Physics72.1 Laboratory Manual

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PHYSICS

72.1,

LABORATORY

MA}{TJAL

by'

Rommel

C.

Gutierrez

Maricor

N.

Soriano

Rumelo

Amor

Marie Ann Michelle Calix

Edmundo Casulla

LizaDavtla

Michelee Patricio PetetJohn Rodrigo Miguel Yambot

-(a

z

NrP-0

0 6

t

qc

6fl

3r

fsqt

).ool

,t.ft

Vair+

--s.t\nu

--

w

_{E6"&? ^;U}

1L^2I"7

Fitst _{Edition, June 2000}

Second Edition, _Jun e 2001,

Edited by: Edmundo Casulla

LizaDavtla

Christine Ison Jonathan Palero PeterJohn Roddgo Miguel Yambot

Policies and

guidelines

i

EXPERIMENTS

1. Electric

field

and

field

potential

1

2.

Ohm's law

7

3.

Resistors

in series and

parallel

19

4.

Ktrchoff's rules

25

5. Electromagnetic induction

33

6.

Introduction

to

alternating current

(ac)

circuits

43

7.

Optical

disk:

reflection and

refraction

57

8. Image

formation

using

thin

lenses

67

1.

Grading

System

Laboratory Reports Practical Exam N-ritten Final Exam Recitation, Quizzes, etc

TOTAL

60% 1,5% 1.50 10% 1,00% Grade

Equivalent

100

>x

92

>x

88

>x

84

>x

80

>x

76

>x

72

>x

>

68

+2.50

68

>x

>

64

+2.75

64

>x

> 60

-+3.00

6o

>x

> 5o

+4'oo

50

>x

> 0

->5.00

Z.

Laboratory

Report Guidelines

Data sheets

(or

the manual itself) are collected

by

the instructor at

the

end

of

each experiment, and ate returned during specified periods for wdting the report. Laboratory reports are accomplished individualty and only during

r.port-*riti.rg

sessions. They are collected

at

the end

of

these periods. References (textbooks and journals only) are allowed during these sessions.

3.

Genetal Guidelines

I.

If

a student misses an experiment, he has to present a medical certificate (in cases

where applicable) from the UP Infirmary within.seven (7) days

of

the absence, or

within

the

first

day he

is

able

to

come

to

class. Failure

to

do

so forfeits

the student's

right

to

a make-up experiment.

Only two

experiments are allowed

for

make-up.

II'

In

the event a student misses the final exam or practical exam,

a

grade

of "INC"

is given

with

the tematk "missed the final exam" or "missed the practical exam."

III.

A

grade

of "DRP"

or

dropped is given upon the

initiation

of

the

student, and provided he submits a copy

of

the dtopping slip

to

his instructor. The same rule applies to students who file a leave of absence

pOA).

fV' A

grade

of

"4.0"

impJies that the student should retake the course as there is no

v.

A

student who has not submitted at least 4 experiments by the droppingdate

will

automatically be given a failing grade _{of "5.0"}

if

the student has not dropped. I.

II.

I}iTRODUCTION

The

electrostatic force

on

charge qo due to charge ₄ is given by (Coulomb's law):

per charge qoin moving the charge berween rwo

points

in

an

electric

field,

E

is

called

the potential difference

AZbetween

the points:

LVu,

_{-Vz-V, -vru}

_{=it Ot}

_Q.4)

40)

where

dl

is

thepath from

A

to B.

For a finite path length Ad the magnirude

of

the electric field is given by:

(1 .1)

where r is the distance between the charges,

i

is the unit vector pointing from q to ,q, _{and the}

consrant ,€ is 9.0

x

10e N-m2

/cz.

The direction

of

the

force

on

a

charge may

be

determined :sing the law

of

charges. Like charges repel and

';ilike

_{charges attr^ct.}

The electric field is defined as the electrical :orce per unit charge, or

(unit is

N/C).

(1.2)

na the case

of

the electric field associated

with

a

s:agle source charge Q,

the

magnitude

of

the

sectric field a distance

r

away from

the

charge q

:s

(1.3)

If

a free charge, _4,, is released

in

the vicinity

:i

a

stationary soufce charge,

it

would

move .{ong a line

of force.

Since a free charge moves

'-

an electric

field by

the action

of

the electric iorce,

work

is done

by

the field

in

moving the 'd:arge from one

point to

another. The

work

IV

oBIECTT\rE

To

determine

the

equipotential surfaces

in

an electrolytic snitude of the electric field.

(1.s)

If

a

charge

is moved

ilong

a

path

at right

angles

ot

perpendicular

to

the field, there is no

work

done

_M=0),

since

there

is no

force component along the

path.

Then along such p path,

LVru

_{=Vt -Ve}

(1.6)

(1.7)

Vu

_=Vn'

Hence, the potential is constant along paths peqpendicular

to

the field

lines.

Such paths are

called equipotential

lines (or

equipotential surfaces in three dimensions).

F

_-

kq!,,

i

r

lal=+

-tr

lr-_ 4o E

_=L=\!r?=

r

=9r

Qo q,r'

r

=Y=g.

4o

\Ea.uJ Institute of Physics, UP Diliman

1. Electric Field and Field Potential

MATERIALS

Fig. 1.1 The experiment set-up, Two cylindrical electrodes ate immersed in a

shallow pool of watet of constant depth. The elecrodes _{ate Placed} at (0r8)

and (0,-4).

PROCEDURE

1.

Pour water on the electtolytic tank. Put two

disc electodes

at

coordinates

(0,8)

and (0,-4).

Attach

the connectors

to

the probe,

pov/er

supply and

voltmeter as

shown

in

Fig. 1.1.

2.

!7ith

the probe

tip

on

the electrolytic tank,

determine

5 to

10

coordinates

with

a

potential value

of

1.0

V.

Do

not

make a

table

of

values, instead

plot

the coordinates

on

Graph 1.1

in

the

data

sheet.

The

symmetry

of the gtven

electrode

configuration allows you

to limit

the

plot

to

the first

and

fouth

quadrants.

It

is

convenient

to

make

eithet

x- or

y-coordinate an integer when locating a

point

in

an equipotential line. Choose the points such

that

they span the

whole

area

of

the

tank. Trace

the

equipotential

line

fot

a

potential

of

1.0 V.

3.

Perform step

2 fot

potentials

of

2.0

V,

3.0

V, 4.0

V,

5.0

V

and 6.0 V.

