Download Electrostatic!charge!

Year%11%Physics%Unit%1,%2015%
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Area!of!Study!1!.!Electricity!
Chapter%2%–%Concepts%in%Electricity%
In!this!chapter!we!will!introduce!the!concepts!of!electricity!including:!!
•!The!concepts!of!electric!charge!and!electric!forces!!
•!The!concepts!of!current,!EMF!and!electric!potential!!
•!Resistance!in!ohmic!and!non?ohmic!conductors!
•!Electric!energy!and!power.!
These!concepts!will!be!used!in!practical!problems!and!experiments!in!chapter!3.!
2.1!Electric!Charge!
Introduction!
When a plastic pen rubbed with a dry cloth is brought near some small pieces of paper, the paper
may ‘dance’. Some of the bits of paper may even jump onto the pen and then jump off again,
seemingly at random. The pen has gained what we call an electrostatic charge, which creates an
electric field around it. This field will cause the paper to experience a force. Why?
As! you! all! matter! in! the! universe! is! constructed! from! about! 92!
naturally! occurring! of! atoms.! And,! all! atoms! are! made! up! of! just!
three! fundamental! particles:! the! proton,! the! electron! and! the!
neutron.!!
Atomic!charge!
If,!for!example,!a!glass!rod!is!rubbed!by!a!cloth!and!the!rod!acquires!
a!positive!charge,!then!the!cloth!will!have!acquired!an!equal!amount!
of!negative!charge.!Overall!the!charge!is!still!zero.!
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Electrostatic!charge!
When! two! different! materials! are! rubbed! together,! this! tendency! for! electrons! to! move!
between!atoms!normally!results!in!one!of!the!materials!gaining!electrons!at!the!expense!of!the!
other.!The!one!that!gains!electrons!will!thus!attain!an!overall!negative!charge!and!the!other,!
now!with!fewer!electrons!than!protons,!will!become!positively!charged.!!
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This!is!where!the!phrase!“opposites!attract”!comes!from.!
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The!Van$de$Graff$generator$is!often!used!as!a!source!of!
electrostatic!charge!in!the!laboratory.!In!effect,!it!deposits!
the! charge! produced! by! the! contact! between! a! plastic!
roller!and!a!rubber!belt!onto!a!metal!dome.!While!the!belt!
is! running,! the! concentration! of! charges! on! the! dome!
becomes!greater!and!greater.!
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A!unit!for!charge!!
In! order! to! measure! the! actual! amount! of! charge! on! a!
charged! object,! a! ‘natural’! unit! would! be! the! charge! on!
one! electron! or! proton.! This! fundamental! charge! is!
referred! to! as! the! elementary$ charge$ and! is! given! the!
symbol!e.##
The$ proton$ therefore$ has$ a$ charge$ of$ +e$ and$ the$
electron$−e.$$
No!charge!smaller!than!e#has!ever!been!found!in!nature.!All!larger!charges!are!whole!number!
multiples!of!e.#
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The!elementary!charge!is!clearly!a!very!small!unit!of!charge.!Even!the!small!charge!rubbed!on!
the!pen!for!the!‘dancing!paper’!experiment!would!involve!many!billions!of!electrons!being!
either!lost!or!gained.!The!SI!unit!is!the!coulomb$(symbol!C).!
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Electrostatic!induction!
A! negatively! charged! pen! induces! a! positive!
charge! on! the! nearer! side! of! the! paper! and! a!
negative!charge!on!the!opposite!side.!Because!the!
positive!side!is!closer,!the!paper!is!attracted.!!
This! process! is! called! electrostatic$ induction.$
The!charges!in!the!paper!are!‘induced’!to!move!by!
the! presence! of! the! charged! object,! thus! creating!
‘induced! charges’! of! opposite! sign! on! opposite!
sides!of!the!paper.!Electrostatic!induction!will!occur!regardless!of!the!sign!of!the!charge!on!the!
pen.! If! the! pen! were! to! be! made! positive,! electrons! in! the! paper! would! move! towards! it,!
causing!the!closer!side!to!become!negative!and!the!further!side!to!become!positive.!!
Conductors!and!insulators!
