7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 113

C983151983154983154983141983150983156983141 E983148983273983156983154983145983139983137

983141983122983141983155983145983155983156983274983150983139983145983137

Prof Rogeacuterio Toniolo

UNIVERSIDADE

POSITIVO

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 213

983126+ gt 983126983085

rArrrArrrArrrArr ∆∆∆∆983126 = 983126+ minusminusminusminus 983126983085 = 983126

983120983151983154 983155983145983149983152983148983145983139983145983140983137983140983141 ∆∆∆∆983126 = 983126

Corrente Eleacutetrica

+

+

++

E

A

983139983151983150983140983157983156983151983154

983126 983085983126 +

D983145983142983141983154983141983150983271983137 983140983141 983120983151983156983141983150983139983145983137983148 (983140983140983152) A983152983148983145983139983137983140983137

C983151983154983154983141983150983156983141 C983151983150983158983141983150983139983145983151983150983137983148 (i ) C983137983154983143983137983155 +

C983151983154983154983141983150983156983141 983122983141983137983148

E983149 983149983141983156983137983145983155 983141983148983273983156983154983151983150983155 rArrrArrrArrrArr C983137983154983143983137983155 minusminusminusminus

eleacutetron de conduccedilatildeo

ldquoPortador de cargardquo

Ligaccedilatildeo metaacutelica uacuteltimos eleacutetrons da camada de valecircncia satildeofracamente ligados

Caacutetion Iacuteon metaacutelico +

Exemplo Al 3+

Modelo do Gaacutes de Eleacutetrons ou doMar de Eleacutetrons

i

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 313

Corrente Eleacutetrica

983122983141983143983145983149983141 983120983141983154983149983137983150983141983150983156983141 983142983148983157983160983151 983139983151983150983155983156983137983150983156983141 983140983141 983139983137983154983143983137983155

D983141983142983145983150983145983271983267983151 983107983151983154983154983141983150983156983141 983117983273983140983145983137

I =

∆∆∆∆Q

∆∆∆∆t 983118983151 983123983113 1 C983155 = 1 A (983137983149983152983272983154983141)

983120983137983154983137 983157983149 983145983150983155983156983137983150983156983141 983140983141 983156983141983149983152983151 i =dq

dt C983151983154983154983141983150983156983141 983113983150983155983156983137983150983156983266983150983141983137

C983151983154983154983141983150983156983141 983125983150983145983142983151983154983149983141

J =i

A i = dAint Jbullbullbullbull

A2A1

i

J 1 J 2G983141983150983141983154983137983148983145983162983137983150983140983151

A9831492

D983141983150983155983145983140983137983140983141 983140983141 C983151983154983154983141983150983156983141 ( 983114 ) 983140983141983155983139983154983141983158983141 983142983148983157983160983151 983140983141 983139983137983154983143983137983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 413

Corrente Eleacutetrica em Um Condutor

+

+

+

+A

983139983151983150983140983157983156983151983154

i

∆∆∆∆ x

D983141983142983145983150983145983271983267983151 n = 983150983151 983140983141 983152983151983154983156983137983140983151983154983141983155 983140983141 983139983137983154983143983137

983157983150983145983140983137983140983141 983140983141 983158983151983148983157983149983141

983118983157983149 983140983141 983139983137983154983143983137983155 983150983151 983141983148983141983149983141983150983156983151 983140983141 983158983151983148983157983149983141

N = nsdotsdotsdotsdot983126983151983148 = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotA

I = nsdotsdotsdotsdotqsdot sdotsdot sdot VdsdotsdotsdotsdotA

D983141983142983145983150983145983271983267983151 983126983141983148983151983139 983140983141 983117983145983143983154983137983271983267983151 983151983157 D983141983154983145983158983137

983126 983140 = ∆∆∆∆ x

∆∆∆∆t983126983140

i

C983137983154983143983137 983141983148983273983156983154983145983139983137 983150983151 983141983148983141983149983141983150983156983151 ∆∆∆∆Q = N sdot sdotsdot sdot q rArrrArrrArrrArr ∆∆∆∆Q = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q

I = ∆∆∆∆Q∆∆∆∆t

= nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q∆∆∆∆t

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 513

983149A983144 983149983145983148983145983137983149983152983272983154983141983085983144983151983154983137

983109983160983141983149983152983148983151983098

983091983086983088983088983088 983149983105983144983098 983152983151983140983141 983137983138983137983155983156983141983139983141983154 983157983149

983137983152983137983154983141983148983144983151 983153983157983141 983139983151983150983155983157983149983137 983091983088983088 983149983105 983152983151983154 983089983088 983144983086

Capacidade de Armazenamento

983149A983144 983125983150983145983140983137983140983141 983140983141 C983137983154983143983137 E983148983273983156983154983145983139983137

3000 983149A983144 = 3000 timestimestimestimes10minusminusminusminus3A timestimestimestimes 3600 983155 = 10800 C 983140983141 983139983137983154983143983137 983137983154983149983137983162983141983150983137983140983137

I∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

I = ∆∆∆∆Q

∆∆∆∆tI∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

Definiccedilatildeo de Coulomb (SI)

1 C eacute a carga eleacutetrica transportada em 1 s por uma corrente de 1 A

C983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983142983151983145 983140983141983155983139983151983138983141983154983156983137 983137983150983156983141983155 983140983137 983139983137983154983143983137 983125983150983145983140983137983140983141 983142983157983150983140983137983149983141983150983156983137983148 983150983151 983123983113

D983141983142983145983150983141983085983155983141 983151 C983151983157983148983151983149983138 983139983151983149983151

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 613

Efeitos Bioloacutegicos

983118983137983156983157983154983141983162983137 983141983148983273983156983154983145983139983137 983140983137 983142983157983150983271983267983151 983150983141983154983158983151983149983290983155983139983157983148983151

983116983157983145983143983145 G983137983148983158983137983150983145 (17379830851798)

Corrente Efeito

Efeitos no Corpo Humano (de modo geral)