Obtain

an

estimate

of

the

electric

field (magnitude and

dkection) at the points

of

intersection

of the

equipotential

Line

V(*,1)

₌

3,0

V

_'nth

x

=

0, 2,

4,6.

Get the values

of

Alby

measuring the perpendicular distance

ftom

each

of

these

points

to

an adjacent equipotential line and

AV

from the

difference

in

potential

between

*re

3.0

V

line

and

this

adiacent equipotential

line. Represent

the

electric field

vector,

-E

at

these points

by

arrows using

a

scale

of

/

cm

: I

uolt/cm. Show sample calculations

for

the magnitude and draw

the

E

vectors on Graph 1.1.

Replace

the

disc electrode

in

(0, 8)

with

a

long rod

oriented peqpendicular

to

the

y-axis.

Repeat

steps

2 to 4

and

_Plot

coordinates on Graph 1.2. 4.

5.

1. Electric Field and Fidd Potc*id

\-ame:

Partners:

lrsrructor:

Gruph

l.l

Electric Field

and

Field Potential

for

Two

Disc

Electrodes

Calculations Date Performed:

Date

Submitted: Section: dd

of

ine

tre

rlar an dre d're

dal

E

rof

ons [ors

ftra

fltt

1. Electric Field and Field Fotential

Graph L.2

Electric

Field

and

Field

Potentid

for

One

Disc Electrode

and One Rod

Electode

Calculations

Physics 72.1 _{1. Electric Field and Field Potcrtid}

QUESTTONS

1.

The direction

of

the electdc field is indicated

on

field lines. on equipotential lines?

\Why are there

no

directions indicated

Use

the

equipotential lines

to

explain

why the

surface charge density

Lt

each electrode

is

not

uniform.

Use the equipotential lines and associated lines

of

force

to

show that there are excess charges at the edge

of

the tank.

+

For

the electrode configurations

in

Graphs 1.1 and1,.2, comment

on

the electric

field

(a) between the electodes, and (b) near the edges

of

the electrodes.

In

what region(s) does the electric field have the greatest intensity? How is this determined from the plot?

1, ElectricField arld Ficld

t,

INTRODUCTION

Ohm's Law

states

the linear

relationship

between the voltage ar-rd current

of

an electrical

&cuit

that contains resistors only.

It

is stated

in

the

following

way:

'If

t])e Empqdture and otbq

fiiyical

conditions of a ntewllic confucnr is unclnngd,

the ratio oftbe potential dffirence to tbe current is

constant."

This

onsant

is

knovrn

to

be

the

resistane

of

the

@ndrctor. Nlarhernatically,

Ohm's

law

may expressed as:

AV:IR

(2.r)

where

AV

is the potential difference (also called voltag.) across the metal conductor measured

in

volts (V),

I

is the current through the conductor measured

in

amperes

(4,

,nd R

is the resistance

of

the

conductor

meazured

in

ohms

(O).

Although

the

definition

of

resistance

for

nonohmic materials is the same as that for ohmic

materials, the resistance R, defined for non-ohmic

materials

is

currentdependent.

Nonohmic

materials

will

not

give

us

a

linear voltage ns.

Errrent

behavior.

The

resistance

of

an

ohmic

conducting

wire

is

found

to

be

proportional to

its length

and

inversely

proportional

to

its

cross-sectional area.

Its

constant

of proportionality

is

called

resistivity of the conductor,

p. The SI

unit of

p is the ohm-meter

(O-*).

Q.2)

The resistivity,

p

of

any metal varies almost

linearly

with

temperature.

It

is usually given

in

tables

in

tenns

of

its value

pa

x

2ffC

and the temperature coefficient,

o.

The

produa pao

is defined as

the

slope

of

th.

p

vs.

T

curve. The

raistivity

at some other temperature

T

_fC), is:

p(T)=p,[t+o(T-20)]

_Q.3)

Table 2.L below shows

raistivity

values at 200C and temperature coefficients

of

resistance

based

on

the

resistance

of

some

corlmon

conductors at OoC.

*: r1

Table 2.1Resi$ivities and temperature coefficients of common metals

IoBIECTTVE

To

determine the behavior

of

an

ohmic

material as a

function

of

vol

German (nickel), silver

!{riood Iostitute of Physics, UP Diliman

Physics 72.1 2. Ohm's Law

MATERIALS

The

materials

we

will

use

fot

this

experiment

ate

enumerated

below

and

are illustrated

in

Figure 2.1.. The circuit diagrams

in

the Procedure makes use of the symbols below.

Multimeter.

This

will

serve

as

the

voltmeter, ammetef and ohmmeter.

Multimeter Variable Supply_Power

2-M Resistance wire

Fig 2.1 Equipment used in the experiment.

PROCEDURE

Read and undetstand the experiments.

Variable power supply.

Its

output voltage

is0Vtoabout6V.

2-m wire. This

will

be our

resistor. The

wire is made of

German-nickel.

l'l-

power

supply

re s isto r

connectors

voltm eter

am m

eter

ohm

m

eter

Fig2.2 Symbols used in the citcuit diagtams.

general instructions

in

the text box

below before proceeding

with

the

To

avoid

damage

to

the

meters, always start

rilrith

the metet on

its

least

sensitive

scale.

Increase

the

sensitilty

of

the meter

only

as needed

fot

accurate measurementr

and temembet

to

retuflr

the meter to

its

least sensitive scale before proceeding.

Voltages afe measured (tacfoss" so,

voltmetets

afe connected

patallel to the

citcuit

element.

Culents

are measured

,,through',

so ammeters are connected

in

series

with

the

circuit

element.

Tum

off

the power supply

when not

measuring.

Before

using

the

ohmmeter

to

measure

the

resistance

of

the

resistance

wire,

always

disconnect the tesistance

wire

ftom

the

powet supply

and

othet

metefs. A.

Variation

of voltage

with

current

1.

Measute

the

following

quantities:

the

resistance

of the

2-m

wire

using

an ohmmetet, the room temPerature duting the

experiment

and

the

diameter

of

the

wite.

Recotd these

values

in

Data Table

2.1.

Perfotm

5

trials

in

measuring

the

room

temperature and the diameter of the wire.

2.

3.

4.

Set up the apparatus as shown in Figure 2.3.

Set the output current

of

the power supply

to

a minimum.