Any!attempt!to!produce!an!electrostatic!charge!by!rubbing!a!metal!rod!instead!of!a!plastic!or!
glass! rod! is! normally! unsuccessful.! Charge! transferred! to! the! metal! rod! will! flow! away!
through! the! rod! and! your! hand.! Unlike! plastic!and!glass,!metals!are!conductors:$ they! allow!
the! movement! of! charge! through! their! structure.! The! structure! of! metals! is! such! that! the!
outermost!electrons!of!the!atoms!are!free!to!move!around!in!the!fixed!crystal!lattice!made!up!
of!the!atoms.!Any!excess!of!electrons!in!one!place!will!soon!be!dispersed!as!the!electrons!flow!
away!from!each!other.!Materials!such!as!plastic!and!glass!do!not!allow!the!flow!of!electrons.!
They! are! called! insulators.$ Another! important! group! of! materials! is! the! semiconductors.$
Most! notably! these! include! silicon! and! germanium,! the! basis! of! the! modern! electronics!
industry.!Pure!semiconductors!are!not!nearly!as!conductive!as!metals,!but!can!be!modified!by!
‘doping’! them! with! small! amounts! of! certain! elements! so! that! they! will! conduct! quite! well.!
They!are!the!materials!from!which!transistors!and!integrated!circuits!are!made.!!
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2.1!Summary!.!electric%charge%%
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Matter! is! made! up! of! vast! numbers! of! positive! and! negative! charges! (protons! and!
electrons!respectively).!Normally!there!is!an!equal!number!of!each.!!
•
Like!charges!repel!and!unlike!charges!attract.!!
•
Charge! cannot! be! created! or! destroyed,! but! it! can! be! transferred! from! one! object! to!
another.!!
•
An!electrostatic!charge!involves!an!imbalance!of!positive!and!negative!charges.!!
•
The! charges! on! a! proton! and! electron! are! equal! in! magnitude! but! opposite! in! sign.! The!
magnitude!of!this!charge!is!referred!to!as!one!elementary!charge.!!
•! One! coulomb! of! charge! is! equal! to! 6.242! ×! 1018! elementary! charges,! or! one! elementary!
charge!is!equal!to!1.602!×!10−19!C.!!
•! If!a!charged!object!is!placed!near!a!conductor,!an!opposite!charge!will!be!induced!on!the!
side!of!the!conductor!nearer!the!charge!and!a!like!charge!on!the!side!further!away!from!the!
charge.!!
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Year!11!Physics!Unit!1,!2015!
!
Area!of!Study!1!.!Electricity!
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Chapter!2!–!Concepts!in!Electricity!
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2.2!Electrical!Forces!and!Fields!
Coulomb’s law
Electricity! is! one! of! nature’s! fundamental! forces.! In! 1785,! Charles! Coulomb,! first! published!
details! of! the! force! that! acts! between! two! electric! charges.! This! force! between! any! two!
electrical!charges!can!be!understood!in!terms!of!the!force!between!point!charges!separated!by!
a! certain! distance.! The! expression! ‘point! charges’! simply! means! that! the! two! charges! are!
regarded!as!being!very!much!smaller!than!the!distance!between!them.!!
Coulomb!found!that!the!force,!whether!repulsive!or!attractive,!between!two!charges!q1#and!q2#
a! distance! r# apart! was! proportional! to! the! product! of! the! two! charges,! and! inversely!
proportional!to!the!square!of!the!distance!between!them.!This!can!be!expressed!by!the!simple!
equation!below!(where!k#is!the!proportionality!constant).!
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The! force! being! inversely! proportional! to! the!
square! of! the! distance! means! that,! for! example,! if!
the!distance!between!A!and!B!is!doubled,!the!force!
will!decrease!to!onePquarter!of!the!previous!value.!
There!are!a!number!of!important!inverse! square!
laws!in!physics.##
Remember# that# between# like# charges# there# will# be#
repulsion#and#between#unlike#charges#attraction.#
The!constant!k#has!a!value!(in!SI!units)!close!to!9.0!
×!109!N!m2!C−2!in!air!or!a!vacuum.!This!means!that!
the!force!between!two!charges!of!1!C!each,!placed!
1!m!apart,!would!be!almost!1010!N—equivalent!to!
the! weight! of! about! ten! large! battleships!! This!
suggests! that! a! 1! C! charge! is! a! huge! amount! of!
charge.!
Another! way! to! get! a! feel! for! the! magnitude! of!
electrical! forces! is! to! realise! that! the! electrical!
forces!between!atoms!hold!all!matter!together.!For!example,!Mount!Everest!is!supported!by!
the!electrostatic!repulsion!between!the!atoms!underneath!it.!The!strength!of!the!hardest!steel!
