current of electricity

8/16/2019 Current of Electricity

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Current of Electricity

Element Symbol

Units

Source ofelectromotive force,emf

Volt

[V]

Conductor ofresistance R

Ohm[Ω]

Direction of

conventional current

m!er

e []

"#" Electric Current, $ % Char&e, '

(erm De)nition*Remar+s

Electric current $ Rate of o- of char&ed !articles

Electric char&e, '

[Unit. C]• /hen a constant current $ o-s

throu&h a cross0section of aconductor for a duration t, theamount of electric char&e '!assin& throu&h it is &iven by '1 $t

• $f the current o- is not

constant, ' 1 2$ dtCoulomb, C mount of electric char&es that

!asses throu&h a !oint in a circuitin one second -hen there is aconstant current of one am!ere 3"C 1 " s4

Electromotive 5orce 3e#m#f4, E

• /hen an electric current is o-in& thru&h conductors in a closed circuit, electrical ener&y is continuouslydissi!ated as heat or other forms of ener&y

• $n order to sustain this constant o- of electric current, a source of electromotive force 3e#m#f4 is needed#

• Sources of e#m#f are any devices -hich can be li+ened to a 6char&e !um!7 in -hich electrical ener&y is

converted from chemical, mechanical or other forms of ener&y 3such as batteries, &enerators, solar cells andfuel cells4


e#m#f, E

[Unit. V]• mount of electrical ener&y !er unit char&e that is converted from other forms to drive a

char&e around a com!lete circuit

• E 1W

Q• 8ot a force, as name su&&ests

• 5or a battery -ith am e#m#f of "#9 V, "#9 : of chemical ener&y is coverted into electricalener&y -ith every coulomb of char&e the battery drives throu&h the circuit

e#m#f E of a source !#d# V across an e;ternal load

E 1W

QV 1

W

Q

/ is ener&y converted from other forms to electricalener&y

/ is the ener&y converted from electrical ener&y to otherforms

Ener&y su!!lied !er unit char&e Ener&y dissi!ated !er unit char&e

Resistance, R and Resistivity, ρ• Electric current in a conductor de!ends on the !otential di


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R ∝ l

A * R 1 ρ

l

A -here constant of !ro!ortionality ρ is the resistivity of the

material [Unit. Ω m4

Ohm, Ω • Resistance of a conductor -hen a !otential di


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8et eo-er >


>o-er

[Unit. /]• s sho-n earlier, if a char&e ' moves throu&h a !#f# V, the amount of electrical ener&y converted

to other forms is / 1 'V

(he rate at -hich ener&y conversion ta+es !lace is > 1dW

dt 1

d (QV )dt

1 $V

• 5rom E 1W

Q, for an ideal source of e#m#f# E, -or+ done by the source is / 1 'E

(he !o-er > su!!lied by source

> 1dW

dt 1

dQ

dt E ∴ > 1 $E

• s sho-n earlier, V 1 $R (he rate at -hich ener&y is dissi!ated across a resistor is> 1 $V

OR > 1 $ ; 3$R4 1 I 2 R

OR > 1 (V

R) ; V 1 V

2

R5or t-o resistors -ith the same current 3e# t-oresistors in series4, !o-er is directly !ro!ortionalto resistance 3!#d# are not the same4

> 1 I 2 R

5or t-o resistors -ith the same !#d# 3e# t-oresistors in !arallel4, !o-er is inversely!ro!ortional to resistance 3currents are not thesame4

> 1V

2

R

$nternal Resistance r of a source of emf

• $n an ideal circuit,the e#m#f source -ould have no resistance,the connectin& -ires -ould have no resistance, andthe !#d# V across the cell terminals 3terminal !#d#4 1 e#m#f# E of the cell

• Io-ever, real cells have internal resistance r#

• Ience, not all electrical ener&y &enerated is available to the e;ternal load as R# Some ofthis ener&y is lost as heat -ithin the cell due to its internal resistance#

• s a result, the terminal !d is not eGual to the emf of the source

odel of a real battery

real battery can be /ithin the source of e#m#f, chemical ener&y is converted to electrical


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modeled as.

• a resistance r,-hich is

• connected inseries to anideal e#m#f#source

ener&y#

>o-er su!!lied by the source, Ps 1 $E

$n the internal resistance r,

>o-er dissi!ated as heat, Pr 1 I 2 r 1 IV r

$n the e;ternal load R,

>o-er dissi!ated as heat, P R 1 I 2 R 1 IV R

By >OCOE,

>o-er su!!lied by source 1 >o-er dissi!ated throu&h r % R

Ps 1 Pr J P R$E 1 I

2 r J I 2 R

E 1 $ 3r J R4

lso, Ps 1 Pr J P R$E 1 IV r J IV RE 1 IV r J IV RV R 1 E 0 $r

Eo-er Out!ut 3>o-er (ransmitted to Aoad4

a;imum >o-er (heorem 3a;imum >o-er (ransmitted to Aoad4

E 1 $ 3r J R4

$ 1 E

(r+ R)∴ >o-er transferred to

e;ternal load R is

P R 1 I 2 R 1

E

(r+ R)¿

¿¿

R

1 E

2 R

(r+ R)2

d P R

dR 1

E2 (r+ R )−2 E2 R

(r+ R)3 1

E2 3r J R4 0 = E

2 R 1

3r J R4 0 =R 1

R 1 r

∴ source of e#m#f# delivers the ma;imum amount of !o-er to a load -hen

the resistance of the load is eGual to the internal resistance of the source# (his isthe ma;imum !o-er theorem#

(y!es of char&e carriers

• By convention, current o-s in the same direction as the o- of !ositive char&es, re&ardless of the actualchar&ed !articles in motion#

• (he char&ed !articles may di


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Semi0conductors

Electrons andholes

Kermanium,silicon

• lthou&h all four electrons in the outer shell are sharedamon& nei&hborin& atoms to form covalent bonds, atroom tem!erature, these electrons may have suHcientener&y to leave the atoms to become 6free electrons#

• (hese electrons leave behind hoes in the atoms -here

nei&hbourin& electrons can move to )ll them and leaveholes from -here they came from

• (he holes seem to behave li+e !ositively char&ed!articles, movin& in the o!!osite direction to electrono-

Electrolytes $ons 8aCl solution • Some salts dissociate into !ositive and ne&ative ions in

-ater• obile ions contribute to electrical conduction

$nsulators 8one Rubber,!orcelain, &lass

• ll electrons in the outer shell of the atoms of aninsulator are involved in formin& covalent bonds

• Unli+e semiconductors, these electrons cannot acGuiresuHcient ener&y to be 6freed7, and are not available forelectrical conduction

current of electricity

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