Turn

the knob

of

the powet

supply to vary the output current.

Take

five

readings

of

curtent

and voltage

for

uniformly

increasing values

of

current

The

suggested

increment

step

is

apptoximately 0.1 A. Measure and record

in

Data Table

2.2

the currenr supplied

to

the

B.

Variation

of

Curent with

Resistance

Use

the

sarne affangement

as

shown

in

Figure 2.3.

Set the voltage

from

the power supply

to

a

minimum.

Increase

the

voltage

from

the

power

supply

until

current

is

read

in

the ammeter. Record this current

irData

Table 2.3.

Decrease

the

length

of

the wire

by increments

of

40

cm

(Figure 2.4).

At

each

length,

measure

the

current.

Take

five different lengths.

Keep

the

voltage constant

throughout

this part

of the experiment.

C.

Variation

of

Potential

with

Resistance

Connect the apparatus as shown

in

Fig. 2.5.

Make sure

that the

terminal

A

is

the

zero end of the 2-m resistance wire.

Measure the voltage and recotd

it

in

Data Table 2.4.

Increase

the

length

of

the wire

between terminals

A

and C by increments

of

40 cm. Take the voltage at 5 diffetent lengths.

Keep

the

current constant

throughout

this part

of the experiment.

wc

a(c

in

am?re

reXiro<'

{\c'

ta'eh'l

!

ZOhmtkt

2-m

wire

and

the

potential

difference

between points

A

and B.

Fig.2.3 Citcuit fot A.

5.

l.

2.

Remove all the wires connected

to

the 2-m

wire.

Measure and record

its

resistance at different lengths using an ohmmeter.

Fig.2.4 Citcuit fot B.

Fig. 2.5 Circuit for C.

3. 4.

I.

z

3.

{.

Physics 72.1

Physics 72.1

Law

2.

OhEt

Name:

Partners:

Data Table

2.1

Theoretical

values

of resistivity

and resistance

Date Performed:

Date Submitted:

*

.

1 : :=: i:+!J ====+tr:,".,===..1I.?# :,'. :i:l::'.r:..;i:;i

0.4

=r:.'r!:.i-f,'

3:.

=.*.#

:::::::t:-.r,ri

+

.-,5 ::::::::t::irri

COMPUTED PARAMETERS

Cross-section area:

Resistivity (from

Eq. 2.3):

Resistance

(from

Eq. 2.2)z Resistance

(ohmmeter):

ToerrOr:

Calculations

Data

Table

2.2Yoltage

vs.

Current

Calculations

LINEAR

REGRESSION

Resistance

(ohmmeter)z

Au')

Phpics 72.1

Irw

2.

Ohn'r

Data

Table

2.3

Current

vs. Resistance

LINEAR

REGRESSION

Slope:

y-intercept:

Constant voltage

(voltmeter):

o/oettOti

l.v

Calculations

Physics 72.1 2. Ohm's Lew

Data

Table 2.4

Voltage

vs. Resistance

TINEAR

REGRESSION

Slope:

y-intercept:

Constant

current

(ammeter):

o/oettOfi

Calculations

Physics 72.1 _{2. Ohmt Law}

QUESTIONS

1'.

Use the data in Data Table 2.2 to plot a curve in the gridlines provided below.

Voltage (V)

Cunent (A)

Inteqpret the significance

of

the shape and intercept

of

the curve. !7hy is the slope

of

the curve the resistance of the 2-m wire?

Account

for

any discrepancies among the values

of

the resistance

in

Data Table 2.1, and Data Table

2.2.

Physics 72.1 2. Ohm's l-aw

4.

Use Data Table 2.3 to plot the variation of current

with

the reciprocal of the resistance. Gurrent (A)

1/Resistance

(o'')

5.

Compare the slope

with

the constant

V

used

fot

this procedure. Account for orry discrepancy.

2. Ohm's Iaw

6.

Use Data Table 2.4 to plot voltage vs. resistance alld resistance vs. length, L.

Voltage (V)

Resistance (Q)

Resistance (Ct)

Length (cm)

Compare the slope

of

the

V

vs. R plot

with

the constant

I

used

for

this procedure.

Account for

any discrepancy

2 Ohm'sLaw

8.

Calculate the tesistivity, p

ftom

the slope

of

the resistance vs. Iength graPh. (Show

yout

calculations

belovr) Compate this result with the p

inData Table2'7'

I i

I- l-i

I

INTRODUCTION

For resistors connected

in

series, the current passing through each resistor

is

the

same, but

the voltage depends on the value

of

the resistor.

The totai

potential

difference

of

resistors in

series

is

the

sum

of

the potential

differences acfoss each resistor.

For

resistors connected

in

parallel,

the

potential difference across each resistor

is

the same,

while

the total

current

of

the

parallel resistors

is

the

sum

of

the

individual currents passing through each resistor.

For

resistors

connected

ifi

series,

the effective resistance of the whole circuit is:

Run

=& +& +&

+...+&

(3.1)

For

resistors connected

in

patallel,

the effective resistance of the whole circuit is:

(3.2)

11111

- =

1-...-r-R"n

_&

R2

_&

R,

Resistors

-flItr--{IITfF

MATERIALS

Breadboard 6V Power Supply

lrARNING

fncrease

the sensitivity

of

the meter

only

as needed

for

accurate to

return

the meter to

its

least sensitive scale before proceeding.

Voltages are

measured ((across"

(in

parallel).

Currents

ueries).

To

avoid

damage

to

the

meters, always start

with

the meter on

its

least sensitive

scale.

measurement,

and

remember

are

measured

ttthtough" (in

To

learn

how

to

implemeht a

circuit

diagram and

to

be able

to

compute

the

effective resistance

of

resistors

in

series and

3, Resistors in Series sfld Pan[el

PROCEDURE

L.

Using the color

bandsx

of

the

resistots, tabulate the values

of

the rcsistances

(R)

in

Data Table 3.1.

Black Brown Red Orange Yellow Green Blue Vioiet Gray White

0123

4 5 6 789

Table 3.1 Numerical equivalents of resistot color

bands

From the above values, comPute and record

the

theoretical effective resistance

_6"n)

"t

each circuit (Data Table 3.2).

Set

up R,,

_&,

and

R3 according

to

the diagram

for

circuit 1. Use

a

S-volt Power supply to drive the circuit, then measure the

voltage

across,

and

the

current

passing

through

each resistor, and

tecord

in

Data

CIRCUIT DIAGRAMS

Circuit 1

Table

3.3.

