physics electrics notes.pdf

8/14/2019 Physics electrics notes.pdf

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03/10/2007 1

SystSystmeme InternationalInternational ddUnitUnitssSeven Basic SI Units

1. Length metre m

2. Mass kilogram kg3. Time second s

4. Electrical current ampere A

5. Temperature Kelvin K

6. Luminous intensity candela cd

7. Amount of substance mole mol

These are the only units necessary to describe any

quantity.


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Examples of Derived UnitsExamples of Derived UnitsEnergy kg m2 s-2 Joule J

Force kg m s-2 = J m-1 Newton N

Power kg m2

s-3

= J s-1

Watt WCharge A s Coulomb C

Potential difference kg m2 s-3A-1 = J A-1 s-1 Volt V

Resistance kg m2 s-3A-2 = V A-1 Ohm

Capacitance A2 s4 kg-1 m-2 = A s V-1 Farad F

In general, the derived unit is used for simplicity.

In any physical expression, the units also balance either side ofthe equation.

This is a useful check on the validity of the expression.


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Prefixes and NotationPrefixes and NotationThe following prefixes indicate

multiples of a unit.In physics numbers areusually recorded in

standard notation, e.g:me=9.110-31 kg

So only the significant

figures are quoted,unlike with a fixeddecimal point.

The number of figuresquoted implies aprecision inmeasurement.


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Converting UnitsConverting UnitsThe basic rule forconverting units is thatin an equality, the unitsmust balance as well asthe numbers.

So a conversion

equation can berearranged andsubstituted into theactual equation, e.g:Suppose you want toknow how manyminutes are in 2.5

hours.

This is effectively:xmin = 2.5 hour

so rearranging:x= 2.5(hour/min)

You know:

1 hour = 60 minso rearranging:(hour/min) = 60/1 = 60

Substituting this in above:x=2.560=150

So 2.5 hour is 150minutes.


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Uncertainty in MeasurementUncertainty in MeasurementA more accurate value for aquantity may be obtained byrepeated measurement.

The best estimate of thevalue of the quantity is thearithmetic mean:

The spread, , of the values

reflects random errorsinmeasurement.

The spread will be differentif different measurement

methods are used.

A statement of aA statement of ameasured value withoutmeasured value without

an accompanyingan accompanying

estimate of theestimate of the

uncertainty is useless.uncertainty is useless.

2

==n

1iixn1


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The Normal DistributionThe Normal DistributionThe normal, Gaussianor error curve arises in

nature from randomprocesses.

Spread of values is the

standard deviation, .Two thirdsof values arewithin of the mean

.

x

0 2 4 6 8 1

f(x)

0.0

0.1

0.2

0.3

0.4

0.5

( )

( )

=2

2

Xexp

xf2

2


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Standard DeviationStandard DeviationThe best measure of thespread is the root meansquare deviation, also called

the standard deviation:

The standard deviation is away of determining thespread of values.

For a few measurements,this is the best estimate ofthe uncertainty (error) of thedetermination of the value.

With many measurements ofa normal distribution themean can be found more

accurately.The uncertainty in the meanis less than the spread.

Standard error in mean is:

Where

( )=

=n

1i

2xn

1

( )=

=

n

1i

21n x1n

1

n1n


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UncertaintiesUncertaintiesAll measurements must bequoted with an associateduncertainty (error):

E.g. the length of the object

was:

The uncertainty tells you

how many figures aresignificant.

Do not quote insignificantfigures.

Combining Uncertainties

AA

m2.03.15

( ) ( ) ( )

( ) ( ) ( )

=

=

+

=

=

+

=

=

+==

+=+=

A

An

Z

ZAZ

B

B

A

A

Z

ZBAZ

B

B

A

A

Z

ZBAZ

BAZBAZ

BAZBAZ

n

222

222

222

222


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Sources of ErrorSources of ErrorSources of Random Error

Blunders not genuineuncertainty, eliminate by

double checking.Human error be carefulin set up, avoid parallax.

Binning error data are

always rounded off depends on the fineness ofscale of instrument.

Statistical fluctuation

when drawingmeasurements from a largesample, there will be anecessary spread of values.

Systematic Error

Instrumental error calibration is never perfect.

Errors caused by the actof measurement takingthe data changes the value.

True Value

Random Error

SystematicError


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Making MeasurementsMaking MeasurementsWhere possible, makemultiple measurements todetermine the random error

properly.Where this is not possible,then regard you singlemeasurement as one drawnfrom a Gaussian population.