F983151983154983149983145983143983137983149983141983150983156983151

A983157983149983141983150983156983151 983140983137983155 983139983151983150983156983154983137983271983285983141983155 983149983157983155983139983157983148983137983154983141983155

983120983137983154983137983140983137 983154983141983155983152983145983154983137983156983283983154983145983137

F983145983138983154983145983148983137983271983267983151 983149983157983155983139983157983148983137983154 983152983151983140983141 983155983141983154 983142983137983156983137983148

983120983137983154983137983140983137 983139983137983154983140983277983137983139983137 983153983157983141983145983149983137983140983157983154983137983155 983143983154983137983158983141983155

1 983149A

10 991251 20 983149A

20 991251 100 983149A

100 983149A 991251 3 A

983137983139983145983149983137 983140983141 3 A

Adaptado DURAN JER Biofiacutesica-Fundamentos e

Aplicaccedilotildees Satildeo Paulo Pearson Prentice Hall 2003 p 178

983119983138983155983141983154983158983137983271983267983151

E983142983141983145983156983151983155 983140983141983152983141983150983140983141983149

983085 983140983151 983156983141983149983152983151 983140983141 983141983160983152983151983155983145983271983267983151

983085 983156983145983152983151 983140983141 983139983151983154983154983141983150983156983141

983137983148983156983141983154983150983137983140983137 (983139983137)

983139983151983150983156983277983150983157983137 (983139983139)

D983141983156983137983148983144983137983149983141983150983156983151 983118983151983154983149983137 98311898312298308510

D983141983155983139983151983138983154983145983157 983137 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 713

Resistecircncia e Resistividade

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983274983150983139983145983137

R = Vi

983118983151 983123983113 1 983126A = 1 ΩΩΩΩ (983151983144983149)

983122983141983155983145983155983156983151983154

E983148983141983149983141983150983156983151 983139983151983150983140983157983156983151983154

983157983155983137983140983151 983152983137983154983137 983151983142983141983154983141983139983141983154

983154983141983155983145983155983156983274983150983139983145983137

983123983277983149983138983151983148983151983155

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ = E

983114

983118983151 983123983113 ΩsdotΩsdotΩsdotΩsdot983149

983120983137983154983137 983149983137983156983141983154983145983137983145983155 983145983155983151983156983154983283983152983145983139983151983155

E983160 C983151983138983154983141 17 timestimestimestimes 10minusminusminusminus8 ΩΩΩΩ sdotsdotsdotsdot983149

E = ρ ρρ ρ 983114 983151983157

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 813

Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 913

Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1113

Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1313

Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 213

983126+ gt 983126983085

rArrrArrrArrrArr ∆∆∆∆983126 = 983126+ minusminusminusminus 983126983085 = 983126

983120983151983154 983155983145983149983152983148983145983139983145983140983137983140983141 ∆∆∆∆983126 = 983126

Corrente Eleacutetrica

+

+

++

E

A

983139983151983150983140983157983156983151983154

983126 983085983126 +

D983145983142983141983154983141983150983271983137 983140983141 983120983151983156983141983150983139983145983137983148 (983140983140983152) A983152983148983145983139983137983140983137

C983151983154983154983141983150983156983141 C983151983150983158983141983150983139983145983151983150983137983148 (i ) C983137983154983143983137983155 +

C983151983154983154983141983150983156983141 983122983141983137983148

E983149 983149983141983156983137983145983155 983141983148983273983156983154983151983150983155 rArrrArrrArrrArr C983137983154983143983137983155 minusminusminusminus

eleacutetron de conduccedilatildeo

ldquoPortador de cargardquo

Ligaccedilatildeo metaacutelica uacuteltimos eleacutetrons da camada de valecircncia satildeofracamente ligados

Caacutetion Iacuteon metaacutelico +

Exemplo Al 3+

Modelo do Gaacutes de Eleacutetrons ou doMar de Eleacutetrons

i

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 313

Corrente Eleacutetrica

983122983141983143983145983149983141 983120983141983154983149983137983150983141983150983156983141 983142983148983157983160983151 983139983151983150983155983156983137983150983156983141 983140983141 983139983137983154983143983137983155

D983141983142983145983150983145983271983267983151 983107983151983154983154983141983150983156983141 983117983273983140983145983137

I =

∆∆∆∆Q

∆∆∆∆t 983118983151 983123983113 1 C983155 = 1 A (983137983149983152983272983154983141)

983120983137983154983137 983157983149 983145983150983155983156983137983150983156983141 983140983141 983156983141983149983152983151 i =dq

dt C983151983154983154983141983150983156983141 983113983150983155983156983137983150983156983266983150983141983137

C983151983154983154983141983150983156983141 983125983150983145983142983151983154983149983141

J =i

A i = dAint Jbullbullbullbull

A2A1

i

J 1 J 2G983141983150983141983154983137983148983145983162983137983150983140983151

A9831492

D983141983150983155983145983140983137983140983141 983140983141 C983151983154983154983141983150983156983141 ( 983114 ) 983140983141983155983139983154983141983158983141 983142983148983157983160983151 983140983141 983139983137983154983143983137983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 413

Corrente Eleacutetrica em Um Condutor

+

+

+

+A

983139983151983150983140983157983156983151983154

i

∆∆∆∆ x

D983141983142983145983150983145983271983267983151 n = 983150983151 983140983141 983152983151983154983156983137983140983151983154983141983155 983140983141 983139983137983154983143983137

983157983150983145983140983137983140983141 983140983141 983158983151983148983157983149983141

983118983157983149 983140983141 983139983137983154983143983137983155 983150983151 983141983148983141983149983141983150983156983151 983140983141 983158983151983148983157983149983141

N = nsdotsdotsdotsdot983126983151983148 = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotA

I = nsdotsdotsdotsdotqsdot sdotsdot sdot VdsdotsdotsdotsdotA

D983141983142983145983150983145983271983267983151 983126983141983148983151983139 983140983141 983117983145983143983154983137983271983267983151 983151983157 D983141983154983145983158983137

983126 983140 = ∆∆∆∆ x

∆∆∆∆t983126983140

i

C983137983154983143983137 983141983148983273983156983154983145983139983137 983150983151 983141983148983141983149983141983150983156983151 ∆∆∆∆Q = N sdot sdotsdot sdot q rArrrArrrArrrArr ∆∆∆∆Q = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q

I = ∆∆∆∆Q∆∆∆∆t

= nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q∆∆∆∆t

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 513

983149A983144 983149983145983148983145983137983149983152983272983154983141983085983144983151983154983137

983109983160983141983149983152983148983151983098

983091983086983088983088983088 983149983105983144983098 983152983151983140983141 983137983138983137983155983156983141983139983141983154 983157983149

983137983152983137983154983141983148983144983151 983153983157983141 983139983151983150983155983157983149983137 983091983088983088 983149983105 983152983151983154 983089983088 983144983086

Capacidade de Armazenamento

983149A983144 983125983150983145983140983137983140983141 983140983141 C983137983154983143983137 E983148983273983156983154983145983139983137

3000 983149A983144 = 3000 timestimestimestimes10minusminusminusminus3A timestimestimestimes 3600 983155 = 10800 C 983140983141 983139983137983154983143983137 983137983154983149983137983162983141983150983137983140983137

I∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

I = ∆∆∆∆Q

∆∆∆∆tI∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

Definiccedilatildeo de Coulomb (SI)

1 C eacute a carga eleacutetrica transportada em 1 s por uma corrente de 1 A

C983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983142983151983145 983140983141983155983139983151983138983141983154983156983137 983137983150983156983141983155 983140983137 983139983137983154983143983137 983125983150983145983140983137983140983141 983142983157983150983140983137983149983141983150983156983137983148 983150983151 983123983113

D983141983142983145983150983141983085983155983141 983151 C983151983157983148983151983149983138 983139983151983149983151

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 613

Efeitos Bioloacutegicos

983118983137983156983157983154983141983162983137 983141983148983273983156983154983145983139983137 983140983137 983142983157983150983271983267983151 983150983141983154983158983151983149983290983155983139983157983148983151

983116983157983145983143983145 G983137983148983158983137983150983145 (17379830851798)

Corrente Efeito

Efeitos no Corpo Humano (de modo geral)

F983151983154983149983145983143983137983149983141983150983156983151

A983157983149983141983150983156983151 983140983137983155 983139983151983150983156983154983137983271983285983141983155 983149983157983155983139983157983148983137983154983141983155

983120983137983154983137983140983137 983154983141983155983152983145983154983137983156983283983154983145983137

F983145983138983154983145983148983137983271983267983151 983149983157983155983139983157983148983137983154 983152983151983140983141 983155983141983154 983142983137983156983137983148

983120983137983154983137983140983137 983139983137983154983140983277983137983139983137 983153983157983141983145983149983137983140983157983154983137983155 983143983154983137983158983141983155

1 983149A

10 991251 20 983149A

20 991251 100 983149A

100 983149A 991251 3 A

983137983139983145983149983137 983140983141 3 A

Adaptado DURAN JER Biofiacutesica-Fundamentos e

Aplicaccedilotildees Satildeo Paulo Pearson Prentice Hall 2003 p 178

983119983138983155983141983154983158983137983271983267983151

E983142983141983145983156983151983155 983140983141983152983141983150983140983141983149

983085 983140983151 983156983141983149983152983151 983140983141 983141983160983152983151983155983145983271983267983151

983085 983156983145983152983151 983140983141 983139983151983154983154983141983150983156983141

983137983148983156983141983154983150983137983140983137 (983139983137)

983139983151983150983156983277983150983157983137 (983139983139)

D983141983156983137983148983144983137983149983141983150983156983151 983118983151983154983149983137 98311898312298308510

D983141983155983139983151983138983154983145983157 983137 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 713

Resistecircncia e Resistividade

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983274983150983139983145983137

R = Vi

983118983151 983123983113 1 983126A = 1 ΩΩΩΩ (983151983144983149)

983122983141983155983145983155983156983151983154

E983148983141983149983141983150983156983151 983139983151983150983140983157983156983151983154

983157983155983137983140983151 983152983137983154983137 983151983142983141983154983141983139983141983154

983154983141983155983145983155983156983274983150983139983145983137

983123983277983149983138983151983148983151983155

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ = E

983114

983118983151 983123983113 ΩsdotΩsdotΩsdotΩsdot983149

983120983137983154983137 983149983137983156983141983154983145983137983145983155 983145983155983151983156983154983283983152983145983139983151983155

E983160 C983151983138983154983141 17 timestimestimestimes 10minusminusminusminus8 ΩΩΩΩ sdotsdotsdotsdot983149

E = ρ ρρ ρ 983114 983151983157

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 813

Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 913

Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1113

Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

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Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

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Corrente Eleacutetrica

983122983141983143983145983149983141 983120983141983154983149983137983150983141983150983156983141 983142983148983157983160983151 983139983151983150983155983156983137983150983156983141 983140983141 983139983137983154983143983137983155

D983141983142983145983150983145983271983267983151 983107983151983154983154983141983150983156983141 983117983273983140983145983137

I =

∆∆∆∆Q

∆∆∆∆t 983118983151 983123983113 1 C983155 = 1 A (983137983149983152983272983154983141)

983120983137983154983137 983157983149 983145983150983155983156983137983150983156983141 983140983141 983156983141983149983152983151 i =dq

dt C983151983154983154983141983150983156983141 983113983150983155983156983137983150983156983266983150983141983137