ComPute

and

tecord

the

individual tesistances (Rr) using Ohm's law.

From the values

in

Data Table 3.3, compute

and

record

the

effective

resistance

pata

Table

3.4).

Compare this

with

the value in

Data Table 3.2 and get the percentage error.

Remove

the power

supply,

then

measure

and

the

effective resistance, Rqfr

using

an

ohmmeter and record

it

in

Data Table 3.5.

Compare this

with

the value

in

Data Table 3.2

md

get the percentage effor'

Measure

the

effective voltaqe

and

cutrent

for

circuit L and tecord them

in

Data Table 3.6. Ftom these values calculate the effective tesistance

and

compare

with the

value in Data Table

3.2.

Get the percentage error. Repeat steps 3

to

6

for

circuits

2,3,

and 4;

Circuit 2

V=5.0V

Rr

₌

1.0

k(l

Rz

_{= 1'2Id)}

Rr

₌

1'5

k(l

4. 6. 3.

ffisofresistots,followthediag,umbelow,withthebandsasA,B,CandD.Thevalueofthe

resistance ls ft=(10A+B) x 10c]A + D. The values of AB, and C ate read accotding to

Table 3.1, while

b

.an b. sitv.r iTOo/o) or.gold (570). Fot exarnple, a resistor with bands'

C-ted, D-gold, has resistancs f,=(45x1@ O

t

snQ, o. 4'!

]9

lj%'

2A

Cirodt 3 Circuit 4

Phvsics 72.1 3. Resistors in Series and Parallel Name:

=EI

the lw. )ute )ata

ein

rof. sure

lafl

3.5. abie Erent lable ctive

ein

)r. 4. f

rhJ

j

Partners:

lnstructor:

Date Performed:

Date Submitted:

Data Table

3.1.

Theoretical

values

of

resistance

Data Table

3.2,

Theoretical

values

of

effective

resistance

3. Resistors in Series and Parallel

Data Table

3.3.

Experimental

values

of

resistance

from

voltage

and

current

measurement

Data

Tabl e

3.4.Effective

resistance

from

Data Table

3.3

W

usc'

brN^'lq

Data Table

3.5.

Effective

resistance

from ohmmeter

Circuit

Experimental

Effective

Resistance,

&n

o/oettot 1

2

3

4

r..lr{-

g

O

6

t

65

Qt

zg fgq>

&rrl

?

3. Resistors in Series aadPardlcl

DataTable

3.6.

Experimental

values

of

effective

resistance

from

effective voltage and

current

llt

7"

c((or

cor{\OanJ

'ol

Tebte

I

'

3. Resistors in Series and Patallel

i i I I ; h F i

INTRODUCTION

In

the

analysis

of

circuits,

Gustav

Kirchhoff

(1824-1,887)

formulated

two

empirical rules

which

can

be

observed

to

be

theoretically consistent w-ith

the

principles

of

conservation of energy and charge.

o

The

Voltage Rule

(or loop rule) states that

the

algebraic

sum

of

the

voltage changes around a closed loop is zero.

The

following

sign

convention

is recommended:

o

lWhen

_going

_around

_a

_loop

_and

_passing

through

a

bafre\,

the

voltage

change is

taken

to

be

positive

when the

battery

is ffaversed toward the positive terminal, and negative when traversed toward the negative terminal.

o

\ff/'hen passing through a resistor, the voltage change across

the

resistor

is

taken

to

be negative ("voltage

drop') if it

is traversed in

the direction

of

the

assigned current, and

positive

if

traversed

in the

opposite direction.

(4.1)

IV,

=

0

I

l"rt

_{ri.g =} E It.u'irg (4.2)

oBJECTT\rE

To be able

to

analvze multi-looo circuits usins Kirchhoffls Rules.

MATERIALS

Two power supplies, multimeter, resistors, breadboatd and connectors.

o

The Current

Rule

(or

_{lunction rule)} states

that the

sum

of

all

currents entering

a

junction must equal the sum

of

all currents leaving the junction.

PROCEDURE

1. Examine

the

resistors. Compute

the

rate

of

resistance from the color bands and their actual resistances

using

an

ohmmeter.

Record

your data in DztaTable 4.1.

2.

Set

up

the

fitst

circuit

(nvo

loop

network).

Switch

on

the

voltage

sources

(adjust

each power supply as closely as possible

to

the values specified

in

the

figute). Measure

I,,

I,

and

I,

using

an

ammetef. Measure

V,,

V,

using

a

voltmeter. Record your data in Data Tzble 4.2.

3.

Using

Kirchhoffs

Rules (and

the

measured voltages and

the

theoretical resistances), solve

for

the currents

I,,

I,

and

I,

passing through the resistors R,,

R,

and

_\

respectively. Show your solution cleady

on your

answer sheet. Indicate also the

directior

of

the currents through each

resistor. Compate these cuffents

with

the

measured

cuffents obtained

in

step

2

by computing the percentage error

of

each current.

Account for these etfofs.

4.

Now

take each loop and measure the volage

across each element

in

the loop.

Add

these voltages (taking

note

of

our

sign convention). What value shouid you obtain?

Physics 72.1 4. Kirchhoffs Rules

5.

After

^fl

lyzing the nvo-loop network, add a

third loop

to

the original

citcuit

usihg a fourth

resistor, Ro

₌

3.3

kQ.

Answer

questions 2-4, solving

fot

and measudng

Ir,

12, 13, In, Iu, and Iu

CIRCUIT DIAGRAMS

Vt=5.0v

Rt ₌ 1.0 kO

as indicated above aod measuring

the

voltage across each resistor. Recotd

your

data

in

Data Tzble 4.3.

V2=4.5V

R2 ₌ 1.2

kC)

R3 ₌ 1.5 kO

Three-loop

netwotk

R+

v2

1,,

I6

Vt=5'0V

Rt ₌ 1.0

kO

R2 ₌ 1.2 kO

Vz=4'5V

RS ₌ 1.5

kO

R+ ₌ 3.3 kQ

Physics 72.1 4. Kirchhoff's Rules i

I

Name:

_{Date Performed:}

Date

Submitted:

Partners:

lnstructor:

Data Table

4.1. Resistance values

Data Table

4,2.