Use commonsense andexperience to estimate what

the uncertainty would be you are looking toaccommodate 2/3 of allmeasurements within the

spread.

Contributions to randomerror include, for example

half the last digit on a

display, ~ half the range of

fluctuating of a needle,

~ half the variation in the

property with time, ~ half the variation in the

property with position,

Often one source of error

will dominate and the othersmay be neglected.

Alwayscarry through errorcalculation to final result.


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Maintaining a NotebookMaintaining a Notebook

It mustcontain a

contemporaneous record ofactions commentary.

Use neat ink records only.

Permanently attach loose pieces

of graph paper, scripts, etc. Cross out mistakes neatly.

Perform calculations in thebook.

Every piece of data that isrecorded musthave an estimateof uncertainty.

The result of every calculationmusthave an estimate of

uncertainty.

Do not use pencil except ongraphs and diagrams.

Do not tear out pages.

Do not use corrective fluid.

Do not use loose leaf paper forrecords aiming to write them uplater.

Do not simply take the

measurements with the aim ofanalysing later: when you startanalysing you often find a datapoint is wrong, or you need afurther piece of information.

The laboratory notebook is the principal tool of a scientist:maintain it to a professionally.


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Plotting GraphsPlotting GraphsA Cartesian graph comprisestwo axes(the abscissaandordinate), which cross at an

origin, upon which data areplotted as coordinates.

Data points have error bars.

The abscissausually has the

independent variable, theordinateusually has thedependent variable.

It is often useful to construct

a plot to give a straight line.A fitted line passes through2/3 of error bars maximumand minimum gradient lines

give estimate of uncertainty. abscissa

0 2 4 6 8 1

ord

inate

0

10

20

30

40

50

60

70


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ChargeChargeStatic electricity can begenerated by rubbing a clothon a plastic rod.

What happens is CHARGE istransferred from one to theother.

Charge can be negative orpositive.

Similar charges repel,opposite charges attract.

When we say a body isuncharged, we mean it hasequal quantities of positiveand negative charge.


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Origin of ChargeOrigin of ChargeAtoms in matter comprisethree particles:

electrons

(electrically negative).protons(electrically positive).

neutrons

(electrically neutral).The protons and neutronsform a positive nucleusthatthe electrons orbit.

The friction in the rubbingcauses electrons to betransferred to the plastic,leaving behind a net positive

charge - ions.


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Conductors and InsulatorsConductors and InsulatorsSome materials allowelectrical charge to passthrough them easily - called

CONDUCTORS.Some do not -INSULATORS.

Conductors such as metals

have free electronsthat cancarry the charge from oneplace to another.

In insulators, the electrons

are bound in place.Semiconductors areinsulating materials that maybe made partially conducting

by adding impurities.


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Field and PotentialField and Potential

Q

q/Fr4

QE

or VmNCField,Electric

20

1-1-

=

=

Q

r4QV

VPotential,Electrical

0=


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Electrical CurrentElectrical CurrentElectrical current inAmps isthe flow of charge.

Conventional d.c. current

flows from out the positiveterminal of a battery, arounda circuit, and into thenegative terminal.

In metals, the chargecarriers are electrons, whichmove in the oppositedirection.

Current is measured usingan ammeter - a deviceused is seriesthat does notimpede current flow butwhich has a deflectionproportional to current.


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Potential DifferencePotential DifferencePotential difference (p.d.) inVolts is the driving forcethat makes current flow

around a circuit.It is the energy delivered tothe circuit per unit charge.

Often called voltage.

The voltage generated bythe chemical reactions in abattery is called theelectromotive force

(e.m.f.).Potential difference ismeasured using avoltmeter, which goes inparallelwith the circuit.


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Electrical ResistanceElectrical ResistanceAll conductors offerresistance to the flow ofelectrical current.

R=L/A is the resistivity in mA cross-sectional area, Llength

The unit of resistance is theOhm ().An electrical componentspecifically made to limitcurrent is called a resistor.

The current that a potentialdifference drives through aresistor is given by

I=V/R

Ohms law.


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Electrical PowerElectrical PowerElectrical power is theenergy delivered per unittime in a circuit.

The power is the voltagetimes the current. The unit isthe Watt, W.

1 W = 1 J/s.

Power P=VISince V=IR then the powerisP =I2R =V2/R.