C983151983154983154983141983150983156983141 983125983150983145983142983151983154983149983141

J =i

A i = dAint Jbullbullbullbull

A2A1

i

J 1 J 2G983141983150983141983154983137983148983145983162983137983150983140983151

A9831492

D983141983150983155983145983140983137983140983141 983140983141 C983151983154983154983141983150983156983141 ( 983114 ) 983140983141983155983139983154983141983158983141 983142983148983157983160983151 983140983141 983139983137983154983143983137983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 413

Corrente Eleacutetrica em Um Condutor

+

+

+

+A

983139983151983150983140983157983156983151983154

i

∆∆∆∆ x

D983141983142983145983150983145983271983267983151 n = 983150983151 983140983141 983152983151983154983156983137983140983151983154983141983155 983140983141 983139983137983154983143983137

983157983150983145983140983137983140983141 983140983141 983158983151983148983157983149983141

983118983157983149 983140983141 983139983137983154983143983137983155 983150983151 983141983148983141983149983141983150983156983151 983140983141 983158983151983148983157983149983141

N = nsdotsdotsdotsdot983126983151983148 = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotA

I = nsdotsdotsdotsdotqsdot sdotsdot sdot VdsdotsdotsdotsdotA

D983141983142983145983150983145983271983267983151 983126983141983148983151983139 983140983141 983117983145983143983154983137983271983267983151 983151983157 D983141983154983145983158983137

983126 983140 = ∆∆∆∆ x

∆∆∆∆t983126983140

i

C983137983154983143983137 983141983148983273983156983154983145983139983137 983150983151 983141983148983141983149983141983150983156983151 ∆∆∆∆Q = N sdot sdotsdot sdot q rArrrArrrArrrArr ∆∆∆∆Q = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q

I = ∆∆∆∆Q∆∆∆∆t

= nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q∆∆∆∆t

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 513

983149A983144 983149983145983148983145983137983149983152983272983154983141983085983144983151983154983137

983109983160983141983149983152983148983151983098

983091983086983088983088983088 983149983105983144983098 983152983151983140983141 983137983138983137983155983156983141983139983141983154 983157983149

983137983152983137983154983141983148983144983151 983153983157983141 983139983151983150983155983157983149983137 983091983088983088 983149983105 983152983151983154 983089983088 983144983086

Capacidade de Armazenamento

983149A983144 983125983150983145983140983137983140983141 983140983141 C983137983154983143983137 E983148983273983156983154983145983139983137

3000 983149A983144 = 3000 timestimestimestimes10minusminusminusminus3A timestimestimestimes 3600 983155 = 10800 C 983140983141 983139983137983154983143983137 983137983154983149983137983162983141983150983137983140983137

I∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

I = ∆∆∆∆Q

∆∆∆∆tI∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

Definiccedilatildeo de Coulomb (SI)

1 C eacute a carga eleacutetrica transportada em 1 s por uma corrente de 1 A

C983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983142983151983145 983140983141983155983139983151983138983141983154983156983137 983137983150983156983141983155 983140983137 983139983137983154983143983137 983125983150983145983140983137983140983141 983142983157983150983140983137983149983141983150983156983137983148 983150983151 983123983113

D983141983142983145983150983141983085983155983141 983151 C983151983157983148983151983149983138 983139983151983149983151

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 613

Efeitos Bioloacutegicos

983118983137983156983157983154983141983162983137 983141983148983273983156983154983145983139983137 983140983137 983142983157983150983271983267983151 983150983141983154983158983151983149983290983155983139983157983148983151

983116983157983145983143983145 G983137983148983158983137983150983145 (17379830851798)

Corrente Efeito

Efeitos no Corpo Humano (de modo geral)

F983151983154983149983145983143983137983149983141983150983156983151

A983157983149983141983150983156983151 983140983137983155 983139983151983150983156983154983137983271983285983141983155 983149983157983155983139983157983148983137983154983141983155

983120983137983154983137983140983137 983154983141983155983152983145983154983137983156983283983154983145983137

F983145983138983154983145983148983137983271983267983151 983149983157983155983139983157983148983137983154 983152983151983140983141 983155983141983154 983142983137983156983137983148

983120983137983154983137983140983137 983139983137983154983140983277983137983139983137 983153983157983141983145983149983137983140983157983154983137983155 983143983154983137983158983141983155

1 983149A

10 991251 20 983149A

20 991251 100 983149A

100 983149A 991251 3 A

983137983139983145983149983137 983140983141 3 A

Adaptado DURAN JER Biofiacutesica-Fundamentos e

Aplicaccedilotildees Satildeo Paulo Pearson Prentice Hall 2003 p 178

983119983138983155983141983154983158983137983271983267983151

E983142983141983145983156983151983155 983140983141983152983141983150983140983141983149

983085 983140983151 983156983141983149983152983151 983140983141 983141983160983152983151983155983145983271983267983151

983085 983156983145983152983151 983140983141 983139983151983154983154983141983150983156983141

983137983148983156983141983154983150983137983140983137 (983139983137)

983139983151983150983156983277983150983157983137 (983139983139)

D983141983156983137983148983144983137983149983141983150983156983151 983118983151983154983149983137 98311898312298308510

D983141983155983139983151983138983154983145983157 983137 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

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Resistecircncia e Resistividade

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983274983150983139983145983137

R = Vi

983118983151 983123983113 1 983126A = 1 ΩΩΩΩ (983151983144983149)

983122983141983155983145983155983156983151983154

E983148983141983149983141983150983156983151 983139983151983150983140983157983156983151983154

983157983155983137983140983151 983152983137983154983137 983151983142983141983154983141983139983141983154

983154983141983155983145983155983156983274983150983139983145983137

983123983277983149983138983151983148983151983155

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ = E

983114

983118983151 983123983113 ΩsdotΩsdotΩsdotΩsdot983149

983120983137983154983137 983149983137983156983141983154983145983137983145983155 983145983155983151983156983154983283983152983145983139983151983155

E983160 C983151983138983154983141 17 timestimestimestimes 10minusminusminusminus8 ΩΩΩΩ sdotsdotsdotsdot983149