Two-loop network

Physics 72.1 4. Kirchhoffs Rules

Calculations

4. Kirchhofft Rules

Data Table

4.3.

Three-loop

network

Calculations

National Institute of Physics, UP Dilimen

NA

NA

NA

Physics 72.1 _{4. Kirchhoffs Rules}

QUESTIONS

1.

Do

the measured values

of

the resistances

fall within

the range indicated

by

the last band

ofl

the resistor label? (tolerance values: gold

t5%,

silver *1070, no band

!20tA

Refet to step (4)

in

the procedrre. What rule does

it

explicidy verift? What is the significance

of

this rule?

What would be the effect

of

using the loop network (e.g. V,=Vr=$.Q

!))

T1a

o

same voltage level

for

the

two

_{Power supPlies}

in

the

Physics 72.1 4. Kirchhoffs Rulcs

4.

The

direction one goes around

a circuit loop

makes

no

difference

in

the

Voltage Rule equation obtained

for

the loop. Show this explicidy by going around the loops (in circuit diagram 1)

in

the opposite directions.

Apply

the

loop

theorem

to

the big outer

loop

(travesing

Vr,

_&,

R"

and

V)

of

circuit

1 and show that

it

is redundant or unnecessary

if

you are already using the trro inner loop equations.

Physics 72.1 4. Kirchhoffs Rules

INTRODUCTION

Hans

Oersted discovered

that

a

magnetic

field

is

associated

with

an

electric current. He

further

established

a

relationship between the

direction

of

the cuffent and the direction

of

the

magnetic

field.

The

magnetic

field lines

are

found

to

be closed circles around

the

current-carrying wire.

The direction

of

the magnetic field is given by a

rigbt-band

rule:

If

o

current-carrying

uire

is

grasped

u)itb tbe

rigbt

band

witb

tbe

thumb

extended

in

tbe

direction

of the

conoentional

canrent,

the curled

_fingers

will

indicate

tbe

circular

sense of tbe _{tndgneti.c fr.eld}

line.

The

direction

of

the

magnetic

field

^t

any

point is then tangential to the circle.

Faruday investigated

the

possible tevetse

effect

of a

current being

produced

by

a

magnetic

field

in

the viciniry

of

a wire. No

effect was

found

with a

stationary magnet or

magnetic field. Howevet,

it

was discovered that

a

cuffent

is

induced

when there

is

relative

motion

or a

changlng magnetic

field.

Thus,

elecftomagnetic

_{induction involves}

a

time-vtryingmagnetic field.

Investigations led Faraday

to

the conclusion

that the important

factor

in

electromagnetic

induction

was

the time

rate

of

change

of

the

magnetic

field

B

thtough

a

loop. The

total magnetic

field through a

loop

of

wire

can be characteized

by what

is

called magnetic

_flwc

@:

O _{= B}

.A=

BAcos9

(5.1)

where

A

is

the

cross-sectional arca

of

the

Ioop and 0 is the angle benveen a normal to the plane

of

the loop and the magnetic field. Hence, the time rate

of

change

of

the rnagnetic field, or

the number

of

field lines, peqpendicuiar

to

and through a loop is given by the rate

of

change

of

the magnetic

flux,

LQ I

Lt

= (AB

I

Lt)A.

The result

of

this

wotk

was

Faraday\ law

of

inductioz,

which relates the induced voltage

or

enf

rn

a

wire

to

the time

rate

of

change

of

flux:

l/=

AO (s.2)

where

V

is r}.e a'verage value

of

the induced voltage over the time interval

Ar.

Note that

(s.3)

That

is,

a

flux

change

can

be due

to

a

change

in

the magnetic field through a

loop

of

constant

area,

andf

ot

due

to a

coflstant magnetic

field

and

a

change

in

the

area

of

the loop.

In

either case, the number or density

of

field lines through the loop changes. The latter effect is commonly obtained by rotating a loop of wire

in

a constant magnetic

field

so

that the

efectiue

area

of

the loop exposed

to

the field, and hence the flux, changes.

The negative sign in equation (5.2) expresses

another important

law of

elecuomagnetic induction, Lenz's

law,

wlichgives

the direction

of the induced current:

An

induced current

is

in

sucb

a direction

tbat its

,ff

at

oppose

the

cbange tbat

produces

it.

Essentially,

this

means the induced cuffent

gives rise

to

a magnetic

field that

opposes the change in the odginal magnetic field.

Lt

Ao

=r44u.8144)

Lt tarJ

l.ar./

l

Physics 72.1 _{5, Electromagretic Induction}

Still

another

way

to

produce

a

time-varying magnetic field, and an induced vokage

in

a stationary wire loop, is

to

vary rhe current

in

a current-carrying loop.

If

there are a number

of

loops

N,

the

flux

change through each loop contributes

to

the

induced current

or

voltage,

and F araday's law becomes

3

=

ltonl

Y=-NA@

Lt

Similarly,

if

loops

of wire

are

wound

in

a

tight helix

so as

to form

a

coil

(solenoid), the

magnitude

of

the

magnetic

field

would

be increased, and near and along

the

axis

of

the solenoid,

it

is given by

oBJECTT\rE

To

studv electromagnetic induction in a simple circuit usins Faradav's law and

knz's

law.

MATERIALS

Pair of insulated cylindrical coils (many turns on secondary relative to pdmary)

Iron

and brass or aluminum-cote rods

Two bar magnets of different pole strengths Low-voltage dc powet supply or dry cell Magnetic compass

Iftife

switch Galvanometer

Metdc ruler or meterstick

Conne.

wires

(5.4)

(s.s) where

z

is the linear turn densiry

of

the coil

(i.e., the number

of

turns per

unit

length

N/L,

where

I,

is the length of the coil).

The

constant

_{Uo is}

called

the permeability

of

free space, and indicates that the

solenoid has

an

air

core.

If

a

material

with

a

magnetic permeability _1t

is

used as

a

solenoid

core, p.o

is

replaced

by

_{ll in}

equation

(5.5).

Physics 72.1 5. Electromagnetic Induction

PROCEDURE

g;./ctmiqe poletr'fo

a(

gdvqwr{rc,lrr

1.. In

this experiment, is important to know the

direction

of

the

induced

current

in

the

circuit. This

is

related

to

the

positive and negative deflections of the galvanometer.