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is! due! to! the! electrical! forces! between! its! atoms.! In! comparison! to! the! Earth’s! gravitational!
forces!on!atoms,!the!electrical!forces!between!them!are!totally!overwhelming—by!a!factor!of!
about! a! billion! billion!! Only! in! the! last! stages! of! collapse! of! a! giant! dying! star! can! the!
gravitational! forces! overwhelm! the! electrical! forces! between! atoms! and! cause! them! to!
collapse!into!the!superPdense!state!of!matter!that!exists!in!what!is!called!a!neutron#star.!
Worked!example!2.2A!
Two!Van!de!Graaff!machines!are!placed!50!cm!apart!and!switched!on.!If!they!both!attain!a!
charge!of!3!μC!of!the!same!sign,!what!will!be!the!force!between!them?!(Ignore!the!size!of!the!
machines!for!the!moment.)!How!would!this!force!change!if:!
a) One!of!the!machines!sparks!and!loses!half!its!charge?!
b) The!machines!are!moved!to!a!distance!of!1!m!apart?!!
c) The!charges!were!of!opposite!sign!instead!of!the!same?!!
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Electric fields
It!is!often!very!difficult!to!use!Coulomb’s!law!directly!to!calculate!the!force!on!a!charged!object!
because,! for! example,! the! force! may! originate! from! many! charges! spread! around! on! a!
conductor.!However,!in!many!cases!it!is!possible!to!measure!or!calculate!the!electric#field.##
The!electric!field,!like!the!gravitational!field,!is!the!amount!and!direction!of!the!force!on!one!
unit!of!(positive)!charge,!the!electric!field!(E)!is!the!force!on!1!coulomb!(C).!If!we!were!to!find!
a!force!of!10!N!on!a!2!C!charge,!we!would!know!that!the!electric!field!is!5!N!C−1.!
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An!electric!field!has!both!direction!and!strength,!and!so!is!a!vector!quantity.!The!electric!field!
is! shown! by! lines! that! represent! the! direction! of! the! field.! The! closeness! of! the! lines! can!
normally!be!taken!to!represent!the!relative!strength!of!the!field.!The!shape!of!the!field!around!
some!charged!objects!is!shown!in!Figure!2.13.!The#shape#of#the#field#around#a#small#charge#is#
radial,# pointing# outward# in# the# case# of# a# positive# charge# and# inward# in# the# case# of# a# negative#
charge.#
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Worked!example!2.2B!
Robert! Millikan! measured! the! charge! on! an! electron! by! finding! the! electric! force! on! tiny! oil!
drops!in!a!known!electric!field.!If!the!force!on!an!oil!drop!was!due!to!the!charge!of!one!single!
extra!electron!on!the!drop,!and!found!to!be!8.0!×!10−14!N!upwards,!what!was!the!strength!and!
direction!of!the!electric!field!he!was!using?!
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2.2!Summary!.!electrical!forces!and!fields!
1. ! Coulomb’s!law!for!the!force!between!two!charges!q1#and!q2#at!a!distance!of!r#is:!!!
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2. ! The! constant,! k,# in! Coulomb’s! law! has! a! value! of! 9! ×! 109! N! m2! C−2,! indicating! that! an!
electrostatic!charge!of!1!C!would!be!enormous.!!
3. ! The! electric! field! E" in! any! region! of! space! is! the! electric! force! per! unit! of! charge! in! that!
space:!E"=!F/q."Conversely,!the!force!on!a!charge!q#in!an!electric!field!E"is#given#by"F=qE.!
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Year!11!Physics!Unit!1,!2015!
Area%of%Study%1%.%Electricity%
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Chap.!2!–!Concepts!in!Electricity!
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2.3%.%Electric%current,%EMF%and%electrical%potential%!
When! a! battery% is! connected! to! a! conductor! (such! as! a!
torch!bulb)!one!end!of!the!conductor!becomes!positively!
charged! and! the! other! end! becomes! negatively! charged.!
This! sets! up! an! electric! field! along! the! length! of! the!
conductor! the! electrons! will! then! move! along! the!
conductor.!This!movement!of!charge!along!a!conductor!an!
electric%current.!
Electric!current!!
We!define!any!moving!charge!as!an!electric!current.!This!
can!be!electrons!moving!through!the!atomic!structure!of!a!
metal,! or! protons! from! the! Sun! flying! through! space,!
moving!charges!make!up!a!current.!!