E = ρ ρρ ρ 983114 983151983157

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 813

Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 913

Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

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Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

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Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

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Corrente Eleacutetrica em Um Condutor

+

+

+

+A

983139983151983150983140983157983156983151983154

i

∆∆∆∆ x

D983141983142983145983150983145983271983267983151 n = 983150983151 983140983141 983152983151983154983156983137983140983151983154983141983155 983140983141 983139983137983154983143983137

983157983150983145983140983137983140983141 983140983141 983158983151983148983157983149983141

983118983157983149 983140983141 983139983137983154983143983137983155 983150983151 983141983148983141983149983141983150983156983151 983140983141 983158983151983148983157983149983141

N = nsdotsdotsdotsdot983126983151983148 = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotA

I = nsdotsdotsdotsdotqsdot sdotsdot sdot VdsdotsdotsdotsdotA

D983141983142983145983150983145983271983267983151 983126983141983148983151983139 983140983141 983117983145983143983154983137983271983267983151 983151983157 D983141983154983145983158983137

983126 983140 = ∆∆∆∆ x

∆∆∆∆t983126983140

i

C983137983154983143983137 983141983148983273983156983154983145983139983137 983150983151 983141983148983141983149983141983150983156983151 ∆∆∆∆Q = N sdot sdotsdot sdot q rArrrArrrArrrArr ∆∆∆∆Q = nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q

I = ∆∆∆∆Q∆∆∆∆t

= nsdotsdotsdotsdot∆∆∆∆ x sdotsdotsdotsdotAsdot sdotsdot sdot q∆∆∆∆t

7242019 Corrente e Resistecircncia - Aula

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983149A983144 983149983145983148983145983137983149983152983272983154983141983085983144983151983154983137

983109983160983141983149983152983148983151983098

983091983086983088983088983088 983149983105983144983098 983152983151983140983141 983137983138983137983155983156983141983139983141983154 983157983149

983137983152983137983154983141983148983144983151 983153983157983141 983139983151983150983155983157983149983137 983091983088983088 983149983105 983152983151983154 983089983088 983144983086

Capacidade de Armazenamento

983149A983144 983125983150983145983140983137983140983141 983140983141 C983137983154983143983137 E983148983273983156983154983145983139983137

3000 983149A983144 = 3000 timestimestimestimes10minusminusminusminus3A timestimestimestimes 3600 983155 = 10800 C 983140983141 983139983137983154983143983137 983137983154983149983137983162983141983150983137983140983137

I∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

I = ∆∆∆∆Q

∆∆∆∆tI∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

Definiccedilatildeo de Coulomb (SI)

1 C eacute a carga eleacutetrica transportada em 1 s por uma corrente de 1 A

C983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983142983151983145 983140983141983155983139983151983138983141983154983156983137 983137983150983156983141983155 983140983137 983139983137983154983143983137 983125983150983145983140983137983140983141 983142983157983150983140983137983149983141983150983156983137983148 983150983151 983123983113

D983141983142983145983150983141983085983155983141 983151 C983151983157983148983151983149983138 983139983151983149983151

7242019 Corrente e Resistecircncia - Aula

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Efeitos Bioloacutegicos

983118983137983156983157983154983141983162983137 983141983148983273983156983154983145983139983137 983140983137 983142983157983150983271983267983151 983150983141983154983158983151983149983290983155983139983157983148983151

983116983157983145983143983145 G983137983148983158983137983150983145 (17379830851798)

Corrente Efeito

Efeitos no Corpo Humano (de modo geral)

F983151983154983149983145983143983137983149983141983150983156983151

A983157983149983141983150983156983151 983140983137983155 983139983151983150983156983154983137983271983285983141983155 983149983157983155983139983157983148983137983154983141983155

983120983137983154983137983140983137 983154983141983155983152983145983154983137983156983283983154983145983137

F983145983138983154983145983148983137983271983267983151 983149983157983155983139983157983148983137983154 983152983151983140983141 983155983141983154 983142983137983156983137983148

983120983137983154983137983140983137 983139983137983154983140983277983137983139983137 983153983157983141983145983149983137983140983157983154983137983155 983143983154983137983158983141983155

1 983149A

10 991251 20 983149A

20 991251 100 983149A

100 983149A 991251 3 A

983137983139983145983149983137 983140983141 3 A

Adaptado DURAN JER Biofiacutesica-Fundamentos e

Aplicaccedilotildees Satildeo Paulo Pearson Prentice Hall 2003 p 178

983119983138983155983141983154983158983137983271983267983151

E983142983141983145983156983151983155 983140983141983152983141983150983140983141983149

983085 983140983151 983156983141983149983152983151 983140983141 983141983160983152983151983155983145983271983267983151

983085 983156983145983152983151 983140983141 983139983151983154983154983141983150983156983141

983137983148983156983141983154983150983137983140983137 (983139983137)

983139983151983150983156983277983150983157983137 (983139983139)

D983141983156983137983148983144983137983149983141983150983156983151 983118983151983154983149983137 98311898312298308510

D983141983155983139983151983138983154983145983157 983137 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

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Resistecircncia e Resistividade

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983274983150983139983145983137

R = Vi

983118983151 983123983113 1 983126A = 1 ΩΩΩΩ (983151983144983149)

983122983141983155983145983155983156983151983154

E983148983141983149983141983150983156983151 983139983151983150983140983157983156983151983154

983157983155983137983140983151 983152983137983154983137 983151983142983141983154983141983139983141983154

983154983141983155983145983155983156983274983150983139983145983137

983123983277983149983138983151983148983151983155

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ = E

983114

983118983151 983123983113 ΩsdotΩsdotΩsdotΩsdot983149

983120983137983154983137 983149983137983156983141983154983145983137983145983155 983145983155983151983156983154983283983152983145983139983151983155

E983160 C983151983138983154983141 17 timestimestimestimes 10minusminusminusminus8 ΩΩΩΩ sdotsdotsdotsdot983149