To

establish

the

direction

of

the galvanometer

deflection

to a

known

current

direction, connect one terminal

of

the

dry

ceil

(or

dc

pov/er supply

at 1.5-3.59

to

one terminal

of

the

galvanometer and

the other

source

terminal tbrougb a large resistance

to

the other

galvanometer

terminal.

_€rg"re

5.1a). Use yourself as the large resistance.

2.

From the known polarity

of

the

source,

relate

the

galvanometer

deflection

to

the

direction

of

current

flow. For

conventional

curtent, this flows

from

the positive source

terminal. Galvanometer deflections

to

the

dght

are

usually labeled

as positive

and

deflections

to

the

left

as

negative.

It

is

convenient

to

have

a

conventional current entering the positive galvanometer terminal to give a positive direction.

3.

Connect the galvanometer

to

the

terminals

of

the

secondary

coil

(the larger

coil

with

the

greater number

of

turns) as shown in

Figure 5.1b. Use the compass

to

determine

the

relative strengths

of

the bar

magnets.

Then, using the stfonger magnet, move the magflet

in

and

out

of

the coil, noting

and

recording

the

effects

(relative

magnitude and direction of the galvanometer deflection

with

(a)

the

speed

at which the

magnet is

moved; and (b) the change

of

the magnet's polariry). Record your results. Repeat using the other magnet and record the results.

Set

up

the primary

coil

circuit as shown in

Figure

5.1c

with

the

switch

S

open.

(

A

secondary

coil

circuit

is

not

needed in

procedures

4

and 5). Close

the

switch and

with

the

compass, investigate

the

magnetic

field

atound the coil. Make a sketch

of

the field pattern.

Open the switch and insert the stronger bat

magnet

into

the

pimary

coil almost the

fuil

Iength

of

the magnet. Close the switch and

slowly

remove

the

magnet

from the

coil.

Note, record, and explain afly

observed effects.

Open the switch and insert the pdmary coil

into

the secondary coil, which

is

connected

to _{the galvanometer @igure 5.1c). Close and} open

the

switch,

noting

and recording the

magnitude

and

direction

of

the

galvanometer

deflection

in

each

case.

Repeat using each of the two metal cores.

Measure

and record

the lengh

of

the

pdmary

coil.

-$7ith

the

switch open, insert

the

primary

coil with the iron

core completely

into

the

secondary coil. Make a

series

of

observations

of

the magnitudes

of

the deflections as the switch

is

opened and closed, withdrawing

the

primary

coil 1

cm

between

the

observations.

Record

the

length

of

the

primary

coil still

inside

the secondary coil in each case. Find the a-verage

magnitude

of

the plus and minus deflections

for

each observation, and

plot

a

graph

of

the average deflection magnitude (ordinate) versus the length

of

the

pimary

coil

inside

the

secondary

coil

(abscissa).

Intelpret

the results of the data.

4.

5.

6.

7.

physics _72.1 5. Electromagnetic Induction

E

masnet

primary coil

secondarY coil

c)

Figute 5.1 Electomagnetic induction setups and citcuits.

Physics

72.1

5. Electromagnetic Induction

Name:

Date Performed:

Date

Submitted:

Section:

Partners:

Instructor:

Data Table

5.1

Galvanometer deflections

from motion of

magnet.

Motion touard coil

v1

vz

) vr

Cfaskr raka( ,han1l-)

Motion auaryfrom coil

v1

vz

)vt

Motion tozoard coil

v1

vz

)vr

Motion aroay _from coil

v1

vz

)vr

ANALYSIS

[n ktms o1 {o'tadagts lau' \

sl'o n ₁ cr ma4rt el ( lar Xcr )

lenz la'u

"

cu'rcof-'cJ'(luhon

Physics 72.1 5. Electrornagnetic Induction

Sketch of

Magnetic

Field

(from

Procedute 4)

Observed effects

(ftom

Ptocedure 5)

Physics72.l 5. Electromagnetic Induction

Data

Table 5.2 Galvanometer deflections

for different primary coil

core

materials.

ANALYSIS

Physics 72.1 5. Electromrgnetic Induction

Data Table

5.3

Galvanometer deflections

for

different primary coil

lengths

in

secondary.

flot

: :11

H*Y'ffi.,,t.'

_.. :.: !:=

NDARY

|,"

^;:*^Y--ANALYSIS

Physics 72.1

, 5. Electromagnetic Indgcrion

QUESTIONS

1'.

Suppose

that

a

bar

magnet

is

dropped

through

a

hoizontal

loop

of

wire

connected

to

a

galvanometer. Explain what would be observed on the galvanometer as the magnet enters, as

it

is

in

the middle, and as

it

leaves the loop, and why.

2.

Describe the change

of

flux

through and the induced current

in

a loop of wire rotated

in

a uniform

magnetic field (rotational axis of loop peqpendicular to field.).

Physics'72.1 5. Electrornagnetic Inductio,n

INTRODUCTION

A.

Resistor

in

an

AC

circuit

An AC

source

is a

device

that

supplies a

sinusoidally

varying voltage

or

current.

The voltage a and current i at any ldme

t

are:

The instantaneous potential difference vo, is thetefore:

v^ (r) ₌ /R cos(ar

t)

(6.7)

(6.8)

(6.e) whete

V

is the maximum voltage amplitude,

I

is

the

maximum current amplitude and

o

is

the angular frequency of the

AC

source.

A

convenient way

of

describing these types

of

quantities

is

the

root-mean-square

(r*0

value.

Most

multimeters

provide

readings

for

tms

values

of

AC

voltage

(V-)

and

current

(I*J,

(6.3)

(6.4)

Figure 6.1.

Consider Figure 1. Using

Ohm's Law,

the instantaneous potential vo across the resistor is:

,^Q)=

iQ)R

(6.s) Since the instantaneous curfent

is

assumed

to be:

iQ)= t

cos(ar

t)

Therefore, the maximum voltage amplitude across the resistor is

V=V*=IR.

B.

Inductor in

an

AC

citcuit

The

inductor

is

basically

a

piece

of

wire

wound closely together

to form

a helix. There exists a potential difference across the inductor

vL

because

the

alternating

current

source

produces

a

self-induced electromotive force.