The! magnitude! of! the! current! is! defined! simply! as! the!
rate%of%transfer%of%charge.!That!is!“it%as%the%amount%of%charge%that%flows%past%any%point%
in%a%conductor%in%1%second”.!!
The!unit!of!current!“Ampere”!is!defined!as!when!1!coulomb!of!charge!flows!past!a!point!in!
1!second.!So!1!ampere!=!1!coulomb!per!1!second.!!
Electric%current%is%given%the%symbol%I.#%
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If!the!charge!is!measured!in!coulombs!and!the!time!in!seconds,!the!current!is!measured!in!
amperes.(Conversely,!the!charge,!in!coulombs,!carried!by!a!current!of!I(amperes!in!t(seconds!
is!given!by!q(=!It.(!
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Worked%example%2.3A!
Determine!the!charge!that!has!flowed!through!a!torch!battery!producing!a!current!of!300!
mA!if!it!has!been!left!on!for!20!minutes.!!
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The!direction!of!current!!
In!the!case!of!a!river,!the!direction!of!the!current!is!clear;!it!is!the!direction!of!flow!of!the!
water.!Unlike!water,!however,!electric!charge!can!be!either!positive!or!negative.!!
So!what!is!the!direction!of!an!electric!current?!We!define!the!direction!of!an!electric!current!
as!the!direction!of!transfer!of!positive!charge.!!
However,!positive!charge!can!be!transferred!to!the!right,(let’s!
say,!either!by!moving!positive!charge!to!the!right,(or!by!moving!
negative!charge!to!the!left.(!
In!a!metal!wire,!for!example,!a!positive!current!to!the!right!is!
carried!by!electrons!moving!to!the!left.!On!the!other!hand,!in!a!
fluorescent!tube!a!positive!current!to!the!right!is!carried!both!by!
positive!ions!moving!to!the!right!and!by!electrons!moving!to!the!
left.!!
Because!the!electrons!in!a!wire!actually!move!in!the!opposite!
direction!to!the!current,!the!terms!electron%current%and!
conventional%current%are!sometimes!used!to!distinguish!
between!them.!It!is!important!to!remember,!however,%that%
current#is%the%rate%of%transfer%of%positive#charge.%%
Figure% 2.19% A! current! to! the! right! might! result! either! from!
positive! charges! moving! in! the! direction! of! the! current,! from!
negative!charges!moving!in!the!opposite!direction,!or!both!at!once.!!
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Figure%2.20%(a)!Current!flows!around!a!circuit!from!the!positive!terminal!of!the!battery!to!
the! negative.! In! the! connecting! wires! the! current! is! carried! by! electrons! travelling! in! the!
opposite! direction.! (b)! the! beam! of! electrons! travelling! down! a! cathode! ray! tube! in! a!
television!set!produces!a!positive!current!in!the!opposite!direction.!!
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Now%complete%Questions%1%to%7%on%page%58%
EMF!and!electric!potential!!
In! order! to! drive! a! current! around! an! electric! circuit! the!
charges!must!be!given!energy.!A!battery!or!generator%is!
the!usual!source!of!this!energy.!!
Another!increasingly!common!source!of!electrical!energy!
is! the! photovoltaic% cell,% or! solar! cell.! These! devices! are!
all!referred!to!as!sources!of!EMF.%%
The!letters!EMF%stands!for!Electro%Motive%Force.%(EMF!is!
still!used!although!it!is!not!accurate,!it!is!the!energy!given!
to!the!charges!rather!than!the!force!on!them)!
It! may! help! understand! EMF! by! thinking! of! the! Van! de!
Graaff!generator!(see!Figure!2.4).!The!source!of!energy!in!
this! case! is! very! obvious.! The! motor! is! pushing! the!
charges! on! the! rubber! belt! up! against! the! electrostatic!
repulsion! of! the! charges! already! on! the! dome.! The! more!
charge!already!on!the!dome,!the!greater!the!force,!and!hence!the!greater!the!work!that!has!
to!be!done!to!bring!more!charge!to!the!dome.!!