E = ρ ρρ ρ 983114 983151983157

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Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

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Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

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983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

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Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

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Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

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Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 513

983149A983144 983149983145983148983145983137983149983152983272983154983141983085983144983151983154983137

983109983160983141983149983152983148983151983098

983091983086983088983088983088 983149983105983144983098 983152983151983140983141 983137983138983137983155983156983141983139983141983154 983157983149

983137983152983137983154983141983148983144983151 983153983157983141 983139983151983150983155983157983149983137 983091983088983088 983149983105 983152983151983154 983089983088 983144983086

Capacidade de Armazenamento

983149A983144 983125983150983145983140983137983140983141 983140983141 C983137983154983143983137 E983148983273983156983154983145983139983137

3000 983149A983144 = 3000 timestimestimestimes10minusminusminusminus3A timestimestimestimes 3600 983155 = 10800 C 983140983141 983139983137983154983143983137 983137983154983149983137983162983141983150983137983140983137

I∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

I = ∆∆∆∆Q

∆∆∆∆tI∆∆∆∆Q sdot∆sdot∆sdot∆sdot∆t=

Definiccedilatildeo de Coulomb (SI)

1 C eacute a carga eleacutetrica transportada em 1 s por uma corrente de 1 A

C983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983142983151983145 983140983141983155983139983151983138983141983154983156983137 983137983150983156983141983155 983140983137 983139983137983154983143983137 983125983150983145983140983137983140983141 983142983157983150983140983137983149983141983150983156983137983148 983150983151 983123983113

D983141983142983145983150983141983085983155983141 983151 C983151983157983148983151983149983138 983139983151983149983151

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 613

Efeitos Bioloacutegicos

983118983137983156983157983154983141983162983137 983141983148983273983156983154983145983139983137 983140983137 983142983157983150983271983267983151 983150983141983154983158983151983149983290983155983139983157983148983151

983116983157983145983143983145 G983137983148983158983137983150983145 (17379830851798)

Corrente Efeito

Efeitos no Corpo Humano (de modo geral)

F983151983154983149983145983143983137983149983141983150983156983151

A983157983149983141983150983156983151 983140983137983155 983139983151983150983156983154983137983271983285983141983155 983149983157983155983139983157983148983137983154983141983155

983120983137983154983137983140983137 983154983141983155983152983145983154983137983156983283983154983145983137

F983145983138983154983145983148983137983271983267983151 983149983157983155983139983157983148983137983154 983152983151983140983141 983155983141983154 983142983137983156983137983148

983120983137983154983137983140983137 983139983137983154983140983277983137983139983137 983153983157983141983145983149983137983140983157983154983137983155 983143983154983137983158983141983155

1 983149A

10 991251 20 983149A

20 991251 100 983149A

100 983149A 991251 3 A

983137983139983145983149983137 983140983141 3 A

Adaptado DURAN JER Biofiacutesica-Fundamentos e

Aplicaccedilotildees Satildeo Paulo Pearson Prentice Hall 2003 p 178

983119983138983155983141983154983158983137983271983267983151

E983142983141983145983156983151983155 983140983141983152983141983150983140983141983149

983085 983140983151 983156983141983149983152983151 983140983141 983141983160983152983151983155983145983271983267983151

983085 983156983145983152983151 983140983141 983139983151983154983154983141983150983156983141

983137983148983156983141983154983150983137983140983137 (983139983137)

983139983151983150983156983277983150983157983137 (983139983139)

D983141983156983137983148983144983137983149983141983150983156983151 983118983151983154983149983137 98311898312298308510

D983141983155983139983151983138983154983145983157 983137 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 713

Resistecircncia e Resistividade

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983274983150983139983145983137

R = Vi

983118983151 983123983113 1 983126A = 1 ΩΩΩΩ (983151983144983149)

983122983141983155983145983155983156983151983154

E983148983141983149983141983150983156983151 983139983151983150983140983157983156983151983154

983157983155983137983140983151 983152983137983154983137 983151983142983141983154983141983139983141983154

983154983141983155983145983155983156983274983150983139983145983137

983123983277983149983138983151983148983151983155

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ = E

983114

983118983151 983123983113 ΩsdotΩsdotΩsdotΩsdot983149

983120983137983154983137 983149983137983156983141983154983145983137983145983155 983145983155983151983156983154983283983152983145983139983151983155

E983160 C983151983138983154983141 17 timestimestimestimes 10minusminusminusminus8 ΩΩΩΩ sdotsdotsdotsdot983149

E = ρ ρρ ρ 983114 983151983157

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 813

Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 913

Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1113

Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1313

Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 613

Efeitos Bioloacutegicos

983118983137983156983157983154983141983162983137 983141983148983273983156983154983145983139983137 983140983137 983142983157983150983271983267983151 983150983141983154983158983151983149983290983155983139983157983148983151

983116983157983145983143983145 G983137983148983158983137983150983145 (17379830851798)

Corrente Efeito

Efeitos no Corpo Humano (de modo geral)

F983151983154983149983145983143983137983149983141983150983156983151

A983157983149983141983150983156983151 983140983137983155 983139983151983150983156983154983137983271983285983141983155 983149983157983155983139983157983148983137983154983141983155

983120983137983154983137983140983137 983154983141983155983152983145983154983137983156983283983154983145983137

F983145983138983154983145983148983137983271983267983151 983149983157983155983139983157983148983137983154 983152983151983140983141 983155983141983154 983142983137983156983137983148

983120983137983154983137983140983137 983139983137983154983140983277983137983139983137 983153983157983141983145983149983137983140983157983154983137983155 983143983154983137983158983141983155

