are pressed together.

The friction equation is Fr = fr x N, where Fr is the resistive force of friction or the

amount of force required to overcome friction, fr is the coefficient of friction between the

two surfaces, and N is the normal or perpendicular force pushing the two surfaces

together. If the force pushing to surfaces together is gravity, then N equals the weight of

the upper object.


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Static and kinetic friction:

For a sliding object, the static coefficient of friction results in the force required to start

the object moving. Once the object is sliding at a steady rate, the kinetic coefficient of

friction results in the force required to keep the object moving at that velocity.

A clever way to determine the static coefficient of friction is to start an object sliding

down a ramp. The component of gravitational force that causes the object to just start

moving is equal to the resistive force to keep the object stationary. That is the static force

of friction. Knowing the force required to overcome the friction and the force pushing the

object onto the ramp, will allow you to determine the static coefficient of friction.

Components of gravity:

When an object that weighs W is on a ramp, the force of gravity can be divided into

components in perpendicular directions. The force pushing the object against the surface

of the ramp is reduced because of the incline. The normal force is () asshow in the picture below. In the case where there is no incline, a = 0 degrees and N =

W.

The component of gravity is pulling the object along the ramp is ()Now when the angle a becomes steep enough, the object starts to move and F = Fr, which

is the force of static friction required to start the object moving.

But you know that Fr = fr x N.

And for the object on the ramp, ()


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Thus () ()Using a little Algebra, we t

() () ()Finally, since () we have Procedure:

1. Place the ramp on the ground and put the object on the ramp2.

Slowly raise one end of the ramp until the object starts to slide

3. Measure the height (A) and length (B) of the inclination, as in the drawing below4. Calculate the coefficient of friction between the surfaces: fr = A /B

Observations and calculations

No of

Obs

Materials

pressing on

Vertical

distance

A

Horizontal

distance

B

Inclination

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