For an inductor, the potential is given by:

,"Q)=

L*,O

Hence,

the

potential

at

any instant

i';

proportional

to

the

time rate

of

change ol' cuffent. Using

8q.6.2,

the potential is expressed

as:

,

_rQ)=

_-IaLcos(at

+

90')

(6.10)

From the previous equation, the voltage and

cufrent

are

"out

of

phase"

by a

quartet cycle (90') and the potential is given a "head start"

of

90"

relative

to

the

current.

The

maximum voltage of the inductor is give as:

,^

(r)= v*

cos(ar

t)

Vr

=

IaL

The inductive teactance is defined as:

Xr=@L

V,

₌

IX,

,Q)=v

cos(at)

iG)= t

cos(ar

t)

(6.1) (6.2)

rz - V

_mr

Jz

I

Jz

f_

,-

_mt (6.11) (6.1,2) (6.13)

National Instjtute of Physics, UP Diliman

(6.6)

))hysics 72.1 6. Introduction to Altemating Current (AQ Circuits

C.

Capacitors

in

an

AC

circuit

The

potential across

a

capacitor

in

an AC

circuit may be written as:

/\

I

v.(/)= ^cos(@t-90")

(6.14)

OL

The

maximum voltage

ampJitude

is

therefore written as:

VC (5.15)

use

the

phasor diagram

to

remind us

that

the

total instantaneous

_:.

voltage

is

equal

to

the

sum

of the proiections

of

the phasors Vo,Vr, and

V..

Also, note that the total instantaneous voltage is the same as the source voltage. Therefore,

V

₌

_tlV

_o'

+ (V

_L

_-Vc)z

(6.1.9a)

(6.1eb)

(6.19c)

=w

Equations 6.1,8,6.19 and 6,20 are valid oniy

for

an LRC

series

circuit.

Equations fot

different

circuit

configurations

would

be derived differently.

As the

angalar ftequency {o

is

varied, the

combination

of

minimum

impedance

Z

and

maximum

current

I

may

be

obtained.

The

phenomena

of

current

at

the

pinnacle

at

a

certain

frequency

is

called resonance angular frequency ot

.

At

this

frequency

the

inductive

and

the

capacitive reactance

are

equal. Therefore:

(6.21) The capacitive reactance is defined as: Impedance,

Z

is given by:

(6.16)

R'

+(X,

- Xc)'

$.20)

such that

V,

=

IX,

(6.1,7)

D.

Resonance

in AC circuits

For

an

inductor,

capacitor

and

resistor

connected

in

series

to

an

AC

soufce, the sum

of

the

instantaneous

potential

across

each device is equal

to

the potential

of

the source at the same time t, or

v(t)

₌ u^ (r) +

vr(t)

+v"(t)

(6.18)

1

frl =-

_"

Jtc

oBJECTT\rE

Determine the response of different electrical devices such as inductors, capacitors and resistots to sinusoidally varying voltage and current signals.

MATERIAI,S

AC circuit apparatus, multimeter and wires.

PROCEDURE

WARNING

The following

experiment

is ditectly

connected

to

the

110

V,

60Hz

mains

supply.

To

prevent electrical shock,

please

be

sure

that the main switch

5L

is

set

to

OFF

when

conirecting

the

setup.

Do not

touch the open terminals wtren operating.

Show

your

setuP

to your

instructor

before

collecting

data.

I

@C 1 v ,LC -CN,

.-V -

_I

R'+(x,

Physics 72.1 6. Introduction to Altemating Cutrent (Aq Circuils

A.

Resistor

in

an

AC

circuit

1.

2.

-1.

Close Switch 54 and leave a1l other switches opefl.

Connect the ammeter across

"I,*0".

Be sure

the ammeter is set to AC mode.

Connect the variable resistor such that the solenoid is omitted as shown below. Set to any value

from

50

to

100Q

by

turninq the knobs.

Variable feslstor

4.

Plug

the

apparatus

to

110VAC,

60

Hz

mains.

5.

Close switch 51.

Draw

the pertinent circuit dtagnm

6.

Record the current and measure,the voltage across the resistor and the

lr-p.l

7.

Increase

the

resistance.

:

Observe

what

happens.

I

I

B.

Inductot in

an

AC

circuit

1,.

Close 54 and leave other switches open.

2,

Connect the ammetef acfoss ttl".,"..,.", Place .il

iumpers across "f ,u-ott.

3.

Move

the

iton-core

to its

outermost

position.

Connect

apparatus mains.

Close

51.

Draw

diagram.

6.

Move

the

iton-core

position

^t

regular

intervals

and record

the

currents

and

the voltages of the solenoid and the lamp.

C.

Capacitors

in

an

AC

circuit

1..

Close 52, 53 and 56 and open 51, 54 and 55.

2.

Place ammetef across "I,^-0".

3.

Plug apparatus to 110VAC, 60 Hz. mains.

4.

Close 51. Draw the pertinent circuit diagram

5.

Record

the

current and

voltage

of

the effective capacitor and lamp.

D.

Resonance

in

an

AC

circuit

Resonance

in

an

LRC

Series

Circuit

fwo

parallel capacitors are connected

in

series

with

the inductor and the lamp)

1..

Close 52, 53 and 55. Leave 51,

54

and 56 oPen.

2.

Connect the ammetef across "Iro1".or6tt. Place a _iumper across

"I,,*".

3.

Move

the

iron-core

to

the

outemost

position.

4.

PIug

the

appararus

to

110

VAC, 60

Hz

mains.

5.

Close switch 51.

Draw

the pertinent circuit

diagram

6.

Move the iron-core at constant intervals and

record

the

current

and the

voltage

drop across each device. Record the current and

voltage

of

each element

when

the

lamp intensity is at the maximum.

Resonance

in

an

LC Parallel Circuit

G*o

parallel

capacitors

are

connected in

parullel

with

the inductor and this combination

in

series

with

the lamp)

1,.

Close

52, 53,

54

and 56

with 51

and

55 open.

2.

Connect the ammeter acfoss "Iro,"no,ut'. Plac'e

a jumper across 'I,u-'".

3.

Move

the

iron-core

to its

outermost

position.

4.

Plug apparatus to 1 10VAC, 60

Hz

mains.

5.

Close switch 51.

Draw

the pertinent circuit

diagram

6.

Move the iron-core at constant intervals and

record

the

current

and the

voltage

drop across each device. Record the current and

voltage

of

each

circuit

element

when

the lamp intensity is at the minimum.