In a resistor, the powerdelivered manifests itself asheating caused by electronscolliding with atoms andgiving them energy.


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Properties of CurrentProperties of CurrentCurrent must flow in acomplete circuit - currentcannot be lost anywhere.

Kirchoffs point rule - thecurrent flowing into anypoint or component must beequal to the current flowingout of it.

Components in seriesmusthave the same current

flowing through them.For components inparallel,the current is split betweenthem.


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Properties of p.d.Properties of p.d.The electric field isconservativeso the potentialat a given point is

independent of the routetaken.

Kirchoffs loop rule thesum of potential differences

around a closed loop mustbe zero.

For a simple circuit, the sumof potential differences isequal and opposite to thee.m.f. of the power supply.If a circuit branches, the p.d.across each branch is thesame and is not split.


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Resistors in Series and ParallelResistors in Series and Parallel

For two resistors in series,the resistances add.

The same is true of three,four, five...resistances

For two resistors in parallel,the resistances add inreciprocal to give thereciprocal resistance.

The same is true of three,

four, five...resistances

21total RRR +=

Rtotal

21total R

1

R

1

R

1

+=

Rtotal


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If a voltage supply is connectedacross two resistors in series, thenwe have a potential divider.

The potential difference acrosseach one is proportional to theresistance.

Any real voltage source has aninternal resistance, so whenever itis connected to a real load there isa potential divider effect.

Potential DividerPotential Divider

( )2111RR

VRV+= ( )21

22RR

VRV+=


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Cells and BatteriesCells and BatteriesCells are portable source ofelectrical power.

A dry cell is a primary cell

the electricity is generatedby a chemical reaction and itis not rechargeable.

A lead acid accumulator is a

secondary cell it storeelectrical energy generatedin another source. As itdischarges, Pb ions dissolveinto the acid and electronsare left behind. Chargingreverses the process.

A batterycomprises severalcells.


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Electromotive ForceElectromotive ForceA cell provides the energy tocreate a potential differenceto make a current flow round

a circuit.It can do this because thechemical action within itcreates an electromotiveforce (e.m.f.).

E.m.f. is the energy createdper unit charge in the cell,i.e. the units are J/C or, thatis the volt.

By contrast, a potentialdifference is the electricalenergy deliveredper unitcharge.


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Internal ResistanceInternal ResistanceA cell or any power supplyhas an internal resistancethat limits the current that it

can deliver.The potential differenceappearing on the output of acell will be reduced by theeffect of the internalresistance.

The term IRi behaves like alost voltage.

iIREV =


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Cell CharacteristicsCell CharacteristicsThe internal resistance of acell is the thing thatdetermines the uses to

which it may be put.A power supply or batterymust be matched to theapplication in both e.m.f.and internal resistance(usually actually specified byoperating current).

When a cell discharges,the parameter that changesis the internal resistance, notthe e.m.f. The internalresistance increases withtime.


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Current MeasurementCurrent MeasurementMay be measured using amoving coil ammeter or adigital multi-meter, which is

put in serieswith the circuit.The range of a meter maybe extended by inserting ashunt resistance in parallel.

Ifi is the full scale deflection(f.s.d.) current of the meter,Rm is the meter resistanceand I is the desired newf.s.d. current, then:


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Voltage MeasurementVoltage MeasurementA voltmeter is really anammeter with a seriesresistance (multiplier

resistance).It is used in parallel anddraws only a small currentfrom the circuit.

The range of the meter maybe varied using the seriesresistance. If v is thef.s.d.voltage across themeter,Vis the desired newf.s.d. and Rm is the meterresistance, then:

( )

v

vVRR m

=


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PotentiometerPotentiometerA potentiometer is a variablepotential divider which maybe used to measure an e.m.f.

To measure e.m.f., it isnecessary to draw no currentso that there is no voltage lossin the internal resistance.

This can be done using aknown driver cell, apotentiometer and agalvanometer.

The potentiometer is varieduntil the galvanometer readszero (null detection) thee.m.f. of the unknown canthen be determined as a

fraction of the known e.m.f.


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Wheatstone BridgeWheatstone BridgePotentiometer rearranged tocompare two resistances.

Unknown e.m.f. replaced by

a divider that produces afraction of the known p.d.

Wheatstone bridge is a nulldetection circuit.

Reads zero whenV2=V4.Therefore R1/R2=R3/R4.