1 983149A

10 991251 20 983149A

20 991251 100 983149A

100 983149A 991251 3 A

983137983139983145983149983137 983140983141 3 A

Adaptado DURAN JER Biofiacutesica-Fundamentos e

Aplicaccedilotildees Satildeo Paulo Pearson Prentice Hall 2003 p 178

983119983138983155983141983154983158983137983271983267983151

E983142983141983145983156983151983155 983140983141983152983141983150983140983141983149

983085 983140983151 983156983141983149983152983151 983140983141 983141983160983152983151983155983145983271983267983151

983085 983156983145983152983151 983140983141 983139983151983154983154983141983150983156983141

983137983148983156983141983154983150983137983140983137 (983139983137)

983139983151983150983156983277983150983157983137 (983139983139)

D983141983156983137983148983144983137983149983141983150983156983151 983118983151983154983149983137 98311898312298308510

D983141983155983139983151983138983154983145983157 983137 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 713

Resistecircncia e Resistividade

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983274983150983139983145983137

R = Vi

983118983151 983123983113 1 983126A = 1 ΩΩΩΩ (983151983144983149)

983122983141983155983145983155983156983151983154

E983148983141983149983141983150983156983151 983139983151983150983140983157983156983151983154

983157983155983137983140983151 983152983137983154983137 983151983142983141983154983141983139983141983154

983154983141983155983145983155983156983274983150983139983145983137

983123983277983149983138983151983148983151983155

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ = E

983114

983118983151 983123983113 ΩsdotΩsdotΩsdotΩsdot983149

983120983137983154983137 983149983137983156983141983154983145983137983145983155 983145983155983151983156983154983283983152983145983139983151983155

E983160 C983151983138983154983141 17 timestimestimestimes 10minusminusminusminus8 ΩΩΩΩ sdotsdotsdotsdot983149

E = ρ ρρ ρ 983114 983151983157

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 813

Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 913

Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1113

Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1313

Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 713

Resistecircncia e Resistividade

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983274983150983139983145983137

R = Vi

983118983151 983123983113 1 983126A = 1 ΩΩΩΩ (983151983144983149)

983122983141983155983145983155983156983151983154

E983148983141983149983141983150983156983151 983139983151983150983140983157983156983151983154

983157983155983137983140983151 983152983137983154983137 983151983142983141983154983141983139983141983154

983154983141983155983145983155983156983274983150983139983145983137

983123983277983149983138983151983148983151983155

D983141983142983145983150983145983271983267983151 983122983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ = E

983114

983118983151 983123983113 ΩsdotΩsdotΩsdotΩsdot983149

983120983137983154983137 983149983137983156983141983154983145983137983145983155 983145983155983151983156983154983283983152983145983139983151983155

E983160 C983151983138983154983141 17 timestimestimestimes 10minusminusminusminus8 ΩΩΩΩ sdotsdotsdotsdot983149

E = ρ ρρ ρ 983114 983151983157

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 813

Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 913

Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1113

Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

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Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

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Resistecircncia e Resistividade

Ai

L ∆∆∆∆V

ρ ρρ ρ =E

983114

983126E =983140

=983126

983116

i 983114 = A

R = 983116 983105

ρ ρρ ρ

983122983141983155983145983155983156983274983150983139983145983137 983140983141 983157983149 983139983151983150983140983157983156983151983154

983107983151983150983140983157983156983266983150983139983145983137

G = 1 R

1 ΩΩΩΩminusminusminusminus1 = 1 983123 (983155983145983141983149983141983150983155) = 1 983149983144983151 (983140983141983155983157983155983151)

983107983151983150983140983157983156983145983158983145983140983137983140983141

σσσσ = 1

ρ ρρ ρ 1 (ΩsdotΩsdotΩsdotΩsdot983149)minusminusminusminus1 = 1 983123983149 = 1 983149983144983151983155 (983140983141983155983157983155983151)

7242019 Corrente e Resistecircncia - Aula

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Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

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983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

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Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

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Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

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Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

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Resistecircncia e Resistividade

983108983141983152983141983150983140983274983150983139983145983137 983139983151983149 983137 983124983141983149983152983141983154983137983156983157983154983137

ρminusρ ρminusρ ρminusρ ρminusρ 983151983101 ρ ρρ ρ 983151sdotαsdot sdotαsdot sdotαsdot sdotαsdot (983124 minus minusminus minus 983124 983151 )

α αα α 983139983151983141983142983145983139983145983141983150983156983141 983140983141 983156983141983149983152983141983154983137983156983157983154983137 983140983137

983154983141983155983145983155983156983145983158983145983140983137983140983141

ρ ρρ ρ 983151 983154983141983155983145983155983156983145983158983145983140983137983140983141 983264 20 983151983107 (983154983141983142983141983154983274983150983139983145983137 983124 983151 )

983108983141 983157983149 983149983151983140983151 983143983141983154983137983148

(983150983277983153983157983141983148 983139983151983138983154983141 983141 983162983145983150983139983151)

α αα α 983101 α αα α (983124) 983101 983139983156983141

983152983137983154983137 983152983141983153983157983141983150983137983155 983158983137983154983145983137983271983285983141983155

983140983141 983156983141983149983152983141983154983137983156983157983154983137

α αα α asymp asympasymp asymp 0 983107983151983150983155983156983137983150983156983137983150α αα α 983102 0

α αα α 983101 0

α αα α lt 0

(983107983157983154983158983137983156983157983154983137 983140983141983155983152983154983141983162983277983158983141983148)

983124

983119983138983155983141983154983158983137983271983285983141983155

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

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Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

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Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

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Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1013

983124983141983154983149983145983155983156983151983154983141983155

983108983145983155983152983151983155983145983156983145983158983151983155 983139983157983146983137 983154983141983155983145983155983156983274983150983139983145983137 983137983148983156983141983154983137 983155983141983150983155983145983158983141983148983149983141983150983156983141 983139983151983149 983137

983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983120983124983107 (983120983151983155983145983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983105983157983149983141983150983156983137 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

983124983141983154983149983145983155983156983151983154 983118983124983107 (983118983141983143983137983156983145983158983141 983124983141983149983152983141983154983137983156983157983154983141 983107983151983141983142983145983139983145983141983150983156)