D

h

h

i ic

t

d

E ,a E E

t

4. 5.

to

110VAC,

60

Hz

the

pertinent

circuit

6. Introduction to Altemating Curent (Aq Circuits

E

N

PI

Ir

I

_L

[}

(t

110 Vac

APPARATUS

I _solennoid

Physics

72.1

6. Introduction to Alternating Current (AC) Circuits

Name:

_{Date Performed:}

Date Submitted:

Partners:

Instructor:

Observations

A.

Resistor

in

an

AC

Circuit

Data Table

6.1

Current

and

vol

and resistor

Data Table

6.2

Dat* for

solenoid

and

lam

6. lntroduction to Alternating Current (AC) Circuir

Physics72.l

_,

_,

*

B.

Inductor

in

an

AC

Circuit

Calculations

!

(

Physics 72.1 6. Introduction to Ahernating Current (AC) Circuits

C.

Capacitors

in

an

AC

Circuit

Data Table

6.3

Data

for

Calculations

r';l:r:iai::i'::',:ii:iar:::,,:rri':.r::ll;ll:

ir::.ij: i:it ,:::l .li ,::!rr:::rjl?t:,!j:,,:t i:'r:,riti:ir:i:tr!::i :::i r,ir:rl

,rirr:l;l'l.i*l::l{iril:l l::i r,ir:::rr i|i:r:,,iil:i..::a:":ri:::.lar:i'a

Physics

72.1

6. Introduaion to Alternating Current (AC) Circuits

D.

Resonance

in

an

AC

Circuit

Calculations

Data Table

6.4 Resonance

in

an

LRC

series

circuit

Data Table

6.5 Resonance

in

an

LC

Calculations

Physics 72.1 6. Inugduction to Altemating Curre"t (49 t{94t _J

!

I

1

QUESTIONS

Answer questions 1 to 3 using your data in Table 6.1

1.

Compute

fot

the following: (a)

V

and

I,

_O)

T

and cD.

Draw the voltage and cuffent as a function

of

time

for

the resistor and lamp combined. Label yout

plots completely.

Voltage (V)

Cunent (A)

Time (s)

Dtaw

the

phasot diagram

for

the

combined voltage and current phasors called?

resistor and lamp.

What

are

the

proiection

of

the

Physics 72.1 6. Introduction to Altemeting Current (Aq Circuits

Answer questions 4 to 6 using your data in Tab\e 6.2.

4.

tU7hat _{is inductive reacance? From your data, compute}

_forftr.

_{Show sample calculations.}

5.

Compute for the impedance of the circuit at each core position. Show sample calculations.

6.

What

happens

to

the interrsity

of

the lamp as he core goes in?

Draw

the phasor diagram

at

this position.

Answer questions

7

oad 8 using your data in Table 6.3

7.

What is capacitive reactance? From your data, compute

foryr.

Show sample calculations.

Physics 72.1 6. Introduction to Altemating Current (AQ Cirarits

8.

Compute fot _Xc using Eqs. 6.16 and 6.17. Compare the results.

Answer questions 9 to 12 using your data from table 6.4

9.

At

what core posirion is the intensity of the lamp maximum in the sedes LRC citcuit?

10.

Compute

for

the impedance at each core position. Show sample calculations.

11.

why

does the lamp intensity increase?

what

brings about this condition?

f

Z.

Vrnat

t

,t.

irrdr.tance at maximum lamp intensity?

Answer questions 13

to

16 using your data from Table 6.5

13.

At

what core position is the intensity

of

the lamp at a minimum?

14. Derive an expression

fot

the total impedance in the circuit.

Physics 72.1 6. Introduction to Altemating Current (Aq Circuits

15. Compute for the impedance at elch core position. Show sample calculations.

16. What happens to the lamp intensity as the iron core is moved in? Explain.

IN

Ai

solt

r$

ori

rlcd

aq

PCq

atd

tcE

firri t

su

.rl

lEq

7:t:

rl

rd

efi,

*{

icl

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fiq

ffi r€f,i

nct

B.'llx I ri rPd

INTRODUCTION

A.

Reflection

\When

_light

_{strikes the surface}

_of

_a

_material, some light is usually reflected. The reflection

of

light rays

from

a plane surface like a glass plate

or

a

plane

mirror is

described

by

the

law

of

reflection:

The

angle

of

incidence

is

equal

to

the angle of

reflection

0,=0,

(7.1)

These

angles

are

measured

from

a

line perpendicular or normal to the reflecting surface at the point of incidence. Also, the incident and

reflected rays

lie

in

the

same plane

with

the normal.

The

rays

from

an

object

reflected

by

a

smooth plane surface appear

to

come

from

an image behind the surface, as shown

in

the Figure

7.1. From equal triangles

it

can be seen that the image distance

d,

fuom

the

reflecting surface is

the

same

as

the

object

distance do

.

Such

reflection

is

called

regulat

or

specular

reflection.

The law of reflection applies to any reflecting surface.

If

the surface is relatively rough, like the

paper

of

this

page,

the

reflection

wili

become diffused or mixed, so that no image of the source

or

object

wiil

be

produced.

This

type of

reflection

is

called

irregular

or

diffuse

reflection.

B.

Refraction

\Mhen _{light passes}

_from

_{one medium}

_into

_an optically different rnedium at an angle other than

Obiect

Figute 7.1 Law of Reflection. The aagle

between the incident tay and a notrrral to the

surface

O

is equal to the aagle between the

teflected tay and the normal 0, _, i,e., _{& =} 0r.

notmal

to

the surface,

it

is

"bent" or

undergoes

a

change

in

direction.

This

is

due

to

the different velocities

of

light

in

the rwo media.

In

the

case

of

refraction,

the

angle

of

incidence

and

the

angle

of

refraction are denoted

by

₄

and 0r, respectively. 0r

Normal---,-I

.\i,,

)@,

sinO,

u. _ I _^

sinl, u,

t'12 (7.2)

where

the ratio tt,,

of

the nvo

velocities (a, in

medium

1

and

a,

in

medium

2)

is

called the

relative

index

of

tefraction and the

above equation is known as Snell's law.

If

ur(u,, the tays are bent toward the normal

in

the

second

medium. And

if

ur)a,, the

rays ate bent away from the normal.

For light

traveling

initially

in

vacuum

(medium 1),

the ratio

of

the

speed

of light

in

vacuum and its speed

in

medium 2 is called the

index

of

refraction

of medium 2 denotedby n,