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Year%11%Physics%Unit%1,%2015%

!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.!%

%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.!!

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%%• 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!!

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).!

!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?!!

!!!!!!!!!!!!! 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.#

!!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%

%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.#%

!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.!!!

%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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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?!!!!!b%How!many!joules!of!energy!does!each!coulomb!of!charge!obtain?!!%%%%c%How!many!joules!of!energy!does!the!alternator!produce!each!second?!!%%%%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?!!!!!!B% how!much!energy!is!lost!by!this!charge?!!!!!!Now%complete%Questions%8%to%14%on%page%58%

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Year!11!Physics!Unit!1!

!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.-

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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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Figure!2.29!examples!of!the!relationship!between!current!and!applied!potential!difference!for!three!common!electrical!devices.!

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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.!

! 3!

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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! 1!

Year!11!Physics!Unit!1!!

Area!of!Study!1!.!Electricity!!

Chapter!2!–!Concepts!in!Electricity!!

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!!!!!!!

!! !

! 2!

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

!!

Worked!example!2.5B!Two!different!torch!bulbs!are!rated!as!2.8!V,!0.27!A,!and!4.2!V,!0.18!A.!

. a!!Which!will!be!the!brightest?!!

. b!!Could!they!be!interchanged?!!

. c!!What!are!the!resistances!of!the!two!bulbs!at!their!operating!voltages?!!Solution!

!!!!!!!!!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.!