EMF!can!be!visualised!as!a!‘concentration!of!charge’.!The!more!charges!put!on!the!dome,!the!
more!concentrated!they!become!and!the!greater!the!force!of!repulsion!between!them.!The!
work!done!pushing!the!charges!together!(by!the!motor!in!this!case)!is!stored!as!electrical%
potential% energy.% The! electrical! energy! can! be! used! when! the! charges! are! allowed! to! fly!
apart!again.!In!the!case!of!the!Van!de!Graaff!this!potential!energy!is!converted!into!kinetic!
energy,!as!it!sparks,!and!as!the!charges!collide!with!the!air!molecules!it!is!turned!into!heat,!
light!and!sound!energy.!!
EMF!is!defined!as!the!amount!of!work!done!for!each!unit!of!charge!in!this!process!of!charge%
concentration.% Because! it! is,! therefore,! actually! the! ‘electric! potential! energy! per! unit!
charge’,! this! quantity! is! most! often! abbreviated! simply! to! electric% potential% or! just!
potential.!
The!SI!unit!for!potential!is!joule(per(coulomb.(One!joule!per!coulomb!is!given!the!name!volt,%
in!honour!of!Alessandro!Volta,!the!inventor!of!the!first!chemical!battery.!!
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This! means! that! if! you! have! an! EMF! of! 9! V! each! 1C! of! charge! is! given! 9! J! of! energy,! or! in!
general:!
Energy!E%=%V%x%q,!where!V!is!in!Volts!and!q!is!the!charge!in!C.!
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Worked%example%2.3B%%
The!alternator!of!a!car!being!driven!at!night!with!the!headlights!on,!is!producing!a!50!A!
current!at!an!EMF!of!12!V.!
a%How!many!coulombs!of!charge!flow!from!the!alternator!each!second?!
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b%How!many!joules!of!energy!does!each!coulomb!of!charge!obtain?!!
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c%How!many!joules!of!energy!does!the!alternator!produce!each!second?!!
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d%Where!does!this!energy!go?!!
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Electric circuits and potential difference!
Any! electric% circuit% consists! of! at! least! one! source! of! EMF,! conductors! that! carry! current!
and!the!various!circuit%elements.%Consider!a!simple!torch!circuit:!a!battery,!a!switch!and!a!
bulb!all!connected!by!wires.!The!current!from!the!battery!goes!from!the!positive!terminal!to!
the!bulb!and!then!via!the!switch!back!to!the!base!of!the!battery,!which!acts!as!the!negative!
terminal.! (Remember! how! we! defined! the! direction! of! current! early).! When! a! battery! is!
connected! in! a! circuit,! it! produces! a! potential% difference;% that! is,! a! difference! in! the!
potential! energy! of! the! charges! in! the! conductors! connected! to! its! terminals.! While! the!
switch! is! off,! All! the! conductors! on! one! side! of! the! switch! will! have! the! same! positive!
potential!and!all!those!on!the!other!side!the!same!negative!potential.!!
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Figure%2.24%the!electric!field!and!the!potential!around!a!circuit!are!related.!(a)!In!an!open!
circuit! there! is! no! potential! drop! around! the! circuit! and! no! electric! field! (except! at! the!
switch).!(b)!In!the!closed!circuit!charge!flows!as!the!result!of!an!electric!field.!As!it!flows!it!
loses! potential.! Where! the! conductor! is! narrow! the! field! is! ‘squeezed’! and! becomes!
stronger,!thus!the!charges!are!pushed!harder.!the!potential!also!drops!more!quickly!through!
the!narrow!region!as!more!work!is!done!and!potential!energy!lost.!
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The!potential!difference!across!a!circuit!element!is!the!potential!energy!lost(by!each!unit!of!
charge! in! that! element.! The! potential! difference,! sometimes! called! potential! drop! or! just!
p.d.,!across!a!circuit!element!is!written!∆V,!the!∆!representing!the!fact!that!there!is!a!change!
of!potential.!In!practice,!the!∆!is!often!omitted!as!there!is!rarely!a!need!to!refer!to!anything!
other!than!a!change!of!potential.!As!∆V!is!the!energy!lost!by!one!unit!of!charge,!a!charge!of!q(
coulomb!will!lose!q∆V(joules!of!potential!energy!as!it!goes!through!a!potential!difference!of!
∆V.!!
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Worked%example%2.3C%%
The!potential!difference!across!a!torch!bulb!is!found!to!be!2.7!V.!the!current!flowing!through!
itis0.2A.!!
A%
how!much!charge!flows!through!the!torch!in!1!minute?!!
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B%
how!much!energy!is!lost!by!this!charge?!!