R3 is usually unknownresistance, other three are

known.Ratio R1/R2 is varied untilbridge balances, andgalvanometer reads zero.

Then R3=R1R4/R2.

=


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The CapacitorThe CapacitorThe capacitor is a usefuldevice for storing electricalenergy (storing charge).

They comprise twoconducting plates in closeproximity to each other.

When the capacitor isconnected to a battery,equal and opposite chargeflows onto the plates untilthe potential differencebetween them is the sameas the battery e..m.f.


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DielectricsDielectricsAn insulating material(dielectric) contains atomswith bound electrons.

A positive charge attractsthese electrons to one sideof the atom, a negativecharge repels them to theother - creates a dipole.

The net effect is to reducethe effective surface chargeon the plates, and so thecapacitance increases.

The electrical permitivity of avacuum is 0 and thepermitivity of a dielectric is

r0.


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Parallel Plate CapacitorParallel Plate Capacitor

Larger area plates meansmore charge can be stored

on each.Closer together plates givesstronger attraction betweendissimilar charges, so more

charge can be stored.Larger dielectric constant ofthe material in between themore charge can be stored.

It can be shown that:

Consider two parallel metal plates of the same area.

d

AC r0

=


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Energy in a CapacitorEnergy in a CapacitorThe energy stored in acapacitor can be used totemporarily drive a circuit.

As a capacitor is chargedusing constant current, I=Q/t for time t, the voltageincreases from 0 toV. So

the average voltage is V.Power is IV, energy isIV x t, so the total energydelivered to the capacitor is:

QV

tVIE

21

21

=

=


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Capacitors in SeriesCapacitors in SeriesIf two capacitors C1 and C2are connected in series, eachcapacitor must store the

same charge, so:

Also

So

21

21

2121

22

11

C

1

C

1

Q

1

C

Q

C

Q

Q

V

C

1

CQ

CQVVV

C

QV

C

QV

+=

+==

+=+=

==

C i i ll l


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Capacitors in ParallelCapacitors in ParallelCapacitors in parallel musthave the same potentialdifference across them.

Total Charge stored,

Combined capacitance,

Capacitors in parallel add

VCVC

QQQ

21

21

+=

+=

21

21

CCV

VCVC

V

QC

+=

+==

Sh ChSh i Ch


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Sharing ChargeSharing ChargeA capacitor C1 is charged toViand then disconnected from thebattery. Then it is connected tocapacitor C2. The voltage on C1falls and that on C2 rises ascharge flows from one to theother. Charge stops flowingwhen the voltage on eachequalises atVf.

Initial charge equals finalcharge:

So

or

When two capacitorsshare the charge thatwas initially on one, Theresultant voltage is

Vf=C1Vi/(C1+C2)

When two capacitorsshare the charge thatwas initially on one, The

resultant voltage is

Vf=C1Vi/(C1+C2)

f2f1i1 VCVCVCQ +==

( )21

i1f

f2f1i1

CC

VCV

VCVCVC

+=

+=

C i Di hC it Di h


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Capacitor DischargeCapacitor DischargeConsider a capacitor beingdischarged through aresistor.

The voltage on the capacitoris proportional to the chargestored. As the capacitordischarges the charge stored

decreases.The rate of discharge is thecurrent, which isproportional to voltage sothe rate of dischargedecreases.

A l i f Di hA l i f Di h


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Analysis of DischargeAnalysis of DischargeCharge, Q=CV, so V=Q/C.

Discharge current, I=V/R.

EliminatingVgives, I=Q/CR,

In time t, the charge flowQ=-I t,so I =-Q/ t

=-dQ/dt dQ/dt =-Q/CR.

This is clearly exponentialbehaviour.

If Q=Q0 at t=0 then:

The quantity RC has units secondsand is known as the time constant.It is the characteristic time over

which the capacitor discharges

( )RCtexpQQ 0 =


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C it i ACC it i AC


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Capacitors in ACCapacitors in ACIn the same way that aresistor has resistance, acapacitor has reactance.

The capacitor will pass AC

current, and the higher thefrequency the less it opposestha passage of current.

However, the current leads

the voltageby a quartercycle (90, /2) becausecurrent is needed to chargethe capacitor before a

voltage appears.

( )

( )( )( )ft2cosfCV2

ft2sinCVdt

d

dt

dQI

ft2sinCVCVQ

0

0

0

=

==

==

fC21

IVX

0

0c

==

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