983108983145983149983145983150983157983145 983137 983154983141983155983145983155983156983274983150983139983145983137 983139983151983149 983151 983137983157983149983141983150983156983151 983140983137 983156983141983149983152983141983154983137983156983157983154983137

Resistecircncia e Resistividade

983109983142983141983145983156983151 983114983151983157983148983141

983121 983101 I 2sdot sdotsdot sdot 983122sdot sdotsdot sdot 983156

983121 983139983137983148983151983154 983143983141983154983137983140983151

I 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137 983139983151983150983155983156983137983150983156983141

983122 983154983141983155983145983155983156983274983150983139983145983137 983140983151 983139983151983150983140983157983156983151983154 983156 983156983141983149983152983151 983140983141 983140983157983154983137983271983267983151

983105983153983157983141983139983145983149983141983150983156983151 983140983141 983157983149 983139983151983150983140983157983156983151983154 983140983141983158983145983140983151 983264 983152983137983155983155983137983143983141983149 983140983141 983139983151983154983154983141983150983156983141 983141983148983273983156983154983145983139983137

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1113

Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1313

Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1113

Energia e Potecircncia

983140983125 = 983126 i 983140983156

983140983125 983126

983140983156= i 983124983137983160983137 983140983141 983156983154983137983150983155983142983141983154983274983150983139983145983137

983140983141 983141983150983141983154983143983145983137

+ 991251

C983137983154983143983137 983140983145983155983155983145983152983137983156983145983158983137

dq

i i

983137 983138

i

983120983137983154983137 983139983137983154983143983137 983141983148983141983149983141983150983156983137983154

983140983125983140983153

983126 =

∆∆∆∆983125=

983153∆∆∆∆983126 = 983126983137983138 = 983126

i =983140983125 = 983126 983140983153 983140983153

983140983156i 983140983153 983140983156=983139983151983149983151 rArrrArrrArrrArr

983120 = 983126 i 1 983126A = 1 983127 (983159983137983156983156)

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1313

Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1213

Lei de Ohm

983126

i

E983148983141983149983141983150983156983151 983150983267983151983085983284983144983149983145983139983151

E983160 983148983266983149983152983137983140983137

=983122 983140983126983140i

983122 = 983156983143θ θθ θ

θ θθ θ

i

983126

E983148983141983149983141983150983156983151 983284983144983149983145983139983151 983151983157 983148983145983150983141983137983154

E983160 983154983141983155983145983155983156983151983154

C983157983154983158983137 C983137983154983137983139983156983141983154983277983155983156983145983139983137 i (983126)

i

983139983156983141=983126

983126 simsimsimsim i i

ρ ρρ ρ 983150983267983151 983140983141983152983141983150983140983141 983140983141 983109

983139983156983141983122 =

Para temperatura constante

983107983151983150983140

983122 = 983156983143θ θθ θ 983101 983139983156983141

θ θθ θ

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1313

Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W

7242019 Corrente e Resistecircncia - Aula

httpslidepdfcomreaderfullcorrente-e-resistencia-aula 1313

Exerciacutecios

4 A que temperatura a resistecircncia de um condutor de cobre seria o dobro da sua resistecircncia agrave 20ordm C Dados relativos ao cobre

ρ o(20ordm C) = 169 times 10 ndash8

Ωsdotm e α = 40 times 10 ndash3

K ndash1

1 Determine a velocidade em mms de migraccedilatildeo dos eleacutetrons de conduccedilatildeo em um fio de cobre ciliacutendrico de seccedilatildeo reta de aacuterea

30 times 10 ndash6 m2 sendo atravessado por uma corrente de 10 A Dados do cobre ρ = 895 gcm3 e M = 635 gmol (peso atocircmico)

2 A seccedilatildeo de aacuterea reta de um condutor eacute atravessada pela quantidade de carga ∆q = 60 times 10minus4 C no intervalo de tempo ∆t = 15 times

10minus2 s (a) Qual a intensidade da corrente eleacutetrica que atravessa essa seccedilatildeo normal (b) Se os portadores de cargas satildeo eleacutetrons

quantos eleacutetrons atravessam essa seccedilatildeo reta nesse intervalo de tempo

5 Um ebulidor eacute capaz de levar 10 L de aacutegua (10 kg) de 20o C a 100ordm C em 30 min Calcule (a) a potecircncia dissipada por esse

ebulidor (b) o consumo mensal de energia eleacutetrica em kW983223h supondo que ele seja utilizado em meacutedia 10 min por dia

6 Um fio de cobre possui seccedilatildeo reta de aacuterea 820 times 10 ndash7

m2

e diacircmetro igual a 102 mm Ele conduz uma corrente i = 167 ACalcule (a) o moacutedulo do campo eleacutetrico no fio (b) a diferenccedila de potencial entre dois pontos no fio separados por uma distacircncia

igual a 500 m (c) a resistecircncia de um segmento do fio de comprimento igual a 500 m

7 Uma lacircmpada feita para operar em 120 V tem uma potecircncia de dissipaccedilatildeo de 75 W Quanta potecircncia seraacute dissipada pela

lacircmpada se ela for conectada atraveacutes de uma diferenccedila de potencial de 220 V

3 Para se fazer uma resistecircncia para aquecimento enrolou-se 20 voltas de fio nicromo (NiCr) em um cilindro de 50 cm de raio

A resistecircncia por unidade de comprimento do fio de nicromo eacute de 46 Ωm Considere que o diacircmetro do fio eacute muito menor que o

diacircmetro do cilindro e que natildeo haacute espaccedilos entre as voltas de fio Se uma ddp de 10 V for aplicada nas extremidades do fio qual

seraacute a corrente produzida

(1) 025 mms (2) 40 mA 38 times1015 eleacutetrons (3) 035 A (4) 270ordm C (5) 19 kW 95 kWh (6) 00346 Vm 175 V 105 Ω (7) 252 W