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Now%complete%Questions%8%to%14%on%page%58%
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5!
Year!11!Physics!Unit!1!
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Area!of!Study!1!.!Electricity!
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Chapter!2!–!Concepts!in!Electricity!
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2.4!
Resistance,!ohmic!and!non.ohmic!conductors!
When! a! potential! difference! is! applied! across! an! electrical! device! in! a! circuit! a! current! will!
flow.! Generally! speaking,! the! greater! the! potential! applied,! the! greater! the! current! that! will!
flow.!The!actual!relationship!between!the!current!and!the!potential!difference!applied!is!the!
subject!of!this!section.!
In!order!to!measure!the!current!through!and!the!potential!difference!across!a!circuit!element!
we!must!introduce!….!
Ammeters!and!voltmeters!
A!voltmeter(is!used!to!measure!the!potential!difference!across!any!circuit!element!or!source!of!
Voltage.!The!voltmeter!measures!the!difference!in!electrical!potential!between!two!points!in!a!
circuit.!This!is!why!the!voltmeter!connections!are!always!placed!across(the!circuit!element.!
The!ammeter(is!used!to!measure!the!current!flowing!in!a!circuit!and!is!therefore!placed!so!that!
the!current!flows!through(the!ammeter!as!well!as!the!circuit!element.!!
Never-place-an-ammeter-across-a-circuit-element-because-it-would-damage-the-meter.-
!
!
Figure! 2.28! (a)!A!simple!circuit!of!one!battery!
and! one! circuit! element,! together! with! an!
ammeter!and!voltmeter!to!measure!the!current!
and! potential! difference.! (b)! Four! examples! of!
symbols! for! possible! circuit! elements:! a! light!
bulb,! a! resistor! or! other! circuit! element,! an!
alternative!symbol!for!a!resistor!used!to!specify!
an!ohmic!resistor!in!particular,!and!a!diode.!
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Current–Voltage!graphs!
Whether! a! simple! light! bulb! or! a! complex! electronic! component,! a! knowledge! of! the!
relationship!between!the!current!and!the!voltage,!the!soOcalled!I–V-characteristic,!is!needed!
in!order!to!predict!the!behaviour!of!the!device.!This!is!often!in!the!form!of!a!graph.!The!voltage!
is! plotted! on! the! horizontal! axis.! Some! examples! of! I–V(graphs! for! some! common! electrical!
devices!are!shown!in!Figure!2.29.!
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1!
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Figure!2.29!examples!of!the!relationship!between!current!and!applied!potential!difference!
for!three!common!electrical!devices.!
!
We!can!divide!these!devices!into!two!groups:!those!that!have!a!straight!I–V(graph!and!those!
that!do!not.!The!resistor! is!in!the!first!group,!the!light!bulb!and!the!diode! are!in!the!second.!
Those!with!a!straight!I–V(characteristic!are!called!ohmic! conductors! and!those!which!don’t!
are!(rather!logically)!called!non.ohmic(conductors.!
!
Resistance!
Georg!Ohm!(1789–1854)!found!that!if!the!temperature!of!a!metal!wire!was!kept!constant,!the!
current!flowing!through!it!was!directly!proportional!to!the!potential!placed!across!it:!I(∝!V.(
This!is!known!as!Ohm’s!law.!
!
Rather!than!writing!this!as!I(=!kV((where!k(is!the!slope!of!the!I–V(graph)!this!relationship!is!
normally!written!the!other!way!around!as!V(=!IR,(where!R(is!called!the!resistance!(it!is!the!
inverse!of!the!gradient).!So!Ohm!basically!said!that!the!resistance!of!a!metal!wire!(at!a!certain!
temperature)!is!constant.!Even!if!the!resistance!of!a!conductor!is!not!constant!(the!graph!is!
not!straight)!it!is!still!defined!as!the!ratio!of!the!potential!difference!across!a!conductor!to!the!
current!flowing!in!it!at!that!potential.!
!
The!expression!V(=!IR(is!sometimes!referred!to!as!Ohm’s!law,!but!that!is!only!correct!if!R(is!
constant.!This!expression!is!basically!the!definition!of!resistance.!Ohm’s!law!effectively!says!
that!R(is!constant!for!some!types!of!conductors—and!they!are!called!ohmic!conductors.!We!
can!see!from!Figure!2.29!that!while!the!resistance!of!the!resistor!is!constant,!that!of!the!light!
bulb!increases!with!increasing!potential,!whereas!the!resistance!of!the!diode!decreases!with!
increasing!potential.!The!resistor!obeys!Ohm’s!law,!but!the!others!do!not.!
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2!
Ohmic!conductors!
Many!conductors!do!obey!Ohm’s!law!quite!closely!and!so!their!I–V(characteristic!is!completely!
specified!by!a!single!number,!the!resistance!R.(The!unit!for!resistance!is!volts(per(ampere(and!
is!given!the!name!ohm((symbol!Ω,!omega).!It!helps!to!think!of!the!resistance!as!the!number!of!
volts!needed!to!make!a!current!of!1!ampere!flow!through!the!conductor.!But!remember!that!
the!resistance!is!a!ratio—the!actual!resistor!may!go!up!in!smoke!if!1!A!actually!flowed!through!
it!!Ohmic!conductors!are!often!simply!referred!to!as!‘resistors’:!
1!ohm!=!1!volt!per!ampere!(1!Ω!=!1!V!A−1)!
Worked!example!2.4A!
A!resistor!of!5!Ω!is!supplied!with!a!potential!that!can!vary!from!1!V!to!100!V.!
. a!!What!will!be!the!range!of!currents!that!will!flow!in!it?!!
. b!!how!much!energy!will!be!dissipated!in!the!resistor!each!second?!!
Solution!
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NonOohmic!conductors!
A!light!bulb!is!a!common!example!of!a!nonOohmic!conductor.!NonOohmic!conductors!include!
devices!whose!resistance!changes!with!light!or!temperature.!These!are!particularly!useful!as!
detectors!in!sensors!that!need!to!respond!to!changes!in!light!levels!or!temperature.!
Worked!example!2.4B!
The!graph!represents!the!I–V(characteristic!of!a!240!V,!
60!W!light!bulb.!What!is!the!resistance!at:!!
a!24V?!b!120V?!c!240V?!
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3!
Year!11!Physics!Unit!1!
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Area!of!Study!1!.!Electricity!
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Chapter!2!–!Concepts!in!Electricity!
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2.5! Electrical!energy!and!power!
Electrical!energy!
Electrical! potential! energy! is! produced! whenever! charges! are! pushed! close! together.!
This!energy!can!be!transmitted!long!distances!from!power!stations!or!simply!produced!
on!demand!from!the!chemical!energy!stored!in!batteries.!
The!voltage,!of!a!power!source!is!a!measure!of!the!number!of!joules!of!energy!stored!
for!each!coulomb!of!charge.!As!the!charges!move!through!the!circuit!they!lose!the!
energy!given!to!them!by!the!source.!The!potential)energy)lost!by!a!charge!q)moving!
through!a!potential!difference!V)is!given!by!!
E"=!qV"
)As!the!current!is!the!rate!at!which!charge!is!moving,!the!total!charge!q)can!be!
expressed!as!q)=!It.)The!total!energy!produced!is!therefore!given!by:
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Worked!example!2.5A!!
How!much!energy!is!used!in!1!h!by!a!240!V!heater!drawing!5!A?!
Solution!
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Electric!power!
Power is the rate of energy use: P = E/t. (Remember that the SI unit for power is the
watt, where 1 watt = 1 joule per second.) Dividing the previous expression by t
gives:
E/t = VIt/t
or P = VI
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Worked!example!2.5B!
Two!different!torch!bulbs!are!rated!as!2.8!V,!0.27!A,!and!4.2!V,!0.18!A.!
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a!!Which!will!be!the!brightest?!!
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b!!Could!they!be!interchanged?!!
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c!!What!are!the!resistances!of!the!two!bulbs!at!their!operating!voltages?!!
Solution!
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Another!unit!for!electrical!energy!
The!total!amount!of!energy!used!by!an!appliance!depends!on!the!time!for!which!it!is!switched!
on.!The!total!energy!is!given!by!the!product!of!the!power!and!the!time:!!
E"=!Pt"
(Remember:!1!joule!=!1!watt!1!second).!
Worked!example!2.5C!!
How!much!energy!does!a!100!W!light!bulb!use!in!half!an!hour?!
Solution!
Here!P=100W!and!t=0.5h.!!
So...E=100W!x!0.5h!=!50Wh!or!0.05kWh.!!
This!could!also!be!given!as!100W!x!1800s!=!180,000!J!=!180kJ.